1. Sampling Inspection

2. Inspection’s role and type
Although the modern QM emphasizes the principle of prevention in advance, sampling inspection has still its special role, especially in inspecting the quality of raw material, WIP and finished goods.
Inspection: a. no inspection
b. Acceptance sampling
c. 100% inspection

3. When to use acceptance sampling?
When testing is destructive.
When the cost of 100% inspection is high.
When 100% inspection is not technologically feasible or would require so much calendar time and/or expenses.
When there are many items to be inspected and the inspection error rate is high.
When the vendor has an excellent quality history, and some reduction in inspection from 100% is desired.
When there are potentially serious product liability risks.

4. Acceptance Sampling Purposes Determine quality level
Ensure quality is within predetermined level 4

5. Advantages of Acceptance Sampling
Less expensive because of less inspection.
There is less handling damage of the product.
It is applicable to destructive testing.
Fewer personnel are involved in inspection activities.
It often greatly reduces the amount of inspection error.
The rejection of entire lots often provides a stronger motivation to the vendor for quality improvement.

6. Disadvantages of Acceptance Sampling
Risks of accepting ”bad” lots and rejecting “good” lots. In the “good” lot, there might be nonconformities.
Sample provides less information than 100-percent inspection
Acceptance sampling requires more time on planning and documentation of the acceptance sampling procedure. 5

7. Data Type Attribute Data：Only conformity and nonconformity
Variable Data ：length, width etc.
-- Liberman, G. J., and G. J. Resnikiff(1955).”Sampling plans for Inspection by variables”Journal of Quality Technology, Vol. 29, No.2.

8. Types of Acceptance sampling Plans
Single-sampling plan
Double-sampling plan
Multiple-sampling plan
Sequential-sampling plan

9. Single-sampling plan (N, p) (n,c) Total number ：N Acc the lot
The proportion of defects :P
Acc the lot
Sn≦C
(n,c)
(N, p)
Reject the lot
Sn>C
Where Sn is the number of the actual defects in the sample.

10. Double-sampling plan (N, p) (n,c1 ,r1) Acc the lot (n1+n2, c2)
Reject the lot
Sn1≦c1
Sn1>c1
(n1+n2, c2)
c1<Sn1<r1
S(n1+n2) ≦c2
S(n1+n2) >c2
(N, p)

12. Multiple-sampling plan
(n,p)
Acc the lot
Reject the lot
Sn1≦c1
Sn1>c1
(n1+n2)
c1<Sn1<r1
S(n1+n2)<r2
S(n1+n2)≧r2
(n1+n2+n3)
c2<S(n1+n2)<r2
……..

13. Sequential Sampling Plan

14. Risk Acceptable Quality Level (AQL) a (Producer’s risk)
Max. acceptable percentage of defectives agreed by the producer and user.
a (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

15. Decision Law Accept the lot Reject the lot Acceptable Producer’s Risk
sentence
quality
Accept the lot
Reject the lot
Acceptable
Producer’s Risk
Un-acceptable
(Rejected)
Consumer’s Risk

16. Operating Characteristic (OC) Curve
Probability of acceptance for the lot to be inspected under different percentage of defectives.
OC (p)=Pr(Accept the lot |p) ≡P (Sn ≦C |p)

17. OC Curve

18. Operating Characteristic Curve1
0.9
a = .05 (producer’s risk)
0.8
0.7
n = 99
c = 4
0.6
0.5
Probability of acceptance
0.4
0.3
 =.17
(consumer’s risk)
0.2
0.1 1 2 3 4 5 6 7 8 9 10 11 12
AQL
LTPD
Percent defective 9

19. Example:
AQL=1 %
LQL=6 %
OC (1%)=0.95
OC(6 %)=0.10
(n,c)=(89, 2)

20. OC-Curve’s calculation for attribute data
Type A (Hyper-Geometric approach)：
Type B (Binomial approach)：
Type C (Poisson approach)：

21. （n ,c）’s effect on OC-Curve

22. 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

23. Example: Acceptance Sampling Problem
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

24. Example: Step 1. What is given and what is not?
In this problem, AQL is given to be 0.01 and LTDP is given to be We are also given an alpha of 0.05 and a beta of 0.10.
What you need to determine your sampling plan is “c” and “n.” 11

25. Example: Step 2. Determine “c”
First divide LTPD by AQL.
Then find the value for “c” by selecting the value in the TN7.10 “n(AQL)”column that is equal to or just greater than the ratio above.
Exhibit TN 7.10 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
So, c = 6. 11

26. Example: Step 3. Determine Sample Size
Now given the information below, compute the sample size in units to generate your sampling plan.
c = 6, from Table
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 Plan:
Take a random sample of 329 units from a lot.
Reject the lot if more than 6 units are defective. 13