Session 7 Green Belt

Process to build a trend chart

1) Decide on the appropriate time increment for your data (hourly, daily, weekly, monthly, etc.). 2) Collect new data or organize existing data into a table. One easy way to do this is with an Excel spreadsheet. 3) Use the chart-building function in Excel or another statistics software package to organize the data into a chart. 4) Incorporate the following elements to build a useful chart: * A clear Title to describe the subject of the chart. * Labels on the vertical Y-axis and horizontal X-axis to describe the measurement and the time period. * A Legend to differentiate the plotted lines - in this case, the actual vs. the goal. * Appropriate Scales that are narrow enough to show variation. * Limited Characteristics on each chart to avoid confusion from too many lines. * An appropriate Time Frame. Notations on any major spikes. * Targets or Goals should be noted on the chart for reference. * Note Who Prepared the chart in case there are questions about the chart or the data.

Out of Control Conditions

1) If one or more points falls outside of the upper control limit (UCL), or lower control limit (LCL). The UCL and LCL are three standard deviations on either side of the mean - see section A of the illustration below. 2) If two out of three successive points fall in the area that is beyond two standard deviations from the mean, either above or below - see section B of the illustration below. 3) If four out of five successive points fall in the area that is beyond one standard deviation from the mean, either above or below - see section C of the illustration below. 4) If there is a run of six or more points that are all either successively higher or successively lower - see section D of the illustration below. 5) If eight or more points fall on either side of the mean - see section E of the illustration below. 6) If 15 points in a row fall within the area on either side of the mean that is one standard deviation from the mean - see section F of the illustration below.

Construct X & Moving Range Chart based on Mean Moving Range Process

1) Plot your individual data points in time series. You can create a meaningful control chart from as few as 6-7 data points, although a larger sample size (20+ subgroups) will provide more reliability. 2) Using the individual values, compute the Average, or X-bar. Plot the X-bar value as the center line on the chart of individual observations. 3) Determine the moving range for each period (the absolute value of the difference between successive individual values) and plot this value on a chart in time-series. 4) Calculate the Average ( Mean ) Moving Range ( mR). This value is also referred to as mR-bar (bar denotes average). Plot this value as the center line on the moving range chart. 5) Calculate the X Chart Upper Control Limit, or upper natural process limit, by multiplying mean mR by 2.66 and adding that value to the average (X-bar). Note: the value 2.66 is a constant that was derived to approximate three standard deviations when multiplied by the mean moving range. UCLX = Xbar + (2.66 x mean mR) Plot the Upper Control Limit on the X chart. 6) Calculate the X Chart Lower Control Limit, or lower natural process limit, for the X chart by multiplying mean moving Range by 2.66 and subtracting that value from the average (X-bar). LCLX = Xbar - (2.66 x mean mR) Plot the Lower Control Limit on the X chart. 7) Calculate the Moving Range Upper Control Limit, or upper range limit, for the mR chart by multiplying the mean moving Range by 3.27. UCLmR = 3.27 x mean mR Plot the Upper Control Limit on the mR chart.

Step 2 Qualify the Measurement System: SPC Chart

A critical, but often overlooked, step in the process is to qualify the measurement system. No measurement system is without measurement error. If that error exceeds an acceptable level, the data cannot be acted upon reliably. For example: a Midwest building products manufacturer found that many important measurements of its most critical processes had error in excess of 200% of the process tolerance. Using this erroneous data, the process was often adjusted in the wrong direction - adding to instability rather than reducing variability. See the Measurement Systems Analysis lesson for additional help with this subject.

Step 3 Improve the Measurement System: SPC Chart

After measuring the capability of the measurement system to yield reliable outputs, steps should be taken to address any shortcomings. This may involve actions such as upgrading equipment to improve resolution, documenting informal procedures, and conducting training of assessors.

What is the purpose of a trend chart? A) Evaluate general performance over time. B) Show the correlation between inputs and outputs. C) Make point to point comparisons. D) Prioritize improvement projects. E) Identify the root cause of a problem.

