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### Tools of quality

Developed by Jim Grayson, Ph.D.

7 QC Tools: The Lean Six Sigma Pocket Toolbook

- Flowchart [p. 33-41]
- Check Sheet [p. 78-81]
- Histogram [p. 111-113]
- Pareto [p. 142-144]
- Cause-and-Effect [p. 146-147]
- Scatter [p. 154-155]
- Control Chart [p. 122-135]

Developed by Jim Grayson, Ph.D.

Developed by Jim Grayson, Ph.D.

Developed by Jim Grayson, Ph.D.

“Failure to understand variation is the central problem of management.”

Developed by Jim Grayson, Ph.D.

Stable vs. Unstable process

Stable process: a process in which variation in outcomes arises only from common causes.

Unstable process: a process in which variation is a result of both common and special causes.

Developed by Jim Grayson, Ph.D.

source: Moen, Nolan and Provost, Improving Quality Through Planned Experimentation

Red Bead experiment

Developed by Jim Grayson, Ph.D.

Statistical Process Control: Control Charts

Process

Parameter

- Track process parameter over time - mean - percentage defects
- Distinguish between - common cause variation (within control limits) - assignable cause variation (outside control limits)
- Measure process performance: how much common cause variation is in the process while the process is “in control”?

Upper Control Limit (UCL)

Center Line

Lower Control Limit (LCL)

Time

Developed by Jim Grayson, Ph.D.

Advantages of Statistical Control

1. Can predict its behavior.

2. Process has an identity.

3. Operates with less variability.

4. A process having special causes is unstable.

5. Tells workers when adjustments should not be made.

6. Provides direction for reducing variation.

7. Plotting of data allows identifying trends over time.

8. Identifies process conditions that can result in an acceptable product.

Developed by Jim Grayson, Ph.D.

source: Juran and Gryna, Quality Planning and Analysis, p. 380-381.

Identifying Special Causes of Variation

source: Brian Joiner, Fourth Generation Management, pp. 260.

See also Lean Six Sigma Pocket Toolbook, p. 133-135.

Developed by Jim Grayson, Ph.D.

Strategies for Reducing Special Causes of Variation

- Get timely data so special causes are signaled quickly.
- Put in place an immediate remedy to contain any damage.
- Search for the cause -- see what was different.
- Develop a longer term remedy.

source: Brian Joiner, Fourth Generation Management, pp. 138-139.

Developed by Jim Grayson, Ph.D.

“In a common cause situation, there is no such thing as THE cause.”

Brian Joiner

Developed by Jim Grayson, Ph.D.

- Stratify -- sort into groups or categories; look for patterns. (e.g., type of job, day of week, time, weather, region, employee, product, etc.)
- Experiment -- make planned changes and learn from the effects. (e.g., need to be able to assess and learn from the results -- use PDCA .)
- Disaggregate -- divide the process into component pieces and manage the pieces. (e.g., making the elements of a process visible through measurements and data.)

source: Brian Joiner, Fourth Generation Management, pp. 140-146.

Developed by Jim Grayson, Ph.D.

A Conversation with Joseph Juran

“Take this example: In finance we set a budget. The actual expenditure, month by month, varies - we bought enough stationery for three months, and that’s going to be a miniblip in the figures. Now, the statistician goes a step further and says, ‘How do you know whether it’s a miniblip or there’s a real change here?’ The statistician says, ‘I’ll draw you a pair of lines here. These lines are such that 95% of the time, you’re going to get variation between them.’

Now suppose something happens that’s clearly outside the lines. The odds are something’s amok. Ordinarily this is the result of something local, because the system is such that it operates in control. So supervision converges on the scene to restore the status quo.

Notice the distinction between what’s chronic [common cause] and what’s sporadic [special cause]. Sporadic events we handle by the control mechanism. Ordinarily sporadic problems are delegable because the origin and remedy are local. Changing something chronic requires creativity, because the purpose is to get rid of the status quo - to get rid of waste. Dealing with chronic requires structured change, which has to originate pretty much at the top.”

