1. Tools for Process Improvement
Quality Management
Chapter 11
Tools for Process Improvement

2. Key questions Why are process diagrams important?
How do two process diagnosis tools work?
What is the main purpose of statistical process control?
Control charts help detect changes in a process by taking advantage of two ideas. What are these two ideas?
What rule of thumb is used to determine when to stop a process when using a control chart, & what tradeoff is considered when determining how tight to set control limits?
What types of process changes are , R, S, & P charts designed to detect?
What do process capability indices measure, how should an index value greater than 1.0 be interpreted, & and what is the meaning of six sigma?
What are the Pareto phenomenon, central limit theorem, & law of large numbers, & how are these principles relevant for process improvement?
What are the managerial insights from the chapter?

3. Road map
Diagnosis
Control and Capability
Summary

4. Diagnosis
A challenge
An apparent problem or opportunity associated with a process
Where to focus improve efforts for most benefit?
Unless a very simple process, the answer may not be obvious
First, ensure a basic understanding of the process
E.g., process is well documented; process diagrams are useful
Second, 2 simple high-level diagnostic tools can be useful

5. Diagnosis
Pareto analysis
PON: Pareto phenomenon – lion’s share of aggregate measure determined by relative few factors
Pareto analysis – separating the important few from the trivial many
Analyze process output
Identify problems in the output & group into categories
Identify the most important category (or categories) – the choice for the measure of “importance” usually reflects a combination of impact & ability to influence
For example
80% of customer complaints are due to order processing errors,
& 70% of order processing errors are due to incorrect pricing,
& 90% of pricing errors are due to improper value-added tax and/or application of discounts
Focus on tax & discounts

6. Diagnosis
Cause & effect diagram
A graphical tool for helping to sort out the root causes of an effect
E.g., may be useful during a brainstorming session
high defect rate
equipment
people
reward system
methods
materials
not holding tolerances
poor climate control
old HVAC system
no preventative maintenance

7. Road map Diagnosis Control and Capability Summary Control Charts
Process Capability
Summary

8. Statistical process control
Big picture
Output from a process is almost the same over time
The challenge is to detect when the process has fundamentally changed amidst apparent random variation
Why?
Rapidly identify source of change & correct
A tool for process improvement
How?
Draws on human ability to visually detect patterns & probability theory (specifically, hypothesis testing)

9. Control
Example
Protecting against a biological warfare attack
Resilient Supply Chains, Yossi Sheffi
The most dangerous attack is one where you don’t know that you’re under attack
E.g., beginnings of epidemic not recognized until too late
SPC analysis of hospital admission rates can be used to help provide early indication of attack

10. SPC basics Periodically take a sample of process output
Control
SPC basics
Periodically take a sample of process output
Compute statistic of interest, e.g., mean part diameter
Plot the sample statistic
If there is pattern in the plot or if a point is outside control limits, then
indicates fundamental change in process
stop the process to investigate, & correct at source if change identified

11. SPC chart A plot of sample means over time
Control
SPC chart
Promoting a cycle of process improvement
evidence that process is out of control; intervene to correct source of the problem
evidence that process is out of control
intervene to correct source of problem
make change to improve the process
control limits updated to reflect behavior of improved process when in control
UCL
LCL CL
A plot of sample means over time

12. Control
Types of SPC charts
Variable data – approximately continuous (e.g., part diameter)
Xbar-chart ( ) - detect change affecting the process mean
R-chart & S-chart – detect change affecting process variation
Attribute data – frequency or count
P-chart – detect change affecting proportion of a feature
Our focus – Xbar-chart basic concepts applied in other charts

13. Xbar-chart control limits
What we need
Sample size (n)
Mean part diameter when process is in control (x)
Standard deviation of part diameter when in control (x)
Control limit level (value of z), e.g., 2 or 3
Compute standard deviation of sample mean & add/subtract from mean

14. Control
Example
You have been collecting daily water samples (10 vials) from the Yakich river over the last year
The pollution level in each vial is measured & recorded
Greenway Chemicals, Inc. has just opened a plant upstream with a pledge to purify any outflow to the Yakich
Interested in assessing whether the company is being true to their pledge
If not, need hard evidence for hope of court injunction to suspend operation

15. Control
Yakich river data
Pollution mean & standard deviation prior to plant operation (based on 3,211 vials) are & 6.07
Values for the last 30 vials since the plant came on-line:
Day 1: , 26.20, 23.82, 27.55, 35.18, 30.01, 19.33, 39.45, 42.88, 34.76, sample mean = 29.66
Day 2: , 21.04, 44.65, 41.11, 21.42, 30.05, 36.11, 23.99, 17.38, 27.00, sample mean = 31.31
Day 3: , 40.90, 22.23, 37.08, 31.08, 29.33, 21.44, 25.74, 37.60, 46.08, sample mean = 32.08
Evidence of wrongdoing?

