1. Chapter 6 - Part 1
Introduction to SPC

2. Proactive approaches to quality
Design of Experiments
Statistical Process Control

3. Design of Experiments
Tool for designing quality into a product or service at the design before production begins.
Quality is designed into product or service by finding the levels of inputs that maximizes customer satisfaction.
How should we design a laptop?
What battery and processor speed?
Longer battery life but slower speed?
Faster speed but shorter battery life?

4. Design of Experiments
When is best room size and color when designing a hotel?
In designing a new drink, what carbonation and sugar levels maximize taste?
Carbonation and sugar levels that maximizes taste become the ???

5. Example of Designed Experiment
Sugar and carbonation (factors) are each at two levels
High
Low
Experiment is called a 2 x 2 factorial experiment, where there are two factors, each at two levels.

6. Example of Designed Experiment
Potential customers rate all possible design combinations.
Taste is rated on a scale of 1 to 10, with 10 being best.
Are there significant differences between mean taste scores for all pairs of design combinations?
Are changes in the mean taste score more sensitive to changes in sugar or carbonation?

7. Factorial Experiment Sugar Carbonation Focus Group 1 Focus Group 2
Mean Taste Score L 4 6
5.0 H 9 2
5.5 8
8.5 1
4.5

8. Factorial Experiment - graph

9. Carbonation vs. Sugar

10. Conclusion
Best combination of inputs is
Low Sugar
High Carbonation
At low level of carbonation, an increase in sugar does not appear to result in a statistically significant gain in the mean taste score.
If carbonation is a the high level, a decrease in sugar results in a statistically significant gain in the mean taste score.
This combination not only maximizes taste, but will lower cost of production if ????

11. Statistical Process Control (SPC)
Tool for predicting future performance of a process.
Main tools of SPC are control charts.
Control charts make it possible to detect problems early enough to take corrective action on the process before too many defective units are produced.
Control charts are proactive because action is taken on the process, and not on the output, to prevent defects from being produced.

12. Control Charts
Allow us to detect earlier shifts in the mean and/or variance of the quality characteristic of a product or service.
Control charts have an upper control limit (UCL) and a lower control limit (LCL).
Control limits are set at 3 standard deviations above and below the estimated mean of the quality characteristic, called the estimated process mean.

13. SPC vs. DOE
If design of experiments is used to determine target levels, then control charts can be used to determine if process is operating on target.
If it is, control charts can be used to detect early shifts from target.
If process is not on target, control charts can be used to determine if corrective action to adjust process mean to target is effective.

14. Control Charts
Control charts rely on sample inspection, not mass inspection.
We may take a sample of 5 invoices every day to check for errors, or
A sample of 5 bottles of a soft drink each hour to estimate the average number of ounces in a bottle.
The samples are used to
Estimate the process mean and to
Compute the control limits
The control limits, the estimated process mean and the means of all the sample means are plotted on the control chart.

15. Control Chart UCL Mean LCL Fraction Defective .50 .40 .30 .20 .10 1 2
UCL
Mean
LCL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hour

16. Control Charts
In addition to detecting shifts in the process mean and/or variation, control charts allow us to determine what sources of variation are in the process.
There are two sources of variation:
Special causes
Random variation (common causes)
Random variation always exists in any process.
Special causes of variation may or may not exits.

17. Random variation (Common Causes)
Inherent in any process
Due to many causes, each contribution a small amount to the total random variation
Occurs within 3 standard deviations of mean (3-sigma limits)

18. Special Causes Not inherent in the process
Occur when something unusual happens
Unusual event can be good or bad
If good, make it part of process
If bad, eliminate it

19. What Sources of Variation are Present?
If all the sample means fall randomly within the control limits, the variation between the sample means is due to random causes or variation.
If at least one sample mean falls beyond the control limits, the variation is due to special or assignable causes of variation.