Source: A Conversation with Joseph Juran, Thomas Stewart, Fortune, January 11, 1999, p. 168-170.

Developed by Jim Grayson, Ph.D.

Process capability

EXCEL: =NORMDIST(x, mean, std dev,1) to calculate percent non-conforming material.

Conceptual view of SPC

source: Donald Wheeler, Understanding Statistical Process Control

Developed by Jim Grayson, Ph.D.

vs.

Process Capability

Wheeler, Understanding Statistical Process Control

Developed by Jim Grayson, Ph.D.

Choosing the Appropriate Control Chart

(MJ II, p. 37)

Attribute (counts) Variable (measurable)

The Lean Six Sigma Pocket Toolbook, p. 123.

Defect Defective

Developed by Jim Grayson, Ph.D.

Different types of control charts

Attribute (or classification) data

Situation Chart Control Limits

Fraction of defectives

fraction of orders not processed perfectly on first trial (first pass yield)

fraction of requests not processed within 15 minutes

p

np

Lean Six Sigma Pocket Toolbook, p. 132.

Developed by Jim Grayson, Ph.D.

source: Brian Joiner, Fourth Generation Management, p. 266-267.

Different types of control charts

Variables (or measurement ) data

Situation Chart Control Limits

Variables data, sets of measurements

X-”BAR” CHART

Xbar and R Charts

R CHART

See MJ II p. 42 for constants

A2, D3 and D4.

Developed by Jim Grayson, Ph.D.

Lean Six Sigma Pocket Toolbook, p. 127.

source: Brian Joiner, Fourth Generation Management, p. 266-267.

Exercise An automatic filling machine is used to fill 16 ounce cans of a certain product. Samples of size 5 are taken from the assembly line each hour and measured. The results of the first 25 subgroups are that X-double bar = 16.113 and R-bar = 0.330.

What are the control limits for this process?

(using simplified X-bar R control limits)

Source: Shirland, Statistical Quality Control, problem 5.2.

Developed by Jim Grayson, Ph.D.

Different types of control charts

Variables (or measurement ) data

Situation Chart Control Limits

Variables data, sets of measurements

X-”BAR” CHART

Xbar and R Charts

R CHART

See MJ II p. 42 for constants

A2, D3 and D4.

Developed by Jim Grayson, Ph.D.

Lean Six Sigma Pocket Toolbook, p. 127.

source: Brian Joiner, Fourth Generation Management, p. 266-267.

Parameters for Creating X-bar Charts

Lean Six Sigma Pocket Toolbook, p. 128.

Developed by Jim Grayson, Ph.D.

Given these charts, how do we know if the process is “in control”?

Developed by Jim Grayson, Ph.D.

Exercise An automatic filling machine is used to fill 16 ounce cans of a certain product. Samples of size 5 are taken from the assembly line each hour and measured. The results of the first 25 subgroups are that X-double bar = 16.113 and R-bar = 0.330.

Source: Shirland, Statistical Quality Control, problem 5.2.

If the specification limits are USL = 16.539 and LSL = 15.829 is the process capable?

Hint: See “parameters” slide for estimating sigma using R-bar.

Developed by Jim Grayson, Ph.D.

Exercise An automatic filling machine is used to fill 16 ounce cans of a certain product. Samples of size 5 are taken from the assembly line each hour and measured. The results of the first 25 subgroups are that X-double bar = 16.113, R-bar = 0.330and S-bar = 0.13.

What are the control limits for this process?

(using textbook X-bar R where sigma x is estimated by s-bar and sigma r is estimated by r-bar)

Source: Shirland, Statistical Quality Control, problem 5.2.

Developed by Jim Grayson, Ph.D.

Developed by Jim Grayson, Ph.D.

What are the X-bar control chart limits for this process?

Developed by Jim Grayson, Ph.D.

Developed by Jim Grayson, Ph.D.

What are the R control chart limits for this process?

Developed by Jim Grayson, Ph.D.

Developed by Jim Grayson, Ph.D.

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