Answer A

Now that we have concluded that the XmR chart of the number of meals per 100 guests shows a non-random increase, possibly due to recent menu changes, what can you conclude about room service meal revenue per 100 guests? Refer to the XmR chart that you have constructed for meal revenue. A) The process is stable, and recent above-average data points are due to random variation. We can't say with any certainty that the team's actions have had any effect. B) The process is unstable, with frequent variation over time due to assignable events (special causes). The team's actions have had no effect. C) With eight plot points above the average line since week 22, the X chart indicates an upward shift in the process due to special cause variation. Something has caused a non-random change in process behavior - presumably the team's actions (or something else). D) The range chart indicates a decrease in the range during recent weeks due to an assignable (special) cause. The team's actions have reduced variation. E) With two points beyond the upper control limit, the X chart indicates that the team's actions were effective at increasing room service meal volume.

Answer A Although the number of meals per 100 guest has increased, the control chart indicates that revenue remains a stable process exhibiting only random variation. Maybe the number of orders is up, but the mix has shifted in favor of less expensive items. As more data is collected, a process shift in revenue may yet become visible.

Several potential revisions have been identified to improve this trend chart: 1) Change the title 2) Use longer time horizon 3) Use narrower/smaller value (y) scale 4) Use wider/larger value (y) scale 5) Use shorter time horizon 6) Indicate chart source/author 7) Set value scale maximum at 100% 8) Plot a trend line Which group of four revisions would most improve the trend chart? A) 1, 2, 4, 7 B) 2, 3, 6, 7 C) 2, 4, 6, 8 D) 1, 3, 5, 7 E) 1, 2, 6, 8

Answer B

A Lean Six Sigma team at an insurance company has been working on a project to reduce the number of claim defects leading to denied claims. A control chart of claim denials is out-of-control. What conclusion should the team draw from this condition? A) The number of denials has gone up. B) The number of denials has gone down. C) The process is unstable over time. D) The process is exhibiting less variability over time. E) The process is exhibiting more variability over time.

Answer C

What is the basis of the theory of statistical process control? A) Control theory B) The law of averages C) The laws of probability D) Correlation analysis E) The law of unintended consequences

Answer C

When the team first reviewed the data on the number of room service meals per 100 guests, it appeared that their menu changes during week 22 had a positive effect. After constructing an XmR chart, how would you describe the behavior of this process? A) The process is stable, and recent above-average data points are due to random variation. We can't say with any certainty that the team's actions have had any effect. B) The process is unstable, with frequent variation over time due to assignable events (special causes). The team's actions have had no effect. C) With nine plot points above the average line since week 22, the X chart indicates an upward shift in the process due to special cause variation. Something has caused a non-random change in process behavior - presumably the team's actions (or something else). D) The range chart indicates a decrease in the range during recent weeks due to an assignable (special) cause. The team's actions have reduced variation. E) With two points beyond the upper control limit, the X chart indicates that the team's actions were effective at increasing room service meal volume.

Answer C

Referring to the last question, which revisions to the sample frame would provide a survey most representative of the company's target market? A) Exclude sailboat owners. Ask open-ended questions. B) Exclude non-ski-boat owners. Include marinas nation-wide. C) Exclude non-ski-boat owners. Include non-marina boat owners D) Include only current customers on a nationwide basis. E) Include only owners of competing products on a nationwide basis.

Answer C Solution: The company makes ski-boats. Therefore, exclude non-ski boat owners. The survey takes place at marinas. Therefore, be sure to also include non-marina boat owners.

A Lean Six Sigma team working to reduce the amount of bad debts is tracking the dollar amount of receivables over 90 days past due. The team is using an Individuals and Moving Range control chart (XmR or ImR chart). The average balance outstanding (X-bar) is $736,500. The Mean Moving Range is $58,000. What is the upper control limit for the Individuals (X) chart? A) $926,160 B) $918,620 C) $910,500 D) $890,780 E) $818,620

Answer D

What proportion of the population lies within 3 standard deviations on either side of the mean of the normal distribution? A) 99.99997% B) 97% C) 68% D) 99.7% E) 95%

