MSI SSBBP

Ace your homework & exams now with Quizwiz!

Risk: Alpha & Beta

If the p Value is greater than the alpha risk, reject the null hypothesis, and accept the alternative hypothesis.

The value of Lean begins with identifying activities to add value to processes or services and making sure that value-added activities are performed effectively and efficiently.

There are several inherent differences in Lean and Six Sigma:

There will be one less data point in the Moving Range chart than the Individual chart.

These are key hypothesis testing terms:

These are the most common SPC charts:

While a Project Management certification isn't necessarily required, having a strong understanding of project management methodology is. This can be achieved in many ways.

The term "value stream" is used in Six Sigma

as a descriptor of the necessary factors that contribute to the value of a product or service from the viewpoint of the customer.

F distributions are a continuous probability distribution:

formed from the ratios of two Chi-squared variables. If X1 and X2 are independent Chi-square variables.

Discriminant analysis:

has one output and it is categorical in nature.

Manova:

has several outputs which must be correlated.

The Taguchi Method (Design of Experiments)

have made major contributions in the reduction of variation and greatly improved engineering quality and productivity by reducing environmental variation.

SIPOC diagram

helps team members determine process activities, stakeholders, and boundaries. A SIPOC shows the Suppliers, Inputs, Process, Outputs, and Customers of a process.

Design for Six Sigma (DFSS):

is an approach-based methodology rather than a stand-alone optimization methodology such as DMAIC. DMADV and IDOV are variations of the DSS.

PDPC charts are used in these situations:

- When the price of failure is high - Before implementing a plan - When the plan must be completed on schedule

Xbar-R Chart:

A _____________ is a term used to denote variance from the mean average of an event.

"sigma"

The Impact of Variation can be:

random or systematic.

When measuring benefits, it is worth having these individual factors feeding into the overall total savings figure. It can be encouraging for all involved to see the greater figure being achieved.

Control charts:

- Xbar-R charts, Plot of the mean and range of a group less than 5 - X bar-S charts, Plot the mean and standard deviation of a group more than 5 - X-R charts, Plot of mean and range of individual measurements.

The deliverables of the Analysis phase involve:

- a root cause analysis for concerns, gap analysis, and a top-to-bottom data and process analysis.

The formula is:

- d = the number of occurrences - and λ = the average number of occurrences

The deliverables for the Improve phase involve:

- developing possible solutions, determining which one's are the best solutions, and then developing a subsequent implementation plan.

U Chart

Factor analysis:

reduces a large number of continuous factors to a small number for analysis.

1 & 2 Sample T-Tests:

The two separate sets of training programs are:

1. One set will be for current stakeholders and staff to learn about the new process and how they should now be working. 2. The second set will be the training for new recruits. It is recommended that old training manuals are replaced quickly after the development of the new.

Some companies have found that an examination of many processes can identify up to ______________ of non-value-added activity that has crept into the historical process methodology.

50%

Spaghetti Diagram

A spaghetti diagram is best used to illustrate the measures and movements within a location of process activity. It will usually be created after a period of observation.

Correctly interpreting control charts is important to effectively adjusting and improving processes.

After you have charted your data, there are 8 standard rules for interpreting what the control charts mean.

Factor and Principal Component analysis

which reduces a large number of inputs into a smaller number of defined inputs.

Random sampling:

is a sampling from a population in which the selection of a sample unit is based on chance, and every element of the population has a known, non-zero probability of being selected.

The U chart center line (mean) (u-bar) is calculated by:

U = Total number of non-conformances in all the items sampled / Total number of items sampled

Confounding effects are when the design is configured so that the effect of one factor is combined with the other.

Ultimately, the effect of the individual factors cannot be isolated by the analysis.

The formula for the quadratic mathematical model is:

Y = ax^2 + bx + c

When sampling data:

a good sample is representative of the population. And each sample point represents the attributes of a known number of population elements. All probability sampling methods rely on random sampling.

The Two Sample t-test is:

a hypothesis test used to compare the means of two small samples to see if they may come from the same population using: - H0 the population means are equal - H1 the popular means are different

The One Sample t-test is:

a hypothesis test used to test the mean of a small sample taken from a population with a normal distribution against a specified value.

Charts and Graphs:

allow us to plot occurrences, frequencies, occasions, and all manner of data together to be viewed without the need for the numbers. They are often used to see patterns to try and make formulas fit into some form of equation.

Defects per Million Opportunities (DPMO) is used instead of Defects per Unit to:

facilitate more direct comparisons between processes with varying levels of complexity. These are used on measurements such as fill rate, shipment on-time percentage, survey complaints, and customer satisfaction.

Experimental Methods:

include one and two-level fractional factorial experiments.

Independent probability:

occurs if the occurrence of one event provides no information about whether or not the other event will occur, meaning the events have no influence on each other.

Work instructions

specify the steps that need to occur for tasks in a process.

Hypothesis Testing with Non-Normal Data

The X-bar chart is most often used for:

large sample sizes and large volume processes.

The Xbar-R Chart is a:

common statistical process control used to sample averages.

Six Sigma Terminologies

- 'function' relates to a process or application -e.g., the manufacturing process is a function. - 'variation' refers to a difference from the expected or likely outcome. - 'variance' and 'standard deviation' are statistical terms of measuring such variations. - 'error' refers to the amount of difference or variation from the perfect expected outcome.

Elements of the Response Plan:

A Six Sigma response plan is a flowchart that tells the data-plotter what to do in the event of an out-of-control or out-of-specification condition. An example of a reaction plan would be a printing press operator who receives an alert for an offset of print and is able to stop the line and make an adjustment based on the data.

Measure - What is your baseline?

Activities Involved: - Develop Detailed Process Maps - Measure your Measurement System - Collect Data - Take Measurements Tools you can use: - Data Collection Plan - Benchmarking - CTQs, Histogram, Pareto Chart, Scatter Diagram, Control Charts, Sigma Level, ROI, FMEA, Validate, Gage R&R

Control Chart Anatomy

As we mentioned previously, Statistical Process Control is most often monitored by control charts, which have an upper and lower control limit indicating a special cause. There are two types of SPC charts: control charts for attributes and control charts for variables.

Process Mapping Techniques

Process analysis tools analyze processes by developing and using value stream maps, process maps, flowcharts, procedures, work instructions, spaghetti diagrams, circle diagrams, etc.

Residual Analysis

Residual analysis is an important part of the analysis in regression analysis and experimental design. The residuals should conform to a normal distribution. If they do not, this may be an indicator of a pattern or cause for the regression.

An example of weak correlation:

Scattered and sporadic placement of data values

Project Management Certification

Should a Six Sigma Black Belt also be Project Management Certified?

Reduce variation

Techniques for reducing variation include four basic steps:

Unit 15 -Selecting Lean Six Sigma Projects

The purpose of this unit: •This unit looks at selecting Six Sigma Lean projects, how to build the project charter, and how to build the necessary business case.

Unit 21 -Simple Linear and Multiple Regression Analysis:

The purpose of this unit: • This unit provides information on performing regression analysis.

The formula for its calculation is:

p = Total number of nonconforming in all samples being considered / Total number of items reviewed in all samples being considered

Design of experiments deals with: planning, conducting, analyzing, and interpreting controlled tests to evaluate the factors that control the value of a parameter.

planning, conducting, analyzing, and interpreting controlled tests to evaluate the factors that control the value of a parameter.

Classes of Distributions

see below

The control plan could possibly be:

the most important part of the entire DMAIC methodology.

An 8th element of waste is emerging called

"knowledge and latent skill." This is where organizations fail to take advantage of skills or talent or are not effective at transferring learning between employees. These wastes can be found by determining the Rolled Throughput Yield. A further explanation of each term follows.

NP Chart:

Six Sigma Statistics:

These are the indications of a process out of control:

1. Any point beyond control limits 2. Two out of three points in a row beyond two sigma 3. Four out of five points in a row beyond one sigma 4. Fifteen points in a row within one sigma 5. Eight points in a row on both sides of the centerline within two sigma 6. Nine points in a row on one side of the center line 7. Six points in a row increasing or decreasing 8. Fourteen points in a row alternating up or down

Improve - Choose the solutions, pilot the solution, mistake proof, roll out the improvement and evaluate the results.

Activities Involved: - List Potential Solutions - Rank Solutions - Select Solution and Try - Check Results - Roll Out - Evaluate Improvement Tools you can use: - Analysis, Brainstorming - Decision Matrix - Capability Study - Pilot - Implementation Plan

Control - Verify the Voice of the Customer is being met, check your ROI, implement your control plan and close out the project

Activities Involved: - Update Standard Operating Procedures and Policies - Build a Transition Plan - Close Out the Project - Verify Improvement Processes - Document Procedures Tools you can use: - Sigma, ROI, Balance Scorecard, Control Chart - Control Plan Document - Control Plan Form - Transition Plan - Project Management Methods for Closing

Experiment Design Considerations:

Design for Six Sigma (DFSS) is different from DMAIC as it is used for designing a completely new product or process that meets customer specifications. DFSS vary from organization to organization depending on the characteristics of the product or business process that needs to be developed.

The pattern of variation in a set of data is called distribution:

Distribution is most often viewed for the shape, spread, and center.

Verification

Even in the simplest of changes, caution and awareness of impact are necessary before going ahead and making the change. Communication among all departments cannot be underestimated at this point.

Once the project has ended, the changed process returns to the business, and the process owners take responsibility for ongoing monitoring of benefits.

It is important to share the metrics expected with them and detail how they will measure the benefits to customers, and in financial terms.

Funnel Report (example)

It is possible to have a round table funnel report created, using the project team. Begin by listing all the variables you wish to consider and then using set criteria. Reduce the numbers by taking out the most trivial and whittling it down to the core elements to be considered. This is sometimes referred to as spiraling or spiral analysis (spiral model) - as you are moving in ever decreasing circular movements towards the core considerations.

The Define Stage

The basic steps in the Define Stage are to: • Develop Project name and Purpose • Complete the Project Charter • Develop a High Level Process Map • Identify the Process Owner, Champion, and Team • Identify Customers and Requirements critical to quality • Define Align Goals with Business Initiatives • Determine the Projected Return On Investment

Elements of the Control Plan

The control plan is a document that lists what is monitored in a product, service, or process as far as characteristics of quality. The control plan plays an important part in sustaining product quality long after a manufacturing process is developed and launched

Unit 6 -Six Sigma Advanced Process Fundamentals

The purpose of this unit: • This unit examines what you need to look at to define your process and determine what is critical in quality to the customers of your process. You will also learn about process metrics.

Unit 14 - The Lean Enterprise

The purpose of this unit: • This unit looks at what you need to think about when setting up a team for a Six Sigma project, focusing on how you determine what you need as well as discussing the roles within the team. • It also gives an overview of the different belts and explains the importance and relevance of communications within a Six Sigma Project.

Unit 13 - Valuing Six Sigma

The purpose of this unit: • This unit concludes the overview understanding to the level of a Six Sigma Green Belt. • The unit covers some more detail about the role, like activities of a Green Belt and how that differs from a Black Belt. It also covers the communications project task that a Green Belt will likely be asked to undertake.

Unit 23 - Statistical Process Control

The purpose of this unit: • This unit describes control tools and statistical process control tool usage.

Passing on the Hard Work

When the agreement to close the project has been achieved, then it is time to close. One of the final acts of the project lead will be to ensure the business has all the necessary tools to maintain and monitor the improvement into the future.

Flowchart

When trying to describe a process, it is often easier to draw it. The most common representation of this is the flowchart.

Mutually Exclusive probability:

When two events are Mutually Exclusive, it is impossible for them to happen together.

Value Streams and Their Analysis

When you have a process map, you can look at each part of the process and identify each stage as having one of three roles: 1. Something that creates value for the customer 2. Something that creates no value to the customer but is a necessary requirement or dependency within the overall process 3. Something that adds no value to the customer and is not needed by any part of the process (waste)

Critical to Quality (CTQ) refers to:

the accuracy or expected look of a product.

One and Two Sample Proportion:

Critical to Quality (Critical to Flowdown)

- CTC or Critical to Cost - CTS or Critical to Safety - CTP or Critical to Process - CTD or Critical to Delivery

These are the formulas to calculate process capability:

- Cp = (USL-LSL)/6s - Cpu = (USL-Xbar)/3s - Cpl = (Xbar-LSL)/3s - Cpk = Minimum of (Cpu,Cpl)

Systematic sampling is:

used in process sampling when data is collected in real time during process operation.

Defining a Process

1. You may begin by determining who is the owner of the process or the Process Owner. This is the single individual or group with responsibility for the end-to-end process. 2. The next step is to define the scope, boundaries, or limitations for a process. 3. The final step is to develop a high-level process map which shows the start and endpoints of the process.