20. Statistical Control
If there are no special causes of variation in the process, the process is said to be in statistical control, or “in control.”
Process mean (and/or variance) is stable and hence predictable.
The sample means will vary randomly around the unknown process mean.

21. Statistical Control – Stable Process
Sample number
UCL
LCL 1 2 3 4
.00135

22. Statistical Control – Stable Process
Since all the sample means come the same stable distribution, each sample mean is an estimate of the process mean.
Rather than using each sample mean as an estimate of the process mean, we can get a better estimate the mean of the process by ???

23. Process Out of Control
If one or more special causes of variation are present, the process is “out-of-control.”
Process behaves erratically
It is unstable and no longer predictable.
It is therefore impossible to get a good estimate of the process mean.

24. Process in Control UCL Mean LCL
Hour
Sample mean
Process in Control
All the sample mean fall randomly within the control limits This variation is due to random causes.

25. Process that is Out of Control
UCL
LCL
Mean
Hour
Sample mean
Process that is Out of Control
All the sample mean fall within the control limits, but pattern is not random. It is a predictable trend. Source of variation is due to a special cause.

26. Process that is Out of Control
Hour
Sample mean
UCL
LCL
Mean
Process that is Out of Control
All the sample mean fall within the control limits, but pattern is not random. It is a predictable cyclical pattern. Source of variation is due to a special cause.

27. Process out of Control
UCL
LCL
Mean
Hour
One point beyond the control limit. Variation beyond control limits is due to unusual or special (assignable) causes

28. Responsibility for Corrective Action
Knowing what sources of variation are present in the process allows us to determine who is responsible for taking corrective action to fix or improve the process.
Removing or institutionalizing special causes— the worker
Reducing random variation – management

29. An Offer You Can’t Refuse
I claim I have a fair coin—50/50 chance of tossing a head or tail
You’re willing to bet $1,000 that I don’t have a fair coin, but you want more data.
I agree to
toss the coin 100 times,
count the number of heads, and
repeat this experiment once a day over the next 10 days.

30. The Results Day # of heads 1 57 2 53 3 51 4 58 5 36 6 63 7 55 8 9 3910 44

31. How Will You Bet?
Based on these results, do you think I have a fair coin or a biased coin?

32. Control Chart for # of Heads
Let P = probability of tossing a head = 0.50
Let n = number of tosses = 100
How many heads would you expect on each toss?
What is the standard deviation of the number of heads tossed?

33. Control Chart for # of Heads

35. Control Chart for # of Heads

36. Control Charts Based on the control chart, what can you conclude?
How would you bet?
Coin is fair?
Coin is not fair?

37. Production Example
Make up a production example that is analogous to coin tossing experiment by answering the following questions:
What do the 100 tosses per day represent?
What do the two outcomes, head and tail, represent?

38. Production Example What is the meaning of P = 0.5?
How can zero defects be achieved?

39. Principle of Rational Subgrouping
Principle states that we want to select samples to minimize variation within the samples but maximize the variation between.
If something unusual is going on, we want it to occur between samples, not within.
If it occurs within samples, we may miss it.

40. Violation of Rational Subgrouping
Day
Sample
(Diameter) 1 2 3
Mean
Monday 5 4
Tuesday 12 18 15
Wednesday 10

41. Conclusion Based on Control Chart
Control Charts Errors
Actual Condition of Process
Conclusion Based on Control Chart
Process In Control
Process Not In Control
In Control
Correct
Type I Error
Out of Control
Type II Error

42. Type I Error Type I Error-Thinking shift occurred when it didn’t—
UCL
Mean
LCL 1 2 3 4
Sample number
Type I Error-Thinking shift
occurred when it didn’t—
false alarm
P(Type 1 Error)=2(.00135)
=.0027

43. Type II Error Type II Error- Shift occurred but we failed to detect it
UCL
New
Mean
Mean
LCL 1 2 3 4
Sample number
Type II Error-
Shift occurred but
we failed to detect it