Stat 513 / IE 530 Midterm 1

Poisson Assumptions

-The probability of occurrences of an event is constant for all sub intervals -There can be no more than one occurrence in an interval -occurrences are independent

Common Cause Variation

-Variation inherent to a process -Can only be reduced by changing the process -Must be Sampled under homogeneous conditions (Rational Subgrouping)

Normal Distributions

1 standard dev from mean both ways - 68% data 2 " " - 95% data 3 " " - 99% data

Rules for out of control process

1.) 3 Sigma Limits 2.) Trends 3.) Runs 4.) Cycles 5.) 8 points on one side of side of the mean

Six Sigma Steps

1.) Define 2.) Measure 3.) Analyze 4.) Improve 5.) Control

Process Mapping Steps

1.) Identify process inputs and outputs 2.)Identify all steps in process 3.) List output variables at each step 4.) List input variables at each step and whether they are controlled or not 5.) Adde process specs for input variables

Gage to Precision to Tolerance Ratio

(P/T) = 6sigma(gage) / (USL - LSL) P/T < .1 is acceptable

Cp Pp

(USL - LSL) / 6 sigma

Rational Subgrouping

-Minimizes special cause variation w/i subgroups -Maximizes change special cause variation will be detected b/t subgroups -Special Cause variation appears in X-Bar chart between subgroups -Should not appear in R chart

Government Course Inspection

-Performed by US gov at suppliers facility -Very Expensive (taxpayers) -Can delay deliveries Used when -Required by contract

Process Audit

-Performed by customer personnel -Assesses one or more processes of suppliers -Used to assure capability and identify weaknesses in process

System Audit

-Performed by customer personnel -Assesses the entire quality system of the supplier -Used to assure capability and identify weaknesses in system

Customer Course Inspection

-Performed by customers personal at suppliers facility -Very Expensive Used when -required by contract -supplier owns large sophisticated test equipment -new supplier

Qualification Testing

-Performed by supplier or third part test lab -Redundant testing might be done by customer -Performed before product used during production AKA -First article testing -PPAP -ISR

Third Part Source Inspection

-Performed by the sub-contractors of the customer at suppliers facility Expensive, but less than customer personal Used When -required by contract -supplier owns large sophisticated test equipment -new supplier

Improving Capability

1.) Standardize Process 2.)Process is in control (can only reduce special cause var) 3.)Capability (process mean and variation dependent) 4.)Measurement System Analysis says estimated common cause variation is due to process/operator/equipment 5.)Process mean is a function of the process inputs 6.)These are obtained from process map 7.)Importance of process prioritized with cause and effect matrix 8.)Prioritized once can be used in a designed experiment to model process 9.)Model process mean 10.)Find the settings to make the best mean on target 11.) Settings can sometimes be used to reduce process variation 12.) Solution does not fundamentally change the process

Binomial

1.) n Independent Bernoulli trials 2.) Number of trials is fixed 3.) There are ONLY two outcomes (success and failure) (p and q) (p and (1-p)) E(x)=np, Var(x) = np(1-p)

Sustained changes in process mean

1.) sustained shift in process mean to a new value 2.)slow trending in the process mean up or down

Hyper Geometric

1.) the population or set to be sampled consists of N individuals, objects, or elements (finite population)

If we used two sigma limits in the X-bar chart instead of three sigma limits, how often would a point be outside of the limits if our process was in control

5%

Six Sigma and TQM

Differentiated by strategy Six Sigma requires commitment of top leadership continuously through years of implementation

No quality initiative can succeed without the support of

Everyone

Sample Receiving inspection

Expensive for customer Reduces risk of using nonconforming material

Skip lot receiving inspection

Expensive for customer, but less than sample receiving relies on inspection personnel to accurately select lots reduces risk of nonconforming material, but not as much as sample receiving

After using a Pareto diagram to decide which defect to work on, to find the cause one should then use

Fishbone Diagram, Cause and Effect Matrix

What is the usual reason for white space in a control chart

Fixed Differences, Overestimated theta

What causes white space

Fixed differences, overestimated sigma, limits too narrow, excessive roundoff

Cp and Cpk

Short Term Spans days-weeks 30-50 data points >1 capable <1 not capable =1 marginally capable