At the end of the Control phase of the DMAIC journey:

1. the organization's financial department or company accountant should confirm the benefits in dollars. 2. The Champion or sponsor will then take these agreed figures into the business and discuss their value and what it means. This will begin the process of confirming benefits and developing a plan for benefits-monitoring that will become the responsibility of the business. 3. Only once everything is agreed upon and the business is ready, can the project begin to close down.

Z-tests:

compare the mean against a specified value when the sample has more than 30 items or the standard deviation is known.

Two sample t-tests

compare the means of two samples of 30 items less.

Resolution is the criteria used to select a fractional factorial design.

Factorial designs involve testing several (n) factors at high and low levels using fractional factorials such as half (2n-1) or a quarter (2n-2).

Poisson distribution is a discrete probability distribution:

It is used when the sample size is not restricted and it is not possible to specify the number of occurrences, but you do know the average number of occurrences.

Process Maps

Not dissimilar to a flowchart, a process map is a fundamental tool throughout all stages of the DMAIC Six Sigma Project work. It can be used to demonstrate a high-level process flow, detail elements within a process, and be part of the simulation activities, costing methods, and communication of the new process. The process map can then be used to demonstrate as-is, to-be, or any process in between. Generally, a process map will follow the same graphics as a flowchart.

Most Green and all Black Belts will demonstrate facilitation skills, and as such, they should be clearly able to overcome conflicts and disagreements within the team.

Occasionally, it may be of benefit to utilize an independent facilitator if project conflicts continue.

The tables are calculated by:

One way ANOVA

Six Sigma projects should be selected...

based on their cost-benefit analysis.

Unit 24 - Leading Six Sigma Teams

The purpose of this unit: • This unit goes through the very basic principles of project management, project teams, and the role of the Black Belt leading the team. • It also looks at the communications of the project leader and Black Belt.

Unit 3: The Six Sigma Team

The purpose of this unit: • This unit looks at what you need to think about when setting up a team for a Six Sigma project. It discusses how you work out what you need as well as discussing the roles within the team. • It also gives an overview of the different belts and explains the importance and relevance of communications within a Six Sigma project.

Unit 9 -Six Sigma Tools

The purpose of this unit: • This unit provides information on a number of different tools that may be useful throughout the many parts of the Six Sigma project. • This unit has a slightly different look than others in that it does not necessarily flow from one page to the next but is a series of factually presented pieces of information.

Six Sigma is used to reduce error rate and process variability Lean is used to reduce waste and non-value-added activities

The two work in an interrelated manner, because a high error rate can lead to excessive waste, and excessive waste can lead to a high error rate. By applying both, organizations can address both waste and errors.

Variations

There are many statistical methods of looking at variations, and we have a completely separate unit looking at the statistics of Six Sigma. For this unit, we will look at ways you can gain insight from the analysis of variation when the statistical work has already been undertaken.

Unit 1 - Introduction to 'Six Sigma'

This first unit provides a general background and history regarding the beginnings of Six Sigma, where it comes from, why it is used, and the foundation concepts upon which it is built. This unit also provides several terms and phrases used within Six Sigma. It is designed to provide a sound foundation to understand the units that follow.

normal distribution

This graph is shaped like a bell and often referred to as a bell chart. In a normal distribution curve, the mean, median, and mode are all the same value.

Basic Statistics:

This includes understanding the core principles and mathematics at the heart of statistics - how to work out averages and variances among other commonly used terms. These can be seen below:

Black Belt Discussion

This is a general balance of how you should spend your time. - 25 percent should be running projects as the project lead. - 20 percent should be used helping Green Belts who are project leads. - 20 percent should be used for teaching Six Sigma. - 25 percent should be used doing analytical work. - 10 percent should be used defining and developing additional projects.

There is no set type or style of project control plan for a specified improvement, but the use of metrics is important to your sustainment.

Use a combination of spreadsheets and text documents to keep track of the measures being improved. In general, you determine all the headers and labels for your control plan which are critical-to-quality, proven to be important to the customer, and include a hierarchical reference number.

Data collection and analysis allows for quality assurance as a project progresses to ensure the project satisfies the required quality standards.

Use a data collection chart to track subsequent data to monitor your controls once they are implemented.

Be consistent and make sure you have control of new materials or tools prior to implementation:

Using a quick-fix will generally just give you more process variation.

U chart sample sizes can vary in size:

but should be kept to within 25% of the average sample size.

Y=f(x)+Ɛ real world example:

When you bake a cake, you take a set number of ingredients, combine them in a certain way, bake the mixture, and after a period of time, you get a cake ready to eat. - 'y' is the cake that you desire - 'x' represents the ingredients - 'f' represents the mixing and baking process that is applied to the ingredients to create the cake - 'Ɛ' is represented by understanding that if you made this cake several times, the outcome may not always be identical. You may use a slightly lower heat setting in the oven, a slightly differing amount of an ingredient, and you may cook it for a few minutes more or less. The end result will be broadly the same, but each will have some variance from the others. That difference is represented by 'Ɛ', the Greek letter epsilon.

Analysis of Variances and Tolerances

When you have several events, you can compare the variances of each event to see if there are lower variances with each observation period. A good use of this occurs through the Analysis and Improve stages of DMAIC when you are trying to determine optimized processes. Looking at the variances with each simulation or walk-through can allow you to determine which processes are most effective and should be considered.

One-factor experiments are:

a method of designing experiments involving the testing of factors, or causes, one at a time instead of all separately.

Randomized block is:

a method used in the design of experiments similar to stratified random sampling where block designs are constructed to reduce noise or variance in the data.

Threshold state

a process is in statistical control but doesn't meet the customer specifications. What will it take to bring the process into an ideal state? Monitor your improvement actions.

Communications:

You should be prepared to communicate regularly within your team and ensure that task allocations are clearly explained and understood. You should show confidence in your team and particularly Green Belt members, demonstrating that you can trust them to deliver by shaping a task for them without detailing the specific elements. That is good leadership as much as project management. You will have regular engagement with your Champion regarding progress and challenges within the project. There should be a good understanding between the two of you, and a clear direction that you both agree on for the future of the project. You should be prepared to challenge the project Champion in a respectful way if needed. These discussions help to ensure that the project stays focused on the problem statement to be solved. You will also need to engage with stakeholders, process owners, and customers affected by the project. These people will probably engage with you at structured meetings, so it is important that these meetings take place regularly. They must clearly convey information about the progress and development aspects of whichever part of the Six Sigma project you have reached. Ensure meetings have agendas and are recorded for reference should any decisions be made. Try to make sure they have a set time so that they do not drift into discussion forums and stay on track. You may also get requests to have one-to-one discussions with those involved who are concerned about the process. You need to be sure to explain what is happening and why it is happening, and then listen to their views and discuss them freely. Often, it is just a misunderstanding that causes concerns. If there is something you cannot answer, work with your Champion to find common ground and work together with the business strategy in mind. Sometimes this one-on-one discussion may take place on the phone, but the same guidance applies. As a final point, both Black and Green Belt Six Sigma practitioners should be able to facilitate a discussion to get to the cause of issues and help within the workings of the DMAIC approach. Be prepared to step up and facilitate a solution-meeting whenever needed. That can instill faith in your abilities as well as demonstrate to others how to get through challenging period within the DMAIC approach.

Lean Controls

and implemented solutions require technically sound applications, including engineering, implementation, training, and long-term support. Lean controls need to be part of a cultural change.

The Taguchi Method (Design of Experiments):

and other methodologies have made major contributions in the reduction of variation and greatly improved engineering quality and productivity by reducing environmental variation.

The line of best fit:

and that relates to a frequency line showing the line of most likely results, almost like a rolling average of results based on the moving data displayed.

Normal distribution is a continuous distribution where:

any two data values may have an interval in between. The bell shaped normal curve has probabilities that are found as the area between any two z values.

F distributions

are a continuous probability distribution formed from the ratios of two Chi-squared variables. X1 and X2 are independent Chi-square variables.

Matrix diagrams (prioritization)

are a planning tool for displaying the relationships among various data sets. During the Champion phase or initial charter phase of the Define stage, organizations often use a prioritization matrix to rank competing priorities. This is a scoring or ranking system which can also be a tool for the voice of the customer. If the customer has multiple issues requiring quality control, they can rank them in order of priority to the organization.

EWMA Chart:

is used as a control chart for variable data. EWMA applies weighting factors that decrease exponentially where the weighting for each older data point decreases exponentially, which gives more importance to recent observations.

Lognormal distribution

is used for modeling material properties.

Statistical Process Control is used to:

monitor processes and may be applied to production or business processes. Statistical Process Control uses statistical methods to ensure that the process is stable and monitor the processes for timely identification of special causes. All processes are subject to variation.

In the Two Population Proportions hypothesis test:

populations are independent

Control plans help verify:

that the Voice of the Customer is being met by verifying improvement processes, documenting procedures, and updating standard operating procedures and policies. This can be accomplished using any combination of these tools: - the balanced scorecard - control chart - control plan document - or control plan form

The cause and effect philosophy of Six Sigma means

that you look at a 'process' and see how the process allows for variation. The inputs, process function, and errors within that process all affect the outcome. They cause the outcome to be a particular way

To properly build the required Measurement Systems Analysis:

the combination of analytical methods that lead the team in the direction to developing a solution for the problem may require a combination of multiple tools.

In a linear mathematical model:

the plotted data follows a straight line. Every data point may not fall on the line but the majority of them will. The overall pattern of the data follows the shape of a line and is the overall shape of the data.

In a quadratic model:

the plotted data follows the shape of what is called a quadratic. A quadratic shape is one that is curved and shaped similar to the letter "u."

Power:

the power of a hypothesis test is a measure of the probability of rejecting the null hypothesis when it is false.

The Moving Range Chart:

uses a default value of 2 so that each data point plots the difference or range between two consecutive data points as they come from the process in sequential order.

Kanban

uses a system of signal cards that is simple and shows someone that something in a process needs attention. It is derived from the combination of two Japanese words, kan -(visual) and ban -(card). Kanban roughly translates to signboard or signal board. Kanban is a process of manufacturing or work-space organization that relies upon visual signals to control inventory.

Design FMEA (DFMEA)

uses the application of the Failure Mode and Effects Analysis method to design a product to determine ways that a product design might fail in real-world use.

When we examined non-value-added activities with a focus on their removal...

we were identifying excesses in the process flow. These excesses, when removed, will likely change the process flow into a simpler process. This new process will have less activity and decision-making choice points.

The Meaning of Six Sigma

• At the 5th Sigma level, 233 defective parts per million occur. • At the 4th Sigma level, 6,210 defective parts per million occur. • At the 3rd Sigma level, 66,807 defective parts per million occur. • At the 2nd Sigma level, 308,538 defective parts per million occur. • At the 1st Sigma level, 690,000 defective parts per million occur.

Cause and Effect Diagram

• Begin by brainstorming all potential relationships. • Next, state the outcomes in terms of problems or issues. Choose significant branches to form the main bones of examination. Follow the path along the bone to agree or dismiss potential causes - remembering that these are potentials and not known until validated.

There are four primary sampling strategies:

• Random sampling • Stratified random sampling • Systematic sampling • Rational sub-grouping

The Seven Elements of Waste (Muda)

• Transport • Inventory • Motion • Waiting • Over Producing • Over Processing • Defects • Skills (8th)

When does a Six Sigma project finish?

• When the benefits are agreed upon and plans put in place to monitor the process in a way that ensures its longevity. • When the training for existing staff has been completed and created for new recruits. • When the project charter has been fulfilled, then the project can close.

Defects

are wastes of correction that are wastes, defects, or imperfections.

Poka Yoke (Mistake Proofing)

- A Poka-Yoke can be electrical, mechanical, procedural, visual, human or any other form that prevents incorrect execution of a process step. - Poka-Yoke helps people and processes work right the first time. - Poka-Yoke builds in techniques that make it impossible to make mistakes. These techniques can drive defects out of products and processes and substantially improve quality and reliability. - Poka-Yoke can be used wherever something can go wrong, or an error can be made.

Review of Applicable Activities and Tools Using the DMAIC methodology

Significance: Practical vs. Statistical

What Are the Benefits?

- Cost savings will likely include workforce savings, where the required numbers of staff to perform an action may reduce. - Other cost savings may result from reduced storage times, reduction in packaging waste, new supplier costs, or just reduced running times of machinery. - All of these are likely to be easy to quantify in terms of dollars by just comparing before and after figures. - It may be a slightly staggered approach in realizing workforce savings as some initial retraining costs and redeployment costs would have to be borne against the reductions in need costs at the outset.

