1. Statistical Quality Control/Statistical Process Control
Acceptance Sampling
Operating Characteristic Curve
Process Control Procedures
Variable data
Attribute or Characteristic data
Process Capability 2 2

2. Basic Forms of Statistical Sampling for Quality Control
Sampling to accept or reject the immediate lot of product at hand (Acceptance Sampling).
Sampling to determine if the process is within acceptable limits (Statistical Process Control) 3 3

3. Acceptance Sampling Purposes Advantages Determine quality level
Ensure quality is within predetermined level
Advantages
Economy
Less handling damage
Fewer inspectors
Upgrading of the inspection job
Applicability to destructive testing
Entire lot rejection (motivation for improvement) 4 4

4. Acceptance Sampling Disadvantages
Risks of accepting “bad” lots and rejecting “good” lots
Added planning and documentation
Sample provides less information than 100-percent inspection 5 5

5. Statistical Sampling--Data
Attribute (Go no-go information)
Defectives--refers to the acceptability of product across a range of characteristics.
Defects--refers to the number of unacceptable conditions per unit--may be higher than the number of defectives.
Variable (Continuous)
Usually measured by the mean and the standard deviation. 6 6

6. Acceptance Sampling--Single Sampling Plan
A simple goal
Determine (1) how many units, n, to sample from a lot, and
(2) the maximum number of defective items, c, that can be found in the sample before the lot is rejected. 7 7

7. Risk Acceptable Quality Level (AQL) (Producer’s risk)
Max. acceptable percentage of defectives defined by producer.
(Producer’s risk)
The probability of rejecting a good lot.
Lot Tolerance Percent Defective (LTPD)
Percentage of defectives that defines consumer’s rejection point.
 (Consumer’s risk)
The probability of accepting a bad lot. 8 8

8. Example: Acceptance Sampling
Zypercom, a manufacturer of video interfaces, purchases printed wiring boards from an outside vender, Procard. Procard has set an acceptable quality level of 1% and accepts a 5% risk of rejecting lots at or below this level. Zypercom considers lots with 3% defectives to be unacceptable and will assume a 10% risk of accepting a defective lot.
Develop a sampling plan for Zypercom and determine a rule to be followed by the receiving inspection personnel. 10 10

9. Sorting It Out For this example, how do we determine AQL? ? LTPD? ?11 11

10. Example: Continued n (AQL) = 3.286
How can we determine the value of n?
What is our sampling procedure? c
LTPD/AQL
n AQL
44.890
0.052 5
3.549
2.613 1
10.946
0.355 6
3.206
3.286 2
6.509
0.818 7
2.957
3.981 3
4.890
1.366 8
2.768
4.695 4
4.057
1.970 9
2.618
5.426
Exhibit TN 7.10 12 12

11. Example: Continued
c = 6, from Table; c is also called acceptance number
n (AQL) = 3.286, from Table
AQL = .01, given in problem
n(AQL/AQL) = 3.286/.01 = 328.6, or 329 (always round up)
Sampling Procedure:
Take a random sample of 329 units from a lot.
Reject the lot if more than 6 units are defective. 13 13

12. Operating Characteristic Curve
AQL
LTPD
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1 2 3 4 5 6 7 8 9 10 11 12
Percent defective
Probability of acceptance
=.10
(consumer’s risk)
= .05 (producer’s risk) 9 9

13. Chance Versus Assignable Variation
Chance variation is variability built into the system.
Assignable variation occurs because some element of the system or some operating conditions are out of control.
Quality control seeks to identify when assignable variation is present so that corrective action can be taken.

14. Control Based on Attributes and Variables
Inspection for Variables: measuring a variable that can be scaled such as weight, length, temperature, and diameter.
Inspection of Attributes: determining the existence of a characteristic such as acceptable-defective, timely-late, and right-wrong.

15. Control Charts: Assumptions
Developed in 1920s to distinguish between chance variation in a system and variation caused by the system’s being out of control - assignable variation.

16. Control Charts - Assumptions continued
Repetitive operation will not produce exactly the same outputs.
Pattern of variability often described by normal distribution.
Random samples that fully represent the population being checked are taken.
Sample data plotted on control charts to determine if the process is still under control.

17. Control Chart with Limits Set at Three Standard Deviations

18. Control Limits
If we establish control limits at +/- 3 standard deviations, then
we would expect 99.7% of our observations to fall within these limits x
LCL
UCL 15 15

19. Statistical Process Control
The McGraw-Hill Companies, Inc., 1998
What other evidence(s) might prompt investigation? 16

20. Attribute Data: Constructing a p-Chart17 17

21. Statistical Process Control--Attribute Measurements (P-Charts)
(Std Deviation) 18 18

22. 1. Calculate the sample proportion, p, for each sample.19
Irwin/McGraw-Hill
The McGraw-Hill Companies, Inc., 1998 19

23. 2. Calculate the average of the sample proportions.
3. Calculate the standard deviation of the
sample proportion 20
Irwin/McGraw-Hill
The McGraw-Hill Companies, Inc., 1998 20

24. UCL = 0.1014 LCL = -0.0214 (or 0) 4. Calculate the control limits.
Irwin/McGraw-Hill
The McGraw-Hill Companies, Inc., 1998 21

25. p-Chart (Continued)
5. Plot the individual sample proportions, the average
of the proportions, and the control limits
UCL
LCL 22 22

26. Variable Data Example: x-Bar and R Charts23 23

27. Calculate sample means, sample ranges, mean of means, and mean of ranges.24 24

28. Control Limit Formulas & Factor Table
Exhibit TN 7.7 25 25

29. x-Bar Chart
UCL
LCL 26 26

30. R-Chart
UCL
LCL 27 27

31. Process Capability
Process limits - determined from manufacturing process data.
Tolerance limits - specified in engineering design drawing
How do the limits relate to one another? 28 28

32. Process Capability
TQM’s emphasis on “making it right the first time” has resulted in organizations emphasizing the ability of a production system to meet design specifications rather than evaluating the quality of outputs after the fact with acceptance sampling.
Process Capability measures the extent to which an organization’s production system can meet design specifications.

33. Engineering Tolerance Versus Process Capability

34. Process Capability Depends On:
Location of the process mean.
Natural variability inherent in the process.
Stability of the process.
Product’s design requirements.

35. Natural Variation Versus Product Design Specifications
(Look for more
economical means of
production)
(Mean out of
sync.)

36. Process Capability Ratio (Text calls it Index)
Cp < 1: process not capable of meeting design specs
Cp > 1: process capable of meeting design specs
As rule of thumb, many organizations desire a Cp ratio of at least 1.5.
Six sigma quality (fewer than 3.4 defective parts per million) corresponds to a Cp (index/ratio) of 2.

37. Effect of Production System Variability on Cp

38. Process Capability Index, Cpk
Shifts in Process Mean 29 29

39. Taguchi’s View of Variation
Incremental
Cost of
Variability
High
Zero
Lower
Spec
Target
Upper
Traditional View
Incremental
Cost of
Variability
High
Zero
Lower
Spec
Target
Upper
Taguchi’s View 30 30