Answer D

A Manufacturer of ski-boats wants to increase sales, and has decided to start by understanding how the company's quality is perceived among Midwestern ski-boat owners, its target market. An interview survey of boat owners is conducted at randomly selected marinas throughout the mid-west during a blitz over a holiday weekend. Which of the following potential conclusions is supported based on this knowledge of the sample frame? A) The survey accurately reflects the perceptions of people comprising the company's target market. B) The survey reflects the perceptions of Midwesterners comprising the company's target market. C) The survey accurately reflects the perceptions of Midwestern boat owners. D) The survey accurately reflects the perceptions of Midwestern boat owners who use marinas. E) The survey reflects the perceptions of some Midwestern boat owners who use marinas, and may be influenced by holiday activities (drinking?).

Answer E Solution: The accuracy of the survey cannot be established without knowing how the sample was constructed.

Measure Phase of DMAIC Check on Deliverables

Can the CTQCs be objectively measured? Has the success target been determined - in customer terms? Have potentially significant process inputs (Xs) been identified for further screening? Has a data collection plan been developed for the process output(s), or CTQC(s), and those process inputs which may be deemed to be significant? Is the Measurement System capable of providing valid and reliable values with an acceptable degree of error? What is the baseline performance (capability) of the process? Are the relevant metrics visible and widely accessible? Are there any opportunities for "Quick Hits" (Kaizen Blitzes or Rapid Improvement Events)? If the process is not capable, have containment actions been implemented to prevent customers from experiencing defects?

Trend Charts should be used whenever you need to evaluate data over time.

Done during Measure of DMAIC Cycle They are first step to understand how much a process varies from time to time.

Statistical Process Control

Has now been incorporated by organizations around the world as a primary tool to improve product quality by reducing process variation.

Chance Variation (Common Cause Variation)

Inherent in the process, and stable over time

XmR Charts can be used to answer the following questions

Is the process stable over time? If the process is stable, how capable is it? (also requires separate capability calculation) What is the effect of a process change on the average or range of the output characteristics? How will I know if the process becomes unstable, or the capability changes over time?

Assignable or Uncontrolled Variation (Special Cause Variation)

Is unstable over time - the result of specific events outside the system

Statistical Process Control charts

Provide improved understanding of process behavior - which in turn provides better leverage to reduce process variability:

Step 1 Determine the Measurement Method: SPC Chart

Statistical Process Control is based on the analysis of data, so the first step is to decide what data to collect. There are two categories of control chart distinguished by the type of data used: Variable (Continuous) or Attribute (Discrete). Variable data comes from measurements on a continuous scale, such as: temperature, time, distance, and weight. Attribute data is based on upon discrete distinctions such as good/bad, percentage defective, or number defective per hundred. If possible, collect variable data because it provides better information about process variability.

Steps to SPC process

Step 1. Determine the Measurement Method Steps 2 & 3. Qualify and Improve the Measurement System

Things Gone Wrong

TGW

Control limits for a process

are based on actual data, and are influenced by the sampling (subgrouping) strategy. Control limits are based on what the process IS, not on what we think the process SHOULD BE.

Control Charts

are more powerful than simple trend charts or run charts because they provide a basis to evaluate the stability of the variation and the mean.

Sampling Frame

defines the group of individuals that will be sampled. If the frame excludes certain groups of individuals, sample error will be introduced. For example, a phone survey about the opinions of all Americans would exclude those Americans who do not own phones. That group tends to be economically disadvantaged, so the resulting survey projection could be biased if corrections are not made. For greatest accuracy, the survey frame should be drawn to provide a fully representative sample.

Sampling strategy

defines the interpretation of the control chart under evaluation. Recall the earlier discussion of sample frames and their impact on the conclusions derived from a sample of data. Like any sample, without a well-founded sampling plan that answers a specific set of questions, control charts are nothing more than wallpaper - or worse - they could lead you to make wrong decisions.

Control Limits

help us distinguish signals (special causes) from noise (random, or common cause variation) based on the data gathering and analysis strategy.

Presenting data in statistically based context

we are able to make better decisions with respect to managing process improvement. One of the significant benefits of statistical process control is the avoidance of OVERCONTROL, which actually increases process variation (see the Deming Funnel Experiment slide show).