Cpk, Cp, Pp, and Ppk are most commonly used and defined as follows:

- Cp = Process Capability. A simple and straightforward indicator of process capability. - Cpk = Process Capability Index. Adjustment of Cp for the effect of non-centered distribution. - Pp = Process Performance. A simple and straightforward indicator of process performance. - Ppk = Process Performance Index. Adjustment of Pp for the effect of non-centered distribution.

The range of metrics within a process and factors that input into the function can therefore be defined by these 4 statements:

- Critical to Cost (CTC) - Critical to Quality (CTQ) - Critical to Schedule (CTS) - Critical to Safety (CTS)

Typical improvements include:

- Decreased setup time - Reduced lead time - Reduced people effort - Reduced inventory - Improved productivity - Reduced facility floor space requirements

First, the deliverables for the Define phase will include:

- Developing a fully-trained project team who is committed to the improvement and has the full support of management, including necessary resources. - Identifying what characteristics are Critical to Quality for the customer, developing a project charter, and mapping the known business processes.

Lean Six Sigma combines the process improvement benefits of the Six Sigma method with the waste reduction benefits of Lean. Lean seeks to reduce waste in these forms:

- Elimination of defects - Continuous improvement - Elimination of non-value added activities - Use of Kanban pull systems - Flexibility to respond to variation

Chi square is calculated by summing the chi square contributions from each category in the hypothesis. The hypothesis is:

- H0 the sample conforms to the specified distribution - H1 the sample does not conform to the distribution

The hypothesis for Chi square is:

- H0 the sample conforms to the specified distribution - H1 the sample does not conform to the distribution

Hypothesis testing uses two propositions:

- H0 where the mean = 0 (the null hypothesis) - H1 where the mean ≠ 0 (the alternative hypothesis)

Return on investment will have both hard and soft returns

- Hard returns are those that are tangible, like reduced waste and personnel reduction which can be measured. - Soft returns are those which are relative in nature, where quantification is difficult but your shareholders see the value, such as societal or environmental goodwill.

The process to apply Poka-Yoke is:

- Identify the operation or process based on a Pareto Chart. - Analyze the 5 whys and understand the ways a process can fail. - Decide the right Poka-Yoke approach, such as using a shut-out process that immediately identifies that an error has been made.

Deming's theories were taught as a part of his System of Profound Knowledge. His knowledge system consists of four interrelated parts:

- In the theory of optimization, the objective of an organization is the optimization of the total system and not the optimization of individual subsystems. - In the theory of variation, his philosophy focuses on improving the product and service variability in design and manufacturing processes. - In the theory of knowledge, Deming emphasized that knowledge is not possible without theory, and experience does not establish a theory by itself. He says copying a best practice without understanding the theory behind it could be devastating for an organization. - In the theory of psychology, he helped explain how to understand people, interactions between people, and interactions between leaders and employees in a system of management.

Six Sigma:

- Is driven by leadership - Synchronizes employee skills - Can be achieved without Lean - Builds on Lean operations

Lean:

- Is driven by middle management - Synchronizes resource utilization - Provides tools to sustain lean - Can be considered a prerequisite for six sigma implemented for the purposes of efficiency and waste reduction.

Closing the Six Sigma project is much like the closure of a general project.

- It will involve a meeting of all relevant stakeholders, customers, and process owners, led either by the project leader or the Champion. - The meeting will examine the contents of the original charter and gain agreement from all present that the aims and goals of the charter have been met. - Then the project manager will prepare a written document that outlines the results for each stage of the project and confirms achievement of the solution to the original problem. - This document is distributed for agreement, and in some organizations, they physically sign off.

Lean controls include these components:

- Leadership and top management commitment. - All leaders and managers should be trained as Six Sigma Champions. This teaches them to ask the right questions of Six Sigma teams and understand their function and roles. - Include Lean Six Sigma planning within the business operating plan. - Ensure that the return on investment for training is strong. - Develop a Six Sigma mentoring process aligning the new team members with the experienced ones. - Ensure projects are financially validated and management is signing off on the project's actual savings.

As mentioned earlier, the types of regression are:

- Linear Regression is a linear relationship with one input and one output. - Multiple Linear Regression is a linear relationship with several inputs. - Logistics Regression is regression where the output is a probability.

The types of regression are:

- Linear Regression, a linear relationship with one input and one output. - Multiple Linear Regression, a linear relationship with several inputs. - Logistics Regression, regression where the output is a probability.

In Lean, you have three types of waste:

- Mura is unevenness in work demand or work flow. - Muri is having a greater demand than capacity in any given time or overburdening the process, series of processes, or system. We can all relate to making mistakes when we are rushed or stressed; this is caused by Muri. We establish the capacity for work and then ensure we do not try and force more into the system than it can handle. - Muda waste has two types: • Muda Type I : non-value added activity, necessaryfor end customer. • Muda Type II : non-value added activity, unnecessary for end customer.

A Gage R&R study quantifies 3 things:

- Repeatability, variation from the measurement instrument - Reproducibility, variation from the individuals using the instrument -Overall Gage R&R, which is the combined effect of (1) and (2)

Experimental Resolution In the design of experiments, the Design Resolution is a key criteria for selecting a fractional factorial design:

- Resolution III RIII: two factor interactions are aliased with main effects. - Resolution IV RIV: two factor interactions are aliased with other two factor interactions, but not with main effects. Main effects are aliased with three factor interactions. - Resolution 5 RV: two factor interactions are not aliased with each other, but are aliased with three factor interaction.

Sample metrics for an Lean enterprise such as supply chain include:

- Return on working capital - Perfect order fulfillment - Order fulfillment cycle time - Supply chain management costs

Contingency tables:

- Select, develop, and use contingency tables to determine statistical significance. - Contingency tables are an application of the chi-square test used to test the relationship between two variables.

Process FMEA (RPN)

- Severity assesses the impact of the failure mode with 1 representing the least safety concern and 10 representing the most dangerous safety concern. - Occurrence assesses the chance of a failure happening with 1 representing the lowest occurrence and 10 representing the highest occurrence. - Detection assesses the chance of a failure being detected with 1 representing the highest chance of detection and 10 representing the lowest chance of detection. - Risk priority number (RPN) calculates = Severity x Occurrence x Detection (Any RPN value exceeding 80 requires a corrective action.)

Measurement systems are subject to variation and error. The following are common MSA terms:

- Stability - Linearity - Measurement error - Percent agreement - Measurement Systems Capability - Calibration - Gage R&R - Precision to Tolerance (P/T) Ratio - Resolution - Repeatability and Reproducibility

This design process has three stages:

- System design, which uses scientific and engineering principles to create a prototype - Parameter design, for products and processes which minimize variation -Tolerances, are used to set parameters to minimize loss

Data collection for SPC explains how and by whom data is collected for improvement. This data includes the following common descriptors.

- The Process Name: Enter the process description and identify the process owner or owners. - Description of Measure: List a detailed description of your specific measures. - Justification for the Measure: What influenced you to pick this as the critical measure? How do you substantiate your choice of control? - Link to Strategic Initiative / Key Business Driver: Identify the key business and strategic influences for this measure. - Data Source: Identify all your data sources - Baseline, Target, Current Results Best Practice, and Measurement Period identify your starting point for all of these. - Measurement or Process Pattern: What are the normalized steps in your process? - Time Documentation: Document time intervals and timestamps of the process.

Basic Six Sigma Metrics

- The Sigma level - The Rolled Throughput Yield (RTY) - Defects per Unit (DPU) - Defects per Million Opportunities (DPMO) - The First Pass Yield (FPY)

Critical to Cost metric refers to:

- The costs of inventory kept on hand - The amount of labor put into production - The cost of raw materials - All sorts of overhead, such as employees and delivery costs

The central limit theorem predicts that:

- The distribution of means will increasingly approximate a normal distribution as the size (N) of samples increases. - The standard deviation of the population of means is always equal to the standard deviation of the parent population divided by the square root of the sample size (N). The mean of the population of means is always equal to the mean of the parent population from which the population samples were drawn.

Central Limit Theorem predicts that:

- The distribution of means will increasingly approximate a normal distribution as the size N of samples increases. - The standard deviation of the population of means is always equal to the standard deviation of the parent population divided by the square root of the sample size (N). - The mean of the population of means is always equal to the mean of the parent population from which the population samples were drawn.

Six Sigma Control Plans

Subgroups, Impact of Variation, Frequency of Sampling

The central limit theorem predicts that:

Again, the central limit theorem predicts that:

Normal distribution has 5 characteristics:

- The mean, mode, and median are equal. - Most values concentrate near the mean and decrease in frequency further from the mean. - Symmetrical about the central value - The curve has only one mode. - All data points fall within the curve, either 50% to the left or 50% to the right.

Normal distribution has 5 characteristics:

- The mean, mode, and median are equal. - Most values concentrate near the mean and decrease in frequency further from the mean. - Symmetrical about the central value. - The curve has only one mode. - All data points fall within the curve either 50% to the left or 50% to the right.

Developing Project Metrics

- The sigma level - The Rolled Throughput Yield (RTY) - Defects per Unit (DPU) - Defects per Million Opportunities (DPMO) - The First Pass Yield (FPY)

Two level include:

- The sparsity of effects principle, where there may be lots of factors, but few are important. - The projection property, where every fractional factorial contains full factorials in fewer factors. - The sequential experimentation, where runs can be added to a fractional factorial to resolve difficulties (or ambiguities) in interpretation.

Two-level fractional factorial experiments include three key ideas:

These are the three main types of hypothesis tests:

- Two Population Means - Matched or Paired Samples - Two Population Proportions

Attribute charts:

- U charts, Detects (errors) per unit in a subgroup - Np charts, Number of defective units in a sample for 'go' or 'no-go' - P charts, Percent or proportion of defects in a subgroup - C charts, Number of defects in a subgroup

When implementing Six Sigma and the Organization Enterprise-wide deployment, it is important to understand these factors:

- Understand who your customers are and what is important to them - Understand customer feedback through the Voice of the Customer and determine the requirements for your product-Prioritize issues related to your product - Determine internal processes and what causes variation - Determine the causes of defects-Develop ways to address defects - Develop metrics to standardize and measure the changes made in the process

The benefits report includes:

- expected realization numbers or ranges for each to fulfill the global savings figure. - The benefits report also states how these elements will be measured, using what tools and by whom. It should also clearly state how often or when the measure will take place. - Within a month of closure is a good starting point, with monthly or quarterly thereafter for a period of 1 -2 years recommended. - This will enable benefits to be not only achieved, but any overshoots or undershoots clearly identified as stability of the process is achieved following integration within the business.

The deliverables of the Measure phase include:

- identifying key measures, developing and deploying a data collection plan, developing a baseline for performance, documenting variation, and communicating it to team members and stakeholders.

Analysis of Variance (ANOVA):

- is a statistical technique for analyzing experimental data. - It subdivides the total variation of a data set into meaningful component parts associated with specific sources of variation in order to test a hypothesis on the parameters of the model or to estimate variance components.

opportunity costs are:

- is the cost of taking one decision over another. This cost is not only financial, but also in time, effort, and utility. - Opportunity cost can lead to optimal decision making when factors such as price, time, effort, and utility are considered. - It's necessary to consider two or more potential options and the benefits of each. Some may place greater value on time, whilst others on price.

Common cause variation

- is the statistical variation in the measurement of a process that comes from understood and predictable sources. - is also natural variation because it can be foreseen, eliminated, and understood using statistical analysis. - Common causes of variation cannot be eliminated by reacting to individual variations.

Special cause variation

- is variability or variation that triggers an essential change that is needed. Special cause variation is found through process analysis, control, or process documentation. - Special cause variation isn't what you expect to see in the context of your processes. It is something unusual that has happened that's influencing the results. - Special cause variation may occur if you don't identify an important variable that affects your process results, or you don't manage the variable appropriately.

Three methods are commonly used for random sampling:

- random number tables - mathematical algorithms - and physical randomization devices

The final deliverables in the Control phase include:

- standardizing processes, documenting procedures, implementing the monitoring plan, and ultimately transferring ownership of the project and closing the project.

In terms of timing benefits?

- this can be a timing improvement across the whole process or within certain stages of the process. - If it is a particularly complex or multi-faceted process, timings for each part of the process should be given and taken. - Sampling exercises to monitor times can be undertaken. If you are looking at the shipping of products, perhaps this would be another factor for customer engagement discussions.

When looking at quality savings:

- you should consider the accuracy of production numbers at each stage of the process. Internal assurance staff should be able to identify this and potentially reduce workload for quality control personnel. - You may also choose to assess the customer's view of achievement by undertaking surveys, focus groups, or stakeholder liaison meetings. The metrics here are likely to be in terms of accuracy or satisfaction levels being achieved.

