TOOLS OF QUALITY

2

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.

Pareto Diagram

Developed by Jim Grayson, Ph.D.

Cause and Effect Diagram

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.

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

Developed by Jim Grayson, Ph.D.

RED BEAD EXPERIMENT

Developed by Jim Grayson, Ph.D.

Red Bead Experiment

What are the lessons learned?

1.

2.

3.

4.

Developed by Jim Grayson, Ph.D.

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”?

Choosing the Appropriate Control Chart

Attribute (counts) Variable (measurable)

Defect Defective

(MJ II, p. 37)

The Lean Six Sigma Pocket Toolbook, p. 123.

12

Different types of control charts

Attribute (or count) data

Situation Chart Control Limits

Number of defects, accidents or flaws# of accidents/week

# of breakdowns/week

# of flaws on a product

C

U

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

Lean Six Sigma Pocket Toolbook, p. 132.

13

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.

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Different types of control charts

Variables (or measurement ) data

Situation Chart Control Limits

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.

Different types of control charts

Variables (or measurement ) data

Situation Chart Control Limits

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.

PARAMETERS FOR CREATING X-BAR CHARTS

Lean Six Sigma Pocket Toolbook, p. 128.

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

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.

What are the control limits for this process? Source: Shirland, Statistical Quality Control, problem 5.2.Filling Weights

subgroup 1 2 3 4 5 Average Range1 16.09 16.16 16.08 16.02 16.11 16.09 0.142 15.95 16.00 15.90 16.17 16.01 16.01 0.273 16.07 16.07 16.08 15.89 16.28 16.08 0.394 16.13 16.15 16.19 16.13 16.19 16.16 0.065 16.16 16.11 16.40 16.14 15.86 16.13 0.54

Sample

Developed by Jim Grayson, Ph.D.

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

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 10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

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”?

Developed by Jim Grayson, Ph.D.

CONCEPTUAL VIEW OF SPC

source: Donald Wheeler, Understanding Statistical Process Control

Developed by Jim Grayson, Ph.D.

Process Stability

vs.

Process Capability

Wheeler, Understanding Statistical Process Control

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.

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.

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.

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.

Developed by Jim Grayson, Ph.D.

“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.

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STATISTICAL PROCESS CONTROLCapabilityAnalysis

ConformanceAnalysis

Investigate forAssignable Cause

EliminateAssignable Cause

Capability analysis • What is the currently "inherent" capability of my process when it is "in control"?

Conformance analysis• SPC charts identify when control has likely been lost and assignable cause variation has occurred

Investigate for assignable cause• Find “Root Cause(s)” of Potential Loss of Statistical Control

Eliminate or replicate assignable cause• Need Corrective Action To Move Forward

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.

What are the control limits for this process? Source: Shirland, Statistical Quality Control, problem 5.2.Filling Weights

subgroup 1 2 3 4 5 Average Range1 16.09 16.16 16.08 16.02 16.11 16.09 0.142 15.95 16.00 15.90 16.17 16.01 16.01 0.273 16.07 16.07 16.08 15.89 16.28 16.08 0.394 16.13 16.15 16.19 16.13 16.19 16.16 0.065 16.16 16.11 16.40 16.14 15.86 16.13 0.54

Sample

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

PROCESS CAPABILITY

29

sigma

LSLx

sigma

xUSLCor

sigma

LSLUSLC pkp *3

,*3

min*6

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

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THE STATISTICAL MEANING OF SIX SIGMAProcess capability measure

• Estimate standard deviation:• Look at standard deviation relative to specification limits• Don’t confuse control limits with specification limits: a process can be out of control, yet be incapable

s = R / d 2

3

Upper Specification Limit (USL)

LowerSpecificationLimit (LSL)

X-3sA X-2sA X-1sAX X+1sA

X+2s X+3sA

X-6sBX X+6sB

Process A(with st. dev sA)

Process B(with st. dev sB)

6

LSLUSLC p

x Cp P{defect} ppm

1 0.33 0.317 317,000

2 0.67 0.0455 45,500

3 1.00 0.0027 2,700

4 1.33 0.0001 63

5 1.67 0.0000006 0,6

6 2.00 2x10-9 0,00