Developed by Jim Grayson, Ph.D. 1. 2 Flowchart [p. 33-41] Check Sheet [p. 78-81] Histogram [p....

1Developed by Jim Grayson, Ph.D.

Tools of quality

Developed by Jim Grayson, Ph.D. 2


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]


Pareto Diagram


Cause and Effect Diagram


“Failure to understand variation is the central

problem of management.”


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.

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


Red Bead experiment


Red Bead Experiment

What are the lessons learned?

1.

2.

3.

4.


Statistical Process Control: Control Charts

Time

ProcessParameter

Upper Control Limit (UCL)

Lower Control Limit (LCL)

Center Line

• 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”?


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.

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

12

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.


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

Brian Joiner


Improving a Stable Process

• 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.


“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.”

A Conversation with Joseph Juran

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

Process capability

17

sigma

LSLx

sigma

xUSLCor

sigma

LSLUSLC pkp *3

,*3

min*6

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


Conceptual view of SPC

source: Donald Wheeler, Understanding Statistical Process Control


Process Stability

vs.

Process Capabilit

y

Wheeler, Understanding Statistical Process Control


Choosing the Appropriate Control Chart

Attribute (counts) Variable (measurable)

Defect Defective

(MJ II, p. 37)

The Lean Six Sigma Pocket Toolbook, p. 123.

Different types of control charts

Attribute (or classification) data

Situation Chart Control Limits

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

fraction of requests not processed within 15 minutes

p

np

source: Brian Joiner, Fourth Generation Management, p. 266-267.Lean Six Sigma Pocket Toolbook, p. 132.




Variables (or measurement ) data


Variables data, sets of measurements

Xbar and R Charts

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

RAX 2

RDLCL

RDUCL

3

4

X-”BAR” CHART

R CHARTSee MJ II p. 42 for constantsA2, D3 and D4.

Lean Six Sigma Pocket Toolbook, p. 127.


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.



Variables (or measurement ) data


Variables data, sets of measurements

Xbar and R Charts

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

RAX 2

RDLCL

RDUCL

3

4

X-”BAR” CHART

R CHARTSee MJ II p. 42 for constantsA2, D3 and D4.



Parameters for Creating X-bar Charts


Number of Observations in Subgroup

(n)

Factor for X-bar Chart

(A2)

Factor for Lower

control Limit in R chart

(D3)

Factor for Upper

control limit in R chart

(D4)

Factor to estimate Standard

deviation, (d2)

2 1.88 0 3.27 1.128 3 1.02 0 2.57 1.693 4 0.73 0 2.28 2.059 5 0.58 0 2.11 2.326 6 0.48 0 2.00 2.534 7 0.42 0.08 1.92 2.704 8 0.37 0.14 1.86 2.847 9 0.34 0.18 1.82 2.970

10 0.31 0.22 1.78 3.078


1 2 3 4 5 6 7 8 9 10111213141516171819202122232425

15.70

15.80

15.90

16.00

16.10

16.20

16.30

16.40

X-bar Chart

x-bar

LCL

CL

UCL

Sub-groups

Wei

gh

ts

1 2 3 4 5 6 7 8 9 10111213141516171819202122232425

0.000.100.200.300.400.500.600.700.80

R Chart

R

LCL

CL

UCL

Sub-groups

Wei

gh

ts

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


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.


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 = 0.330 and 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.


X Bar Chart


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


R Chart


What are the R control chart limits for this process?


S Chart

Developed by Jim Grayson, Ph.D. 1. 2 Flowchart [p. 33-41] Check Sheet [p. 78-81] Histogram [p....

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