The role of the Yellow Belt

-Assisting in the gathering of measurements and metrics during the Measure stage - Acting as a subject matter expert on the process being reviewed - Ensuring the Six Sigma project uses correct terminology relevant to the business in describing the process. - Working with the Green Belts to create communications that will explain the improvements and process changes to employees and departments affected by the project. - Communicating with work colleagues and acting as a change agent for the Six Sigma project. - General collation of metrics after the improvement is implemented in support of validating metrics and data gathering to validate, verify, and control implemented changes.

Tests of Equal Variance, Normality Testing and Sample Size Calculation, Performing Tests, and Interpreting Results:

The most common nonparametric tests and their uses are:

1 Sample Variance:

Binomial distribution is different from a normal distribution, although the shape of the curve will be similar.

Building the Business Case and Project Charter

Center Line & Control Limit Calculations

Chi-Squared (Contingency Tables):

Confidence & Prediction Intervals:

Control Methods:

Design principles:

Designed Experiments:

Fit, Diagnose Model, and Center Points:

Hypothesis Testing with Normal Data:

Hypothesis testing:

Lean does not eliminate people or employees, is not a shortcut, and does not micromanage. Lean focuses on removing the non-value-added delay, waste, and rework from your processes. Lean can be used in any industry or business to improve speed, quality, and cost. When implemented properly, Lean Six Sigma focuses on results, not training.

Lean enterprise eliminates waste and non-value-added activities. Lean focuses on delivering more value to the customer and addressing the voice of the customer. It creates efficiency based on optimizing flow in a process and empowers employees to improve their work. Lean always asks, "how can we get better?"

Linear & Quadratic Mathematical Models:

P Chart:

Lean principles can work on any organizational improvement. Employees play a critical role in Lean implementation. Significant improvements can be the result of Lean initiatives for cycle times, lead times, productivity, throughput, and processes.

...

This chart shows some of the most common tools you will use (Leaning)

.• Kaizen • Poka yoke • Takt time • 5 Whys • 5S • Spaghetti diagram • Touch time • Work times • Kanban • Theory of Constraints • Value Stream Maps • Cycle times

Team Dynamics:

1. Once stakeholders have been identified, they should be grouped into key and non-key stakeholders, depending upon the decision making and range of influence - a simple stakeholder analysis may help this split. 2. Once these two groups are set up, the team needs to include one member from each group. Each of these will be a supporter of the change, enthusiastic in their approach but also credible within the group. 3. The total team should range between 5 and 7 members for ideal meeting efficiency. You'll pull in people from various areas of the business at the appropriate times throughout the schedule of the project. 4. The team has collective responsibility for the success or failure of the project. There should be no blame or finger-pointing, but acceptance to learn from errors and to move forward. 5. The team leader will be responsible for planning, managing, and delivering against the project charter and keeping the team focused on achieving the goals of the charter throughout the whole DMAIC process.

Lessons Learned Activity

1. Review of Project Charter and checking that all elements have been met 2. Review outcome of each stage of DMAIC 3. Compendium of metrics and measurements taken throughout the exercise 4. The development of the changed process 5. Acceptance of the process within the workplace 6. Communication activities and the project's engagement levels with the business

1. Sort: Remove what is not needed. 2. Straighten: Organize what remains. 3. Shine: "Clean" the work area. 4. Standardize: Make sure a regular cleaning and maintenance schedule is in place. 5. Sustain: Embed 5S as part of the culture.

Defects per Million Opportunities (DPMO):

A defect is an event of non-conformance to specification. Defects are most often measured in Defects per Unit (DPU), Defects per Opportunity (DPO), Defects per Million Opportunities (DPMO), or a level of Sigma.

Passing on the Hard Work (checklist)

1. The benefits plan will be passed on with its detail as described above. 2. The control plan will be handed over to the process owner, together with all associated documents agreeing how continued compliance will be achieved. 3. The Champion will also get a copy of these documents since they typically report to the executive board of the business on the success of the Six Sigma Project. 4. All created training information and content, new documents, technology, contracts, and environmental controls will also be passed on to the business for use and application. 5. The project can then be closed down and remaining papers filed away.

Analyze - Analyze the data for variation and root causes

Activities Involved: - Define Performance Objectives - Identify Value and Non Value Processes - Determine the Root Cause Tools you can use: - Value-Stream, Historical Data - 5 Whys, Fishbone, Hypothesis testing, DOE, Histogram, Pareto Chart, Scatter Diagram, Control Charts, Statistical Analysis

Define - define the problem, agree on the goals, and listen to the voice of the customer

Activities Involved: - Identify Process Owner, Champion, Team - Define Customers and Requirements CTQ - Align Goals with Business Initiatives - Determine Projected ROI - Develop Project name and Purpose - Complete Project Charter - Develop a High-Level Process Map Tools you can use: - Project Charter Template - Brainstorming - Graphs - Stakeholder Analysis - Historical Data - Voice of the Customer

The Principle of Determinism is a core belief running through Six Sigma.

All outcomes are determined by the way inputs are transformed - according to some said process.

Selecting Lean Six Sigma Projects

An organization most often chooses Lean Six Sigma projects through a link to the overall strategy of the organization and the return on investment for a project. There are several methods for the selection of a Six Sigma project.

Benefits Report

At the same time, a benefits report is created based around agreed benefits. These may or may not have been discussed at the closure meeting, depending upon the confidentiality in relation to those present. This will detail not just the high-level savings in terms of cost, but will detail how this is broken down in terms of time and quality.

Concept of Stability:

Control chart monitoring can display: • The historical record of the behavior of a process • Allow for monitoring a process for stability • Detecting changes from a previously stable pattern of variation • Signaling the need for the adjustment of a process • Help detect special causes of variation

Design For Six Sigma uses the:

DMADV or DMADOV sequence rather than the DMAIC sequence.

Confounding:

Factors are confounded when the design array is configured so that the effect of one factor is combined with the other.

Standardize materials and sources of them:

Failure to standardize sourcing exposes your processes to a range of variation. Lock in on a supplier and reduce your variation, risk, and costs.

The New Process

Following a successful Analyze stage, new practices to replace those currently in existence should be in development or have been created already.

Lessons Learned

Following the sign-off and conclusion of the Six Sigma project, a lessons-learned activity should take place.

Green Belts vs. Black Belts

For most people trained to Green Belt capability, there is a natural expectation that they will transition to Black Belt over time. The increased capability of a Black Belt is more about their management and leadership skills than their statistical capability.

Unit 2 - Fundamentals of Six Sigma

Fundamentally, the training and use of Six Sigma philosophies and principles will allow employees and project teams to understand how systems interrelate and how to use the application of quality improvement methodologies that complement Six Sigma, such as Lean.

Impacts (measuring)

Given that you have measured and monitored everything through the project process, it would make sense that you measure the baseline impact of the new process within the business. There should be impacts on the customer as well as financial impacts of the change.

Process Drivers

Having identified that variation may exist, exercises are now required to pinpoint the specific changes needed.

Next, the people who do the process will need to be updated on the new process.

Here it's not just about meetings and discussions, but also ensuring that any operational and training manuals are updated to reflect the new process. Instructions to any of the internal customers or colleagues of the process owners should also be updated, so they understand what the change means to them. It can sometimes be necessary to rework websites and publications too.

Training requirements should make full use of existing training methods for new staff, but also develop a training method for existing staff.

Here you can make the best use of your subject matter experts (Yellow Belts) and also engage with trainers to construct and develop two separate sets of training programs.

Typically your processes can be in four states after analysis and as you prepare to go into the Improve stage.

Ideal state Threshold state On the brink state Red light state

Standardize gauging:

If it takes longer to gauge a part with one measuring device rather than another, standardize it. If one method takes longer than another, it adds to your cost. If a caliper is faster than a metal ruler and has the same consistency, use it.

Six Sigma Statistics

In the very early stages, we stated that its use of statistics is one of the key elements that separate Six Sigma from many other quality methodologies.

Controlling potential regression is not an easy thing...

It can only really be achieved with 100% monitoring of every activity and constant reminding of the process at each stage. This is not very practical for most businesses, so a control plan may be drawn up.

It is normal for benefits not to be fully realized for several months following implementation, so a benefits plan needs to reflect points of reference several times into the future.

It should contain a list of the financial benefits as well as a list of the potential improvements for customers, details how these will be measured, and the frequency of measure.

Binomial distribution is a discrete probability distribution:

It shows the probability of getting "X" successes in a sample of "N" from an 'infinite' population, where the probability of a success is "Y."

Once the control limits are calculated, they are placed on a control chart seen here.

It shows you the upper control limit, control, and lower control limit of the process.

It uses a whole set of tools:

Kanban - enabling just-in-time delivery within production, so that stock is not held waiting to be used TIMWOOD - an acronym for Transport, Inventory, Motion, Waiting, Overproduction, Over processing, and Defects; all areas for examination of savings that are probably the most commonly referenced.

What is Lean?

Lean is a manufacturing process that was developed by Toyota in 1988. It is based upon two key principles - the removal of irregularity and the removal of irrelevance. That is, attempting to get uniformity within production and removing wasteful processes. The main idea behind a Lean process is to get the most streamlined process within a production environment. It wants to create the most consistently "good product" in the most efficient way.

Standardize work to reduce in-process variation:

Look at control charts; many times, people blame product materials when it is often a machinery or personnel problem.

a cost flowchart can be equally beneficial...

Make a table of the results of the cost for a range of production numbers for each process under consideration. Account for the whole cost of the output being achieved, not just the elements.

Six Sigma concentrates on 4 types of process measurements:

Measurements are made in terms of cost, quality, safety, or time.

Culture and Perceptions

Most businesses have a culture which dominates the way they do things. This can likely be something that reflects the personalities of the people who have developed the business or simply evolved over time. It can be difficult to get a grasp of the nature of a culture at first, but using an experienced change management professional can give insight into this. It is important to understand the culture's tendencies and gain an understanding of a company's culture.

An example of Strong correlation:

Narrow and tight placement of data values

Benefits

Now that you have an optimized, or range of optimized processes, you need to show the gains to the business and key stakeholders.

The adoption of the process is your verification of acceptance.

Now you must make sure that the process is maintained, is achieving its goals, and is becoming common practice.

By beginning with waste removal, Lean processes can build in synchronized activities that minimize unnecessary or excessive activities.

Once processes have had waste removed, Black Belts typically review performance and design to reduce error rates and variability, thereby reducing waste and non-value-added activities. These are the two main goals of Lean.

Gaining Buy-in

One of the key requirements for introducing any Six Sigma change is gaining the buy-in of the business and the people impacted. This can be no easy feat, but considering what we have discussed above about change management and cultural awareness, it is possible. When you are ready to introduce the change, have a few "change agents" within the mix of staff. These are people who embrace change as a general rule, will be ready to talk to their colleagues about the change, and be encouraging of the need to make the change. Make sure you have suitable communications channels. Don't try and change the way employees communicate unless it's needed. If there is to be any downsizing or reorganization, ensure that the full details of this are transparent and clearly understand. Allow people to go through the change curve from denial to acceptance. Make sure that the process for determining relocations or redundancy is clearly explained, and management endorses the process publicly. Ensure training and education is readily available to train those relocating or having to change their existing ways. They need to see the willingness to invest in them to show you are serious about the change. Finally, have an "escape route" available for those who don't want to make the change - that is somewhere for those people who just don't want to transition and cannot find the enthusiasm for it. Whether it be deployment elsewhere within the company or options to leave the business.

Communications

One of the most frequent activities that a Green Belt will undertake will be communications. This may be communicating within the team or outside it. It is important that a Green Belt understands how to communicate professionally to all members of the organization, irrespective of their position.

A simple method of evaluating projects uses the Pareto Priority Index (PPI):

PPI = Savings ($) x Probability of Success / Cost ($) x Completion Time

The variance is the result of squaring the standard deviation.

So, where the Standard Deviation(SD) is often represented by σ (the Greek letter sigma), then variance (VAR) will be represented by σ2 (sigma squared).

The main activities in developing the Project Charter include:

Project Definition • Define the problem statement • Define the project scope and reference data • Create deliverables to be measured against for success of the project • Identify and confirm the project stakeholders, team members, and timeline for the project • Have a commencement or kick-off meeting to describe the high level process being looked at in terms that the stakeholders and project teams can relate to • Agree to all the items above with the stakeholders, team members, Process Owner, and sponsor or Champion.

One level include:

Randomized and Latin square design.

Six Sigma reduces costs and waste by determining the Cost of Poor Quality.

Reducing poor quality is accomplished by: - Understanding who your customers are and what is important to them - Understanding customer feedback, called the Voice of the Customer, and determining the necessary requirements for your product - Prioritizing issues related to your product - Determining internal processes and what causes variation - Determining what causes defects - Developing ways to address the defects - Developing metrics to standardize and measure the changes made in the process

Simple Linear Regression:

Regression analysis finds the line of best fit through a series of points. The least squares method is used to calculate regression.