16. Xbar-chart Sample standard deviation = 6.07/(10)1/2 = 1.92
Control
Xbar-chart
Sample standard deviation = 6.07/(10)1/2 = 1.92
2 values in a row outside the 2 control limits
Highly unlikely without fundamental change to the process
It is likely that the plant is polluting

17. What about the selection of z?
Control
What about the selection of z?
Controls limits = x  zn-1/2
With z = 3 (3-sigma level)
A 99.7% chance that a sample mean will fall within the control limits when the process is “in control”
With z = 2 (2-sigma level)
A 95.5% chance that a sample mean will fall within the control limits when the process is “in control”

18. Control
A trade-off
Recall that stop the process whenever a sample mean falls outside the limits (in addition to appearance of pattern)
The basic trade-off in the selection of z:
cost of stopping the process unnecessarily
i.e., process is in control, or behaving as designed
versus
not stopping the process when appropriate
i.e., process is not behaving as designed

19. Two principles of nature
Control
Two principles of nature
Central limit theorem
As sample size (n) increases, the sample mean becomes approximately normally distributed
Reason why 2-sigma corresponds to 95.5% & 3-sigma corresponds to 99.7% - normal distribution is basis for setting control limits
Law of large numbers, which is?
The larger the sample size, the more likely to detect change in process
Evident in formula for sample standard deviation

20. Road map Diagnosis Control and Capability Summary Control Charts
Process Capability
Summary

21. Measuring process capability
Cp & Cpk process capability indices
A measure of how well a process can satisfy specific market requirements
E.g., with respect to tolerances on acceptable dimensions
Cp = Cpk if process mean centered within upper & lower specification limits
Cpk is more accurate measure of capability when the process mean is not centered,
Large difference between Cp & Cpk signals improvement opportunity
E.g., can improve capability if process mean is shifted to be centered within specs

22. Cp process capability index
USL – upper specification limit
LSL – lower specification limit
X = random variable for measure of process output
X = standard deviation of X
Cp = (USL – LSL)/(6X)

23. Capability
Example
Part diameter needs to be between 2.97mm & 3.03mm
USL = 3.03, LSL = 2.97, X = 0.01
Process mean is centered, i.e., X = 3.00
Cp = (USL – LSL)/(6X) = 0.06/0.06 = 1.00

24. Interpreting Cp If process is centered, then
Capability
Interpreting Cp
If process is centered, then
Cp = 1.00  99.7% of parts within specs
Cp < 1.00  less than 99.7% of parts within specs
Cp > 1.00  more than 99.7% of parts within specs
Cp = 1.00 generally viewed as benchmark for minimum level of acceptable process capability

25. Cpk process capability index
For comparison: Cp = (USL – LSL)/(6X)
Cpk = min{(USL – X)/(3X), (X – LSL)/(3X)}
Cpk = Cp if process mean is centered within specs
Centered  X = LSL + (1/2)(USL – LSL)
(USL – X)/(3X) = (USL – [LSL + (1/2)(USL – LSL)])/(3X) = (USL – LSL)/(6X) = Cp
(X – LSL)/(3X) = ([LSL + (1/2)(USL – LSL)] – LSL)/(3X) = (USL – LSL)/(6X) = Cp
Otherwise Cpk < Cp

26. Example Part diameter needs to be between 2.98mm & 3.04mm
Capability
Example
Part diameter needs to be between 2.98mm & 3.04mm
USL = 3.04, LSL = 2.98, X = 0.01, X = 3.00
Cp = (USL – LSL)/(6X) = 0.06/0.06 = 1.00
Cpk = min{(USL – X)/(3X), (X – LSL)/(3X)} = min{1.33, 0.67} = 0.67

27. Interpreting Cpk Cpk = 1.00  at least 99.7% of parts within specs
Capability
Interpreting Cpk
Cpk = 1.00  at least 99.7% of parts within specs
Cpk > 1.00  more than 99.7% of parts within specs
Cpk = 1.00 generally viewed as benchmark for minimum level of acceptable process capability
Cpk more accurate indicator of capability than Cp
Cp highlights degree to which Cpk can increase if process is centered

28. Road map Diagnosis Control and Capability Summary Control Charts
Process Capability
Summary

29. What we saw
Summary
Two simple tools to help identify where to focus improvement efforts
SPC is tool to detect change - meant to provide quick feedback to decision maker (e.g., worker controlling the process)
A tool to aid process improvement
Two measures of process capability, e.g.,
to provide feedback for motivating improvement
to help Identify where to focus improvement

30. Managerial insights
Summary
A measure that is aggregate of independent random variables is approximately normally distributed (central limit theorem)
Many decisions/policies must account for uncertainty
CLT provides basis for estimating underlying probability distribution
Focus process improvement near the source
E.g., SPC used by machine operators
Quick feedback is often critical for effective & continual improvement
E.g., process stopped & investigated immediately after results of sample indicate out of control

31. Back to key questions Why are process diagrams important?
How do two process diagnosis tools work?
What is the main purpose of statistical process control?
Control charts help detect changes in a process by taking advantage of two ideas. What are these two ideas?
What rule of thumb is used to determine when to stop a process when using a control chart, & what tradeoff is considered when determining how tight to set control limits?
What types of process changes are , R, S, & P charts designed to detect?
What do process capability indices measure, how should an index value greater than 1.0 be interpreted, & and what is the meaning of six sigma?
What are the Pareto phenomenon, central limit theorem, & law of large numbers, & how are these principles relevant for process improvement?
What are the managerial insights from the chapter?