Sampling Inspection

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

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.

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

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.

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

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.

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

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.

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)

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 ……..

Sequential Sampling Plan

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

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

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)

OC Curve

Operating Characteristic Curve 1 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

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

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

（n ,c）’s effect on OC-Curve

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

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

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 0.03. 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

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

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