Regression Equations:

Shows the relation between the inputs ('X') and the output ('Y') that is created by either a regression analysis or the Design of Experiments. The equation for linear regression is Y = A + Bx

What is Change Management?

Some of the key considerations around change management link to organization structures, where the reporting or managerial roles may change priority or seniority. It also ties in with workforce development, which ensures that the workforce is trained and has sufficient skills to perform their required duties. It will also look at organizational culture and communication, determining the nature of the business culture and how best to work with it to gain acceptance of change.

Six Sigma Green Belt

Someone who is qualified to a Six Sigma Green Belt standard has all the knowledge and capability to organize and run a Six Sigma project. They should have a good and solid understanding of the DMAIC process, a number of Six Sigma tools within their toolkit, and an understanding of how process changes can be implemented.

The Lean Enterprise

Standardization of metrics helps to measure collaboratively, control, and manage processes.

The term "Six Sigma" comes from

Statistics

One value stream examination always worth looking at is the start-up or "setting up period" for any activity:

This can be particularly relevant to clerical offices and other non-manufacturing processes. We define "Setup" in terms of preparation, replacement, location, and adjustment.

Chi squared contingency tables are called Yates correction:

The 2 x 2 tables allow teams to evaluate the accuracy of the approximation and the value of this correction.

Cost Benefit Analysis

The Cost Benefit Analysis (CBA) is similar to the return on investment calculation or a 'go-no-go' determination. The CBA will help determine costs of not doing a Six Sigma project, the costs if the project fails, and opportunity costs.

Project Charter

The Project Charter is an informal contract that is created at the start of the project to profile the working arrangement of the project.

The Basics of Six Sigma

The Six Sigma methodology uses proven strategies, tools, and statistical methods to improve virtually any process. The goal of Six Sigma is improved process performance and increased customer satisfaction through variability and defect reduction, resulting in consistently producing high-quality services, products, or processes.

The Order of Operations is shown below.

The acronym PEMDAS is often used.

The Deming Cycle is also known as the Plan-Do-Check-Act (PDCA)

The steps in the Deming PDCA Cycle are: 1.Plan a change or test it (P). 2.Do it (D) by carrying out the change or test on a small scale. 3.Check it (C) by observing the effects of the change or test. 4.Study it (S) by reviewing what you have done or changed. 5.Act on what you have learned (A). 6.Repeat and continuously evaluate the process.

Common cause and special cause variation

The common causes all fall in the typical "cause" of the variation. The special cause is the factor that does not fall in the range of the others.

Although Six Sigma talks a lot about statistical analysis and measurements and various other mathematical applications, at the core of the process is one simple equation: Y=f(x)+Ɛ

The core parts of this equation are described as followed: - 'y' represents the desired outcome, result, or goal you want to achieve. - 'x' represents the input, factors, variables, or elements required to create the outcome. - 'f' represents the function or process applied to the variables, by which they are modified, changed, or altered -the transformation processor. - 'Ɛ' represents some level of error or the amount of difference due to uncertainty or predictability when the process is applied and how near or far it is from the desired outcome.

X-Y Diagrams

The equation y = f (x) in quality terms explains the following: - The input x which results in the output y - The framework for Ishikawa diagrams - Process failure causes-The sigma level

Control

The fifth stage focuses on developing control plans and activities to monitor and sustain your improvement.

Improve

The fourth stage uses the information found in your analysis and develops possible solutions. Once the best solutions are developed, they are deployed as an improvement.

Unit 5 - Supporting Delivery

The purpose of this unit: • This unit provides a general overview of the role of a Yellow Belt Six Sigma practitioner and their responsibilities in supporting a Six Sigma project.

Unit 8 -The Measure Stage

The purpose of this unit: • This unit provides information on the activities that would normally be expected at the measure stage of a Six Sigma Project. • It looks at getting more detail to the process, what metrics and measurements are involved as well as estimating the baseline of the current "as is" process.

Unit 4 - An Overview of DMAIC

The purpose of this unit: • This unit will provide a basic understanding of the Define, Measure, Analyze, Improve, and Control (DMAIC) fundamentals at the core of Six Sigma methodology.

Unit 18 - Process Capability

The purpose of this unit: • This unit explains process capability. Process Capability Studies are used to determine whether a process is capable of consistently achieving specifications using system design, parameter design, and tolerances.

Unit 26 -Making the Change

The purpose of this unit: • This unit gives an overview of change management within the context of Six Sigma projects, how to assess the organizational culture, and how to gain buy in from those experiencing the change.

Unit 16 -Six Sigma Statistics

The purpose of this unit: • This unit goes through the statistical knowledge required for Six Sigma Projects as well as how to use them most effectively. • There is also some discussion around software usage in Six Sigma.

Unit 25 - Ending Six Sigma Projects

The purpose of this unit: • This unit provides information on how and when to end a Six Sigma project, how to monitor benefits, and the responsibilities being passed on to the business.

Unit 20 - Hypothesis Testing

The purpose of this unit: • This unit provides information on hypothesis testing to see if a potential solution will work.

Unit 19 -Inferential Statistics:

The purpose of this unit: • This unit provides information on statistical theories which involve inference.

Unit 10 -The Analyze Stage

The purpose of this unit: • This unit provides information on the activities that would normally be expected at the Analyze stage of a Six Sigma project. • The value stream proposition and analysis are examined as well as determination of the factors that influence the process output.

Unit 11 -The Improve Stage

The purpose of this unit: • This unit provides information on the activities that would normally be expected at the Improve stage of a Six Sigma project. The new process is defined, potential benefits examined and verification of the new process determined.

Unit 12 -The Control Stage

The purpose of this unit: • This unit provides information on the activities that would normally be expected at the final control stage of a Six Sigma project. • We discuss the standardization of new practice, verifying the impacts /savings, and how to document lessons learned.

Unit 7 -The Define Stage

The purpose of this unit: • This unit provides information on the activities that would normally be expected at the initial Define stage of a Six Sigma Project. • The Project Definition and scoping of goals and objectives are discussed, how the process is defined in terms of stakeholders, and the functionalities of the process. • We will also discuss the formation and requirements of the project team in more detail.

Unit 22 - Designed Experiments

The purpose of this unit: • This unit will show the design of experiments and factorial experiments to determine the x and y variables that affect a response.

Unit 17 - Measurement Systems Analysis

The purpose of this unit: •This unit explains when to use a Measurement Systems Analysis when the apparent variation of a process is caused by variations in the measuring system.

The chart is used with the X as the range chart (R).

The range is the highest minus lowest numbers placed in a chart plot of the range for each sample with calculated control limits.

Measure

The second stage is where the starting point metrics are recorded to baseline the current performance level and constraints of the process to be worked upon.

Analyze

The third stage reviews the metrics, and using a variety of tools, gains an understanding of the cause and effects interactivity within the system being looked at.

The Black Belt Role

There are a couple of key differences in the role of the Black Belt as opposed to that of the Green. The main elements are greater statistical knowledge and capability, as well as managerial ability, either in a general sense or as a project manager. Generally, a Black Belt will have worked on projects at a Green Belt level or completed project simulations before taking on the Black Belt role within a real-world project. It is often the case that the Six Sigma Black Belt will be someone within a junior executive position, maybe a Director level within the business, or, if not, sitting in a broadly equivalent position. Most companies will have only a few Black Belts and may look to get one trained to Master Black Belt level. Within the realm of training, this set of units gives you an overview or general idea of the requirements and responsibilities to become a Black Belt. Strictly speaking, to truly understand your Black Belt certification title, you will need to complete one or two projects before your certification will be completely recognized. This is true of all training, online or physical.

Standardization

There are several ways of solidifying standardization, but the key contributors are: • Common and equal training and education for all involved. • Follow up instructions, charts, documents, etc., are all in line with the new process . • Plans to monitor and control deviation from the process.

Funnel Reports

There are software tools available to help you funnel factors into the key and trivial points, and inherent in Six Sigma is the notion of removal of variations to reduce discrepancies at each point in the DMAIC methodology.

Unfortunately, some perfectionists may think that Six Sigma teams should keep working on improvements indefinitely.

There comes a point of minimal return and there are no more process improvements that can be done. This is when the process is optimized. When optimized, benefits can be calculated and presented to the business for agreement.

Tollgates

These are meetings include an in-depth discussion of the stage that was just completed, and formal approval to move on to the next stage. Stage reviews will include questions such as: • Should the project team continue with the project? • Are current deliverables being met?•Is the project on-track? • Are there any roadblocks preventing the project from succeeding? • What actions are required next?

Time Based Charts:

These are used to show change over a period of time and can often be similar to the graphs as shown above, but the horizontal or x-axis is reflective of the progress of time. These are useful for determining if a process has optimum time periods or if things degrade after a certain amount of time - particularly useful with monitoring automated or semi-automated processes using equipment in use for long periods of time. This can also demonstrate when employees should be taking breaks, indicating periods of sustained performance before degradation.

Cause and Effect Diagram (Fishbone)

They are graphical representations of brainstorming and think-tank periods when looking at all the potential causes of underlying process factors investigated during the Analyze stage.

The Black Belt's role is now complete.

They might need to prepare for the organization's next Six Sigma project or work on other process improvement tasks.

Begin with discussing the new process with the Champion who sponsored the project.

They should quickly come on board, and in turn, give the authority to proceed with the implementation of the new process.

p Control Charts:

are used to plot units nonconforming when the samples are not of equal size.

Statistical Process Control (SPC):

This course covers statistical process control measures that a Black Belt would use in the Control phase of Six Sigma.

Define

This first stage sets the context within which the Six Sigma project is to be performed.

Process Owner

This is the single individual or group with responsibility for the end-to-end process.

This is referred to as The Principle of Determinism.

This principle explains that every outcome is the result of a process being applied to it or determined by the application of a function.

A quick read through the previous slide and you will immediately see the overlap between Six Sigma projects and general project management.

Thus, a Six Sigma project can be 'project managed' - following whatever project management philosophy suits. The important thing is that it is structured, accountable, and has a sequential approach to activity.

Process Flow Map

To get a comprehensive and detailed process flow map, the personnel who do the daily process should be enlisted in creating it. It's worth noting that human engagement within a process over time is likely to create the most variation within that process. The slight differences in output may be the result of differing personnel and their variety of customization. You will need to capture all these variations within the process flow.

The formula to calculate the NP chart is:

Total number of nonconforming items in all samples being considered / Total number of samples

I-MR Chart:

Two charts in the I-MR charting:

Correlation:

Two variables are said to be closely correlated if there is a strong relationship between them.

The range shown in the chart is sensitive to shifts in process width, and it shows the uniformity of a process.

Unfortunately, the X-bar chart does not show problems quickly because of the effect of averaging averages.

Transition to the new process will take time and happen at varying rates.

Until training in the new process has been undertaken by all relevant personnel, the project team may continue to work and support the operational unit through the change.

When Does a Six Sigma Project Finish?

We have discussed some of the end elements of a Six Sigma project in other units, particularly unit 10 - the Control stage. A Six Sigma project will end when all benefits have been signed off by the sponsor, and the process has become a normal part of the business. That sounds simple enough, but there wouldn't be a section devoted to ending a project if it was that straightforward.

Box Plots:

are used to represent relatively small data sets. The outliers are points that are more than 1.5 times the interquartile range above the third quartile or below the first quartile. The whiskers extend to the largest and smallest data values that are not outliers.

The One Sample Sign Test is:

a simple nonparametric test equivalent to the parametric One Sample t-test and used to test the probability of a sample median being equal to hypothesized value. This is where: - H0: m1=m2=m3=m4 (null hypothesis) - Ha: At least one is different (alternate hypothesis)

The design of experiments is:

a systematic series of tests used to determine relationships of x and y variables that affect a process and response. The results of the experiment are analyzed to find the regression equation that relates the factors to the response.

First Time Yield Or First "Pass" Yield is

a tool for measuring the amount of rework in a given process. It is a good example of a cost-of-quality metric.

Scatter diagrams:

are also used and they show the correlations between variables.

Discrete variables:

are data that cannot be broken down into smaller units. Only a finite number of values are possible. Discrete data has one set of discrete values such as pass or fail or yes or no.

Procedures

are documents (instructions) that specify how a process is to be carried out. They may also indicate standard operating procedures.

Black belts

are generally the most knowledgeable and capable of people within the Six Sigma arena, often being the lead on projects of significant size.

Executive leaders

are responsible to the organization to provide support for the Lean enterprise and process improvement initiatives. The success of Six Sigma and Lean is based on building a culture of support to support the program.