Name three ways in which we can use a Pareto chart to prioritize which problem to address first

Shows which defects show up the most, what the customer prioritizes, which are critical to the process

You would use an XmR chart if the subgroups were

Size of 1

Shifts in process mean and process knowledge

detected in x-bar chart these are usually not detected by the 4 rules of thumb

Poisson

lambda is mean occurrence gives probability of a given number of events occurring in a fixed interval of time E(x) = lambda = V(x)

Cpk Ppk

min(USL - Xbar, Xbar - LSL) / 3 sigma

How many observations are used in computing ranges for moving a range chart

one per time period

Traceability

organizations are contractually required to maintain a measurement system that is traceable, like ISO

Hierarchy of Standards

owing to the technology required to maintain the primary reference standards, a hierarchy of standards

Cpk

short term capability

Give one reason for using an XmR chart instead of an X-bar and R-chart

subgroup is too small

Estimate of common cause

sum of true product variation, variation due to different operations (reproducibility) and variance of measurement equipment error (repeatability) sigma(m)^2 = sigma(p)^2 + sigma(o)^2 + sigma(e)^2 Product variation too large, invest in process. Operator variation too large, invest in training Error variation too large, invest in measurement eq.

Cpk >= Ppk

this is because variability increases over the long term

Process Flow Charts

Graphical Display of Process, identifies value added and non value added process steps, inputs/outputs, data collection points

How do you make sure that within a subgroup variation reflects Common Cause

Homogeneous Conditions

The main components of Quality Cost

Prevention, Appraisal, Failure

Three Components of Quality Cost

Prevention, Appraisal, Failure

Name two important uses for Flowcharting a process

Understanding a process, identifying where/what you need to control

Pp and Ppk

Long Term weeks-months 100-200 data points <1 not meeting specs >1 meeting specs =1 marginally meeting specs

Ppk

Long term capability

Six Sigma

Measure of variability, name is based of the laws of six sigma (Data distribution) Six sigma defect rules 3.24 defects per million

Sampling Plan - Rational Subgrouping

choose subgroups in small region of space, time

White Space

comes from subgroups across fixed differences

Deming said that the improvement of processes should be

critical

What are the four parts of the continuous improvement cycle

Plan, Do, Check, Act

Signs that a process is out of control

8 points on one side, cyclical, out of limits, seasonal,

Distribution Rules of Thumb

Binomial - number of successes/failures in a sample size n Poisson - number of blemishes in a continuous area of a certain size Normal- continuous characteristics of an item and average the values Geometric- monitor for stability and wait for a process to become unstable

Qualitative Data

C & U, Poissan, p and np binomial, XmR Binomial

What attributes charts are used for discrete data

C, u ; np, p ; XmR

Why Define Processes?

Individuals can understand tasks at hand, documentation and standardization, common understanding of procedures

Certificate of Compliance

Legal documents signed by an officer or supplier, part fully comply with contract requirements

If the data is skewed to the right, which is larger the mean or the median

Median

What is a standardized Process

One where everyone follows the same agreed upon procedures

In doing a root cause analysis, name three people who must be involved

Operator

Standardized Processes are not necessarily

Optimal, Current Best Methods

If you detect the presence of an out of control point that probably means that the process is

Out of control, special cause

Moving Average Charts

UWMA (uniformly weighted moving average chart) -for sustained shift in the process mean to a new value) EWMA (exponentially weighted moving average chart) -for a slowly trending process mean

For quantitive data use

X, R, XmR

What attributes charts are used for cont. data

X-bar, R charts, XmR

Gage Capability

accuracy, repeatability, reproducibility, and stability combined into a single unit Poor reproducibility would indicate a need for the operator training in use of the gage or a req for better readability. Poor repeatability would suggest need for gage maintenance, gage redesign or selection of another measure device

Modern methods of training should be instituted for

all employees to institute control

Best way to decrease variation

better measurement equipment