Risk Priority Numbers

are the value assigned to: - the severity (scale of 1 to 10 or low to high) - and occurrence of each potential failure (scale of 1 to 10 or low to high) By multiplying these 2 factors, the risk priority number (RPN) is determined by, and equals, severity times the occurrence.

Overproduction wastes

are those of over producing and making too much.

Cyclical variations:

are time based with a repeated pattern.

Green Belts

are trained in the fundamentals of Six Sigma and may occasionally lead projects of a smaller caliber. More often than not, they will work on a team led by a black belt. They will often be less skilled in statistical analysis and more "people or organization" focused. Frequently, a Green Belt will have more involvement with the business and act as a conduit to the core operations from the Six Sigma team.

Subgroups:

are used to compare the control limits and patterns of variation between each subgroup through analysis.

Process Capability Studies:

are used to determine whether a process is capable of consistently achieving the specifications.

c Control Charts:

are used to plot the number of nonconformities per unit when the sample size is constant. It is used in situations where each unit can have several nonconformities.

u Control Charts:

are used to plot the number of nonconformities per unit when the sample size varies.

np Control Charts:

are used to plot units nonconforming when samples of equal size are taken from the process.

Normal distribution is:

bell shaped and the majority of the data falls in the center.

Go through the simulation using numbers of inputs and outputs that are likely to occur...

but also challenge the process to adapt and manage irregular patterns or potential failures within the process. Check that you are not just providing a process that works in a perfect environment.

The least squares method is used to:

calculate regression

Hypothesis testing

can compare two lots of data to see if there is a true variation or if it is just a number that confirms the other.

T-tests

compare the mean against a specified value using a sample of 30 items or less.

T-tests:

compare the mean against a specified value using a sample of 30 items or less.

Z-tests

compare the mean against a specified value when the sample has more than 30 items or the standard deviation is known.

Paired t-test

compare the means of two samples of 30 items or less, when the items in the two samples can be paired.

Paired t-tests:

compare the means of two samples of 30 items or less, when the items in the two samples can be paired.

Two sample t-tests:

compare the means of two samples of 30 items or less.

Critical to Quality (CTQ) flow-down is used to

convert the voice of the customer to specific needs using a treemap, where the tree map is the voice of the customer and the branches lead to the specific features. It helps determine the big Y's and little y's or the effects of the causes.

Random variation and systematic variation should be evaluated for the:

critical causes of your process and their impact on variation, either for (spread) or for central tendency (centering). Hypothesis testing can help determine the cause based on your target for specified limits.

Design of experiments

deals with planning, conducting, analyzing, and interpreting controlled tests to evaluate the factors that control the value of a parameter.

Confidence intervals:

define the area around a sample mean which the true population will fall into with some degree of confidence. There is a 95% probability the true population mean will lie within the 95% confidence interval of the sample mean.

Measurement Systems Analysis (MSA)

designed to improve the process when the apparent variation is caused by variations in the measuring system.

Multiple Linear Regression

follows the equation Y=A = Bx and shows in a linear display responses to several inputs. The purpose of linear regression is to find the line that comes close to the data.

When you have a general idea of the new process...

draw up a paper process map with sufficient information that you can do a desktop simulation. There are software programs that will help with simulations, but with Six Sigma, human involvement is almost always required.

ROI is defined for

eliminating defects in terms of increased profitability or cost savings. The ROI is a key measure of the financial performance of an organization.

Statistics

enable informed analysis of data from sampling through to modeling potentials. They help the practitioner make an informed decision with validity as the project progresses.

Hypothesis testing allows you to:

evaluate if a project or proposed process improvement calculation is statistically significant, or if the same thing could have occurred by random chance. It also helps you to understand the probability distribution of the data sample. The normal distribution is used to determine the probability of occurrence of an event based on historical data. Hypothesis testing can also help determine which factors in process inputs and outputs are significant.

Multiple regression analysis is used to:

examine a relationship to any other factors that may be nonlinear independent variables (either quantitative or qualitative) to determine the effects of a single variable or multiple variables.

Process capability:

examines the variability in process characteristics and whether the process is capable of producing products which conform to the required specifications.

Central Limit Theorem

explains why many distributions tend to be close to the normal distribution. The central limit theorem describes the characteristics of the population of the means created from the means of an infinite number of random population samples of size.

Fit:

finds the line of best fit through a series of points.

To calculate the SD from the variance:

first the square root is taken of it (√). The formula to calculate the VAR can be seen below. Before working through the equation the mean average must be calculated.

Order:

is the numeric progression in which a product or service is produced.

Residual Analysis shows:

how well the regression model represents a process being studied and the special causes. Residual Analysis is part of experimental design and the residuals should conform to a normal distribution.

The following chart shows possible solutions for a full factorial experiment:

https://www.itl.nist.gov/div898/handbook/pri/section3/pri3332.htm

Spaghetti diagrams

identify potential improvements to a physical layout to remove unnecessary movement or bottlenecks. Spaghetti diagrams are primarily used for Lean manufacturing in production facilities.

Process decision program charts (PDPC)

identify what may go wrong in a plan under development. Once possible issues are identified, prevention controls and countermeasures can be developed to prevent the problems.

Using the statistical definition of the 95% confidence interval:

if a poll of 100 people were taken, 95% of respondents would be within the calculated confidence intervals, and 5% would be either higher or lower than the range of the confidence intervals.

An experimental design is orthogonal:

if each factor can be evaluated independently of all the other factors. In a two-level factorial design, this is achieved by matching each level of each factor with an equal number of each level of the other factors.

Two-level fractional factorial experiments:

include three key ideas

The Lean enterprise

includes all types of enterprises, including manufacturing, service, transactional, product, and process design, as well as innovation.

Addition and Subtraction

includes simplifying addition and subtraction in the order that they appear from left to right.

Multiplication and Division

includes simplifying multiplication and division in the order that they appear from left to right.

Exponents

includes simplifying the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Parentheses and brackets

includes simplifying the inside of parentheses and brackets before the set of parentheses or removing the parentheses.

Five S (5S)

is a Lean tool that allows examination of a process to identify non value-added elements. Although the original 5S words were Japanese, an anglicized version has been created using the following words: Sort, Straighten, Shine, Standardize, and Sustain.

Student's t (Student's t-distribution)

is a Probability Distribution Function which gives the height of the distribution. The shape of the t distribution is similar to the normal distribution and converges on the normal distribution as the number of degrees of freedom increases.

Variance:

is a calculation across a range of data that shows how spaced out the information is. Similarly, the standard deviation will be a spacing value of information.

Bench marking

is a comparison and cross-referenced review of similar processes within associated businesses. This can also give insight and knowledge of how you might fine-tune a new process into a practical and usable vehicle.

Poka-yoke (error-proofing)

is a concept in quality that means mistake-proofing. The phrase initiated in Japan during the 1960s by Shigeo Shingo

Normal distribution

is a continuous distribution where any two data values may have an interval in between. The bell-shaped normal curve has probabilities that are found as the area between any two z values.

Monitoring and measurement of processes:

is a continuous process for organizational quality improvement. Methods for monitoring should demonstrate the ability of processes to achieve planned results. When the planned results are not achieved, corrective action should be taken.

A Measurement Systems Analysis (MSA):

is a designed experiment that seeks to identify the components of variation in the measurement. The analysis evaluates the test method, measuring instruments, and the entire process of obtaining measurements to ensure the integrity of data.

Poisson distribution

is a discrete probability distribution. It is used when the sample size is not restricted, and it is not possible to specify the number of occurrences, but you do know the average number of occurrences.

A Balanced Design (Balanced Experiment):

is a factorial design in which each factor is run the same number of times at the high and low levels.

A capability analysis:

is a graphical or statistical analysis tool that visually or mathematically compares actual process performance to a set of performance standards. It is used to assess whether a system is statistically able to specifications or requirements of a process.

Linear Regression:

is a linear relationship with one input and one output.

Multiple Linear Regression:

is a linear relationship with several inputs.

Bias:

is a measure of the distance between the actual value and the average value of a part. Bias occurs when the survey sample does not accurately represent the population. The bias that results from an unrepresentative sample is called selection bias.

Friedman's Test:

is a nonparametric alternative to two-way analysis of variance. The hypothesis is: - H0 the means of all the samples equal - H1 the mean of at least one of the samples is different

Mood's Median:

is a nonparametric equivalent of ANOVA where the hypothesis is: - H0 the samples are all drawn from populations with equal medians - H1 the median of at least one of the samples populations is different

Kruskal-Wallis:

is a nonparametric test used to compare several samples and test the hypothesis that: - H0 the samples are all drawn from populations that have equal means - H1 the mean of at least one of the populations is different

Mann-Whitney:

is a nonparametric test which compares the means of two samples. • It tests the hypothesis that: - H0 the samples are drawn from populations with equal means - H1 the mean of the population of sample 'm' is less than/greater than/not equal to that of sample 'n'

A population parameter

is a number describing something about a whole population, such as the population mean or mode. It is fixed and used as the value of a variable in a general distribution. The population parameter is used in statistics and is a measurement of the population that is being studied. Large populations are often measured by taking samples to represent the entire population.

Operational Excellence

is a philosophy of leadership, teamwork, and problem-solving, resulting in continuous improvement throughout the organization. This is accomplished by focusing on the needs of the customer, empowering employees, and optimizing existing activities in the process. It stresses the need to continually improve by promoting a stronger team using greater ownership of activities and making the environment better for both employees and customers. Operational Excellence (OE) is based on the fact that you cannot improve if you do not measure. Metrics and KPI definition for any process is of pivotal importance, and this means that it has great sway within Six Sigma process improvement as it uses metrics to validate all changes. It also encourages continuous improvement by continuously improving on existing metrics and performance measures. OE's main objective is to reduce operation cost and wastes without affecting quality, time, delivery, and cost of products and services being offered.

Defects per unit (DPU):

is a product's or service's non-fulfillment of an intended requirement or reasonable expectation for use. These may be in the form of "blemishes," "imperfections," and "nonconformities." These are items that do not meet the customer's expectations.

Mode or modal point:

is a range that occurs most frequently. So, if you have a set of results, the mode can be attributed to that result found the most often.

A process

is a series of tasks that are repeated time and again.

Analysis of Variance (ANOVA)

is a statistical technique for analyzing experimental data. It subdivides the total variation of a data set into meaningful component parts associated with specific sources of variation in order to test a hypothesis on the parameters of the model or to estimate variance components.

Mutually Exclusive Probability

is a statistical term used to describe a situation where the occurrence of one event is not influenced or caused by another event.

Process FMEA

is a structured analytical tool used to identify and evaluate the potential failures of a process for existing products or services.

A control plan

is a summary of potential activities to ensure key parts of the production process are controlled with detection methods and prevention strategies. They may also include some remedial activity to return those areas to the required state.

Failure Mode and Effects Analysis (FMEA)

is a systematized technique that identifies and ranks the potential failure modes of a design or manufacturing process to prioritize improvement actions. FMEA acts as a way of identifying and preventing problems before they occur. FMEA provides information in quantifying weighted priorities, risks, and contributing characteristics of a problem.

Nonlinear regression:

is a technique to fit a curve through data. It fits data to any equation that defines Y as a function of X.

Blocking:

is a technique used to manage nuisance factors that may affect the results of an experiment. The experiment is organized into blocks and the nuisance factor is maintained at a constant level in each block.

Blocking:

is a technique used to manage nuisance factors that may affect the results of an experiment. The experiment is organized into blocks, and the nuisance factor is maintained at a constant level in each block.

DMADV

is an acronym for Define, Measure, Analyze, Design and Verify. The last 2 stages of the DMAIC process are replaced with Design and Verify to indicate that you design the best process and verify that it is the best process.

Six Sigma

is an improvement methodology that uses the following phases to make changes to any process: Defining, Measuring, Analyzing, Improving, and Controlling "Six Sigma" measures the capability of a process to perform defect-free work with a failure rate of 3.4 parts per million or 99.9997%.

Stability of a measurement system:

is analyzed using control charts. Your goal is to ensure the measurements taken by the appraisers for the process are stable and consistent over time. Use the control charts you develop to monitor measures over time so that you can make corrections to processes and operating procedures. Don't forget when thinking about measurement that special causes can also occur with the process control limits, and these must be given corrective action before proceeding to validate the measurement system.

Waste of inventory

is any cost associated with items not on just-in-time inventory.

Response bias:

is bias that results from problems in the measurement process. Bias due to measurement error can occur with a poor measurement process. - This includes leading questions where the wording of the question may be loaded in some way to favor one response over another.

The Project Charter

is composed of details and tasks which may vary with each organization and project. - The basic structure for projects and charters is to begin with an executive summary. - The charter is written as a roadmap for the project. - It is geared towards senior management as a plan, and for the project team as a summary, of what is to be done. - The next section of the charter aligns the project with organizational strategy.

Binomial distribution

is different from a normal distribution, although the shape of the curve will be similar. The binomial distribution is a discrete probability distribution. It shows the probability of getting "X" successes in a sample of "N" from an 'infinite' population, where the probability of a success is "Y."

Balance:

is evenly distributing both the quantity and variety of work across available work time, avoiding overburden and underuse of resources.

The median:

is found by ordering a set of numbers from lowest to highest and finding the exact middle. The median is just the middle number. So if your number set is (10, 10, 20, 40, 70), the median is 20.

Yellow Belt

is generally the person who is a contributing member towards a Six Sigma project because of their knowledge of the business. They act as subject matter expects (SMEs) in their respective area of expertise.

Data integrity:

is maintained by using a Measurement Systems Analysis which evaluates the test method, measuring instruments, and the entire process of obtaining measurements to ensure the integrity of data.

Capability analysis:

is most easily calculated using pre-built calculations and formulas.

The Central Limit Theorem:

is one of the most powerful and useful ideas in all of statistics. The Central Limit Theorem is a theorem, which means that it is not a theory or just somebody's idea of the way things work. The Central Limit Theorem is concerned with drawing finite samples of size (n) from a population with a known mean, μ, and a known standard deviation, σ. The conclusion is that if we collect samples of size (n) with a "large enough n," calculate each sample's mean, and create a histogram (distribution) of those means, then the resulting distribution will tend to have an approximate normal distribution.

Logistics Regression:

is regression where the output is a probability.

A sample statistic

is something that describes a sample, such as the sample mean. In statistics, a sample statistic is one that is a subset of individuals from within a statistical population to estimate characteristics of the whole population.

Repetition:

is synonymous with replication.

Transportation waste

is that of material movement back and forth from storage.

Waste of over-processing

is that with unneeded steps in production.

The Gage Repeatability and Reproducibility:

is the amount of measurement variation introduced by a measurement system, which consists of the measuring instrument itself and the individuals using the instrument.

Business Process Reengineering (BPR)

is the analysis and design of workflows and processes within an organization. It defines a business process as a set of logically-related tasks performed to achieve a defined business outcome. Re-engineering is the basis for many recent developments in management, including ideas around multi-skilled and cross-functional teams. Business Process Reengineering may also be referred to as Business Process Redesign, Business Transformation, or Business Process Change Management. As we've looked at Six Sigma, we have been highlighting the need to examine processes and to change them to meet the needs of the project goal. BPR was originally developed within the IT industry, and as such, it uses a lot of terms and descriptors that are akin to software development. However, its methods of looking at shortest point routes and repetition reduction are found within Six Sigma, and an understanding of BPR philosophy and its existence can be a benefit to any Black Belt.

Interaction:

is the combined effect of inputs instead of the sum of the individual effects.

Resolution

is the criteria used to select a fractional factorial design.

Resolution:

is the criteria used to select a fractional factorial design.

Efficiency:

is the lowest possible variance from any estimator divided by the expected variance of the selected estimator.

Process Owner

is the manager or member of the operational team that currently has responsibility for the part of the business about to be improved.

First Time Yield (FTY):

is the number of defect-free units produced divided by the number of total units going into the process. The FTY is calculated by the total number of processes multiplied by the number of defect-free products/the total number of products.

The mean average:

is the one most frequently used and referred to as average, but it requires some basic math to work it out. It is worked out by adding together all of the values and dividing by the number of total values. For example, if you receive 50 responses to an item and the results are all added together, then this result is divided by 50 to give the mean average. The mean average will often be represented by a ("x bar").

Champion

is the person that comes up with the idea to undertake a Six Sigma project within a part of the business.

Conditional Probability:

is the probability of an event given the information that an event B has occurred indicated by P(A/B).

Conditional probability:

is the probability of an event given the information that an event B has occurred, indicated by P(A/B). Order of operators is important when simplifying expressions and equations. The order of operations is a standard that defines the order in which operations such as addition, subtraction, multiplication, and division occur.

The significance level:

is the probability of making a Type I Error. In a Hypothesis Test, a Type I error occurs when statistically unlikely test results lead to the incorrect conclusion that the null hypothesis should be rejected.

Rolled Throughput Yield (RTY):

is the probability that a product will pass through the entire production or service process without rework and defects.

A tolerance:

is the room around which a set value can fluctuate, and an allowable tolerance is given in all functionality. Six Sigma aims to reduce that tolerance need as much as possible.

Cost of Poor Quality (COPQ)

is the sum of internal and external failures. It is measured differently depending on the industry. For example, sometimes companies will relate the Cost of Quality as a percentage of sales towards total sales.

The goal of the Design of Experiments:

is to discover the relationship between the factors that affect a process and the response. In the experiment, the factors are varied systematically, and then the resulting response observed. The results of the experiment are analyzed to find the regression equation for the response.

Sample size:

is typically annotated by (n) and is the number of units in a sample.

Waste of motion

is unnecessary travel around a factory.

Exponential distribution

is used for reliability engineering where the failure rate is constant.

The standard deviation

is used frequently in determining confidence levels and probability of a result falling within a certain range.

Confounding:

is used in experimental design. Factors are confounded when the design array is configured so that the effect of one factor is combined with the other.

Randomization:

is used in experimental designs to prevent systematic patterns and to convert patterns into variation that can be detected in analysis.

Weibull distribution

is used in reliability engineering because it can be adjusted to the product characteristics such as wear and tear.

Multi-Vari Analysis

is used to analyze processes that have several different inputs and outputs.

Multivariate analysis:

is used to analyze processes that have several inputs and outputs.

Regression analysis:

is used to determine the strength of a relationship between data output and input. In part 2, we mentioned the line of best fit; well, the purpose of regression is to find that line and thus describe that functional relationship between x and y. The main benefit in doing this will be to enable predictability of future events around the variables without actually needing to undertake elongated experiments.

Logit:

is used to find the relationship between a probability and quantity.

The NP Chart:

is used to measure the number of defective items in a sample when the sample size (n) is constant. The NP chart is used to track the number of items that are nonconforming, and each item may be counted only once. It would be used when the number of items with the characteristic is a small number within the total population under consideration.

Replication:

is used to remove systematic errors. The number of tests should equal the number of replications.

Bivariate distribution

is used to show the joint probability distribution of two random variables. The shape depends on the standard deviation.

The Chi-Square test:

is used to test whether a sample is drawn from a population that conforms to a specified distribution.

Chi square

is used to test whether a sample is drawn from a population that conforms to a specified distribution. Chi square is also called goodness of fit.

ANOVA

is used to test whether the means of many samples differ, but it does so using variation instead of mean. It compares the amount of variation within the samples to the amount of variation between the means of samples.

The P Chart:

is used to track a proportion of a population or whole, and each unit is considered conforming or nonconforming.

The Hypergomeric distribution

is used when a small sample is taken from a small population without replacement. It is most often used in inspections.

Temporal variation:

is variation with time.

Waste of waiting

is when resource labor and equipment could be making other products.

If you consider the outcome of variance or SD calculations:

it can be linked that your tolerance level should be no more than a set number of the SD on either side of the perfect midpoint choice. This will allow you to factor in likely volumes of failure while giving a verifiable mathematical explanation of your choice of tolerance level.

To design a control experiment,

keep everything the same except for the single variable being tested. A variable is something that can be changed in the experiment. It is what you are testing. Everything else must be the same, and only one variable or condition is altered or changed.

Sample homogeneity:

means the characteristics of the sample are uniform and representative of the population.

Linearity:

measures the consistency of bias over the range of the measuring device. Accuracy is the degree of closeness to an expected mark.

Measurement correlation:

measures the strength of a linear relationship between two variables.

Six Sigma focuses on

measuring and quantifying the impact of an improvement project. It requires buy-in across the business for the project to make changes based upon those measurements, irrespective of personal views. Guesswork and assumptions have no place; it is a precise process.

Independent Probability:

occurs if the occurrence of one of the events provides no information about whether or not the other event will occur, meaning the events have no influence on each other.

Non response bias:

occurs when individuals chosen for the sample are unwilling or unable to participate in the survey.

Voluntary response bias:

occurs when sample members are self-selected volunteers; the resulting sample tends to over-represent individuals who have strong opinions.

Under-coverage bias:

occurs when some members of the population are inadequately represented in the sample.

Social desirability bias:

occurs when survey respondents are reluctant to admit to questions in the survey if the results are not confidential. Their responses may be biased toward what they believe is socially desirable.

The Individual Chart:

plots each measurement as a separate data point, where each data point stands on its own and where the subgroup size is or = 1.

In the Two Population Means test:

populations are independent and population standard deviations are unknown, or populations are independent and population standard deviations are known (which is not likely).

Preparation

refers to gathering materials required to begin, whether that's logging into a computer or collecting forms for examination. Each stage of a process has a preparation phase.

Replacement

refers to the additions or removal of items used within a process. Loading paper in a copy machine or filling the paint sprayer are good examples of this.

Exponential distribution is used for:

reliability engineering where the failure rate is constant.

Random sampling helps produce:

representative samples by eliminating voluntary response bias and guarding against under coverage bias.

Master Black Belt

represents someone who is trained to Black Belt capability, but is also able to coach, train, and support others in understanding Six Sigma or acting as a consultant within an organization. They may occasionally lead a project that is large and significance, but generally do not.

Using paper and pen...

run through the simulation in a mock environment as if you were following the process. Discuss each decision point and confirm that there are no more or less activities required as the production flow is passed along. Ensure you identify the resource needs at each point.

Process Capability Studies are:

short-term studies conducted to collect information on the performance of new or revised processes related to customer requirements. This occurs when processes, employees, or equipment change, and as many possible measurements should be used to get an accurate reflection.

Value stream maps

show the "value stream" of a process and allow project teams to visualize processes. Value stream mapping is used to identify major sources of non value-added time in a value stream, envision a less wasteful future state, and develop an implementation plan for future activities.

Flowcharts

show the steps in a process from start to finish.

Process Capability Indices:

show the value of the tolerance specified for the characteristic divided by the process capability.

Stratified sampling is used to ensure:

smaller sub-groups are not overlooked. Stratified sampling is used when there are smaller sub-groups that need to be investigated, when you want to reduce standard error, and when you want to achieve greater statistical significance in a smaller sample.

Chi square is calculated by:

summing the Chi square contributions from each category in the hypothesis. The hypothesis is: - H0 the sample conforms to the specified distribution. - H1 the sample does not conform to the distribution.

Management

supports these initiatives through the development of a constant "mindset of improvement" by encouraging and supporting the design of the best possible processes. Leadership also prioritizes projects, approves them, and celebrates the success of them. Leadership is then responsible for mentoring to ensure the tools, support, and knowledge are available to succeed.

Enumerative statistics

tell about the specific data that is being analyzed. Enumerative may also be called Descriptive statistics.

Precision/tolerance (P/T):

tells how well a given measurement can be reproduced. This is a standard deviation around a mean value. Tolerance may have two errors: systematic and random.

Full Factorial Experiments:

test several factors at two levels, high and low. In a full factorial experiment, every possible combination of factors and permutations is tested.

Full factorial experiments:

test several factors at two levels, high and low. In a full factorial experiment, every possible combination of factors and permutations is tested.

The Chi-Square is used to:

test whether a sample drawn from a population conforms to a specified distribution.

Six Sigma relies on a Body of Knowledge (BOK)

that contains information on general content and topical areas users should know and pursue in their initiatives.

A cumulative cost diagram

that mimics a process map can be used, where each item and path has a specific cost associated with it.

Regression Analysis is a data model:

that predicts a regression so that variation in a process can be reviewed, comparing the actual values from a process to the predicted regression values which are the residuals.

For example,

you may have fathomed that the volume of flour being used by the bakery has significant variation in the quality or baking, but how do you determine the optimum point at which the flour quantity is most effective?

Work Breakdown Structure (WBS) defines

the scope of the project and breaks the work down into components that can be scheduled, estimated, and easily monitored and controlled. The idea behind the WBS is simple: you subdivide a complicated task into smaller tasks, until you reach a level that cannot be further subdivided.

Critical to Schedule (CTS) relates to:

the time it takes to pass through one or more stages of a process. It relates to delivery timing, time on hand of goods stocked, and arrival times for materials.

In addition to the prioritization matrix, project viability matrices are used to determine the viability of a project.

the weighting goes 1 to 5, with scoring of: • Definitely no • No • Possibly • Definitely • Etc...

Average

there are 3 types of averages most commonly used in statistics: the mode, median, and mean average.

Inferential statistics are used:

to draw conclusions (an inference) about a population based on sample data. Inferential statistics may also be called Analytical statistics.

Six Sigma's implicit goal is

to improve all processes to 3.4 Defects per Million Opportunities (DPMO) of quality or better.

Hypothesis testing is used in Six Sigma:

to screen for potential causes of a problem. The hypothesis test calculates the probability that an observed difference between two or more sets of data can be explained by random chance alone and not a fundamental difference between the underlying sample populations that the samples came from. The p-value is most often used to represent this.

The U Chart is used to:

track the number of characteristics of interest per item or unit examined. The measurement scale for U charts is continuous. The U chart is similar to the C chart except that the sample size can change over time.

In the Matched or Paired Samples hypothesis test:

two samples are drawn from the same set of objects, and the samples are dependent.

Red light state

your processes are neither in statistical control, nor do they meet the customer's specifications. You need to look at removing special causes from the process before you can begin to change.

Sample size is:

typically annotated by (n) and is the number of units in a sample.

Random sampling helps achieve:

unbiased sample results in a study by choosing subjects from a population through unpredictable means. All of the subjects have an equal chance of being selected out of the population being researched.

Random sampling is:

used in population sampling when reviewing historical or batch data.

Stratified random sampling is:

used in population sampling when reviewing historical or batch data.

Rational sub-grouping is:

used in process sampling when data is collected in real time during process operations.

Statistical Process Control (SPC) is used to help understand:

variation and process capability and performance by using: - control charts of Cp, Cpk, Pp, Ppk, x-bar, and R chart, and attribute charts of p, np, c and u. The Black Belt will be able to develop control charts for x-bar and s charts, median charts, XmR/ImR charts, short run SPC, and moving average (MA) charts.

Nonparametric tests can be used:

when the population does not conform to a particular distribution or normal distribution.

The projection property:

where every fractional factorial contains full factorials in fewer factors.

The sequential:

where runs can be added to a fractional factorial to resolve difficulties (or ambiguities) in interpretation.

The sparsity of effects principle:

where there may be lots of factors, but few are important.

Ideal state

where your processes are in statistical control and meet the customer's requirements. Knowing that a process is in statistical control and meets the factors that are critical to quality for the customer are ideally where you want to be. Using control charts, you can easily show this.

Remember that Chi square is used to test:

whether a sample is drawn from a population that conforms to a specified distribution. Chi square is also called 'goodness of fit.'

ANOVA is used to test:

whether the means of many samples differ, but it does so using variation instead of mean. It compares the amount of variation within the samples to the amount of variation between the means of samples. - ANOVA is effective in separating inherent variance and special cause variance, and it also provides a methodology to evaluate the robustness of a process to various levels of a factor.

Student's t is a Probability Distribution Function:

which gives the height of the distribution. The shape of the t distribution is similar to the normal distribution and converges on the normal distribution as the number of degrees of freedom increases.

Process Control is most often monitored by control charts:

which have an upper and lower control limit indicating a special cause. There are two types of SPC charts: control charts for attributes and control charts for variables.

MANOV Analysis:

which is the acronym for Multiple Analysis of Variance.

The central limit theorem explains:

why many distributions tend to be close to the normal distribution. The central limit theorem describes the characteristics of the population of the means created from the means of an infinite number of random population samples of size.

A Yellow Belt

will usually be a general member of the workforce, utilized for their skills, knowledge, or experience within the process that is being reviewed by the Six Sigma project. This most likely will not be a full-time role, although it may be undertaken for a short period of time on a full-time basis depending upon the project being reviewed.

Linear mathematical models use the formula:

y = mx + b

In other words:

you calculate the differences between the results and the mean average, then square them, add them up, and divide by the number of results. The SD is just the square root of this result.

On the brink state

your product meets the customer's requirements but is not in statistical control. What's so bad about that? It meets the customer's needs. The answer is simple: your process has special causes and is unpredictable.

Interpreting Results: (for best data accuracy)

• Accept all data as it is collected and scrutinize it later. • Record the data at the time it occurs. • Avoid rounding the data. • On the data collection plan, record as many details around the data, such as the exact source, machine, operator, conditions, collector's name, material, gage, and time. • Record legibly and carefully. • Screen data for misplaced decimal points, duplicate data entries, improper recording procedures, and missing date points. • Verify the gages (Gage R&R) are accurate through calibration. • Sample size is typically annotated by (n) and is the number of units in a sample. • Balance is evenly distributing both the quantity and variety of work across available work time, avoiding overburden and underuse of resources. • Repetition is synonymous with replication. • Replication is used to remove systematic errors. The number of tests should equal the number of replications. • Order is the numeric progression in which a product or service is produced. • Efficiency is the lowest possible variance from any estimator divided by the expected variance of the selected estimator.

Control limit calculations are found by:

• Calculating the mean by summing the measurements and dividing by the sample size. • Then, calculating the standard deviation by subtracting each measurement from the mean and squaring the results individually. • Then, summing the set of individual numbers. Take that number and divide the sum by the sample size minus one. • Then, the last step is to square the result to compute the standard deviation.

Six Sigma Roles and Responsibilities

• Champions guide the team through organizational support and resources, removing roadblocks. • Master black belts train black and greenbelts and manage the strategic direction of the Six Sigma program. • Black belts lead problem-solving Six Sigma teams. • Green belts assist with data collection and analysis for black belt projects. • Yellow belts review overall activities and participate as project team members and subject-matter experts (SMEs) in their area of work.

Control methods will include combinations of these: (checklist)

• Chart Champion: Name of the process owner • Critical to Quality Characteristic: End-product characteristic proven to be important to the customer, along with hierarchical reference number • Significant Characteristic Description: Process characteristics that have a significant impact on the Critical to Quality Characteristic • Significant Characteristic Number: Reference number to organize Significant Characteristics within a hierarchy that relates to the corresponding CTQCs • Chart Type: X-bar & R chart, P-chart, C-Chart, Trend chart • Chart Location: Location where the cart is kept • Measurement Method: Method used to collect the measurement data (e.g., scale, caliper) • Measurement Study: Denote whether a measurement system analysis has been completed. If Yes, show the % total error. • Gage Number: Reference number for the gage that corresponds to the calibration tracking system. • Sampling Plan: How many samples are drawn at what frequency. • Process Stability: Is the process in a state of statistical control -Yes or No. • Cp/Cpk: If process is stable, calculate Cp and Cpk.

You may choose to use some good project management practices to help move along development of your Six Sigma project.

• Consider releasing regular project reports detailing progress. • Consider using risk and issue logs that identify likely or potential challenges to the successful delivery. • Consider the use of checkpoint meetings as a structure for regular engagement with your business customer, stakeholders and team.

In the DPMO formula:

• D is the number of defects • O is the number of opportunities for a defect • U is the number of units • TOP is the total number of opportunities = U times O • DPMO equals DPO times 1,000,000

The steps used to develop the PDPC chart include:

• Developing a tree diagram of the proposed plan, reviewing each task • Brainstorming what could go wrong • Reviewing all the potential problems and brainstorming possible countermeasures for each potential problem • Determining which to implement.

Questions to ask include:

• Do they like change? • Do they strongly resist change? • Do they question decisions a lot or are they an organization that accepts without challenge? • Do they enjoy training? • Do they prefer class based training, CBT, paper? • What is their perception of management? • What is their perception of reward and recognition? • they know what Six Sigma is? • How do they communicate? • How do they like to communicate?

Fundamentals of Six Sigma

• Implement statistical process control(SPC). • Strategically plan improvements. • Understand tactical design principles for organizational application. • Perform hypothesis testing. • Perform statistical and process capability calculations. • Perform and analyze the results of correlation and regression. • Analyze and interpret risk studies and implement improvement processes. • Deploy control plans and sustainment opportunities.

There are a few key things that define a project:

• It has an end goal to achieve - a desired outcome. • It has a schedule or timeline for delivery. • It has a budget. • It has a plan of activity. • It has a sponsor and manager. • It has project team members. • It has structure and documentation of activity. • It is monitored on progress and reports achievement

The WBS creation involves:

• Listing all the project outputs (deliverables and other direct results) • Identifying all the activities required to deliver the outputs • Subdividing these activities into sub-activities and tasks • Identifying the deliverable and milestone(s) of each task • Identifying the time usage of all the resources (personnel and material) required to complete each task

The role of the Green Belt will include the following:

• Managing and delivering communications with the operational business • Developing plans and task sheets for collation of statistical information • Agreeing how metrics will be collated•Developing communications for the customer or stakeholder • Examining some outputs from Six Sigma tool applications • Creating plans and workflow charts • Working through simulation and failure processes • Monitoring input from Yellow Belts • Supporting Yellow Belts in their activity•Managing project teams in the absence of a Black Belt • Agreeing on as-is and to-be process states with the business • Agreeing on activity plans for training, education and control, or verification of to-be process • Day-to-day task management, administration, record keeping, and report writing

Key fundamentals are that users should be able to:

• Master data collection techniques, project charter development, and document usage • Apply and use Six Sigma tools and process analysis • Understand team dynamics and apply project management skills

As a project manager, the Black Belt leading the project would be responsible for:

• Monitoring expenditure within the project • Determining tasks to be undertaken and assigning them • Monitoring achievement against expectations of a project plan • Arriving at an end-state on time, in budget, and using the expected resources agreed with the sponsor at the outset of the project.

Patterns of Variation

• Natural process limits - measure variation in a process. The natural process limits are positioned at plus and minus three standard deviations from the target. Thus, if the process is stable, about 99.7% of the process output will be within the natural process limits. • Specification limits - are limits required by the customer that the supplier must ensure the process can produce to the required process capability value or specification. • Cyclical variations - are time based with a repeated pattern. • Temporal variation - is variation with time.

Monitoring Techniques Measurement tools will aid in monitoring techniques. These are tools you can use to measure processes and change:

• Process Maps • Takt Time • Data Sampling -Population vs. Sample • Data Classification • Data Collection • SPC - Charts to assess Measurement System Stability • MSA - Measurement System Analysis • Statistical Process Control (SPC) Charts • Root Cause Analysis • 5-WHY • Fishbone Diagram / Cause and Effect Diagram • Correlation Matrix • FMEA -Failure Mode Effects and Analysis • Overall Equipment Effectiveness (OEE) • Spaghetti Diagram•Establishing a Baseline Measurement • DPU -Defects per Unit • DPO -Defects per Opportunity • DPMO - Defects per Million Opportunities •Process Yield Metrics • FY - Final Yield • TPY - Throughput Yield • RTY -Rolled Throughput Yield

Project Management Suggestions:

• Project Management Institute (PMI) - They offer the PMP and CAPM certifications, depending on your experience level. • MSI - Offers the PMQ, and PM-LPCcertifications, as well as the Free PMEC. These are good choices if you have limited project experience. • CompTIA - If you work in I.T., the Project+ certification is a good option.

SIPOC

• Suppliers to the process provide the inputs, and every input should have a supplier. • Inputs to the process are the activities that trigger the process, such as a customer order. • Processes are activities that are carried out to convert the inputs into outputs. • Outputs of the process are the tangible product or service that the process produces. • Customers of the process are the people who receive the Outputs. Every Output should have a Customer.

As a Six Sigma Black Belt, you may need to work with the Champion to build the Project Charter. As a reminder, the actual project charter is a formal document used to summarize key deliverables and information for a Six Sigma project. It provides the official authorization to move through with the project. The project charter includes these components:

• The key problem/s to be resolved • The need for the resolution • The mission statement or goal of the project • The details of the project team composition • Key stakeholders • The scope of the project • The resources required and authorization • Project phase critical path and timelines

Your charter should include and ask the following questions in the business case:

• The name of the project • The aim of the project, called Aim statements • Why the project is needed? • What are the consequences of not doing the project? Opportunity costs? • What other projects have high priority? (Priority Matrix) • What strategic goals are met by this project? • Problem Statement: Summarizes and describes the problem, opportunity, or objective in concise, measurable terms. • Goal Statement: Describes the team's improvement objective this should tell what you intend to improve, reduce, eliminate or control.

MSI SSBBP

Related study sets

Chapter 38: The Child with a Gastrointestinal/Endocrine Disorder

Spanish Video Juegos

Bones of Hands and Feet

Software Language Engineering (CS3480)

HTML

US History Set 2 (separate from folder)

Intro to Computing

Exam 4

CRYPTO

SharePoint Framework - SPFx 01

Biol 1406 learning curve ch 8

Chapter 38: Agents to Control Blood Glucose Levels

public speaking exam 2 (ch 7-11, 15)

Exam 2

Chapter 12 - The Respiratory System

Final Exam Chapter 12

Apes iBook #12 Air Pollution

BA105W Ch1

Theory Week 5

Chapter 8 A&P