Acceptance Sampling Plans by Variables

1. Acceptance Sampling Plans by Variables CH 16

2. Contents • Advantages and Disadvantages of Acceptance Sampling by Variables. • Types of Acceptance Sampling by Variables. • Chain Sampling. • Continuous Sampling.

3. Advantages of Variables Sampling • The same OC curve can be obtained with a smaller sample size than would be required by an attributes sampling plan. • Measurement data provide more information about the manufacturing process. • When AQLs are very small, the sample sizes required by attributes sampling plans are very large.

4. Disadvantages of Variables Sampling • The distribution of the quality characteristic must be known. • A separate sampling plan must be employed for each quality characteristic that is being inspected.

5. Types of Variables Sampling Plans • Plans that control the lot or process fraction defective. • Plans that control a lot or process mean.

6. Plans to Control Process Fraction Defective • Since the quality characteristic is a variable, there will exist either LSL, USL, or both, that define the acceptable values of this parameter. • Fig. 1 illustrates the situation in which the quality characteristic x is normally distributed and there is LSL on this parameter. Fig. (1)

7. Plans to Control Process Fraction Defective • Procedure 1 (k-Method) • Take a random sample of n items from the lot and compute • If there is a critical value of p of interest that should not be exceeded with stated probability, we can translate this value of p into critical distance k. • If ZLSL≥ k, we would accept the lot because the sample data imply that the lot mean is sufficiently far above LSL to insure that p is satisfactory.

8. Plans to Control Process Fraction Defective • Procedure 2 (M-Method) • Compute ZLSL . • Use ZLSL to estimate the fraction defective of the lot or process . • Determine the max. allowable fraction defective M (using specific values of n, k). • If exceeds M, reject the lot; otherwise, accept it.

9. Plans to Control Process Fraction Defective • Notes • In the case of an USL, we compute • If is unknown, it is estimated by s. • When there is only a single specification limit (LSL or USL), either procedure may be used. • When there are both LSL and USL, M-method should be used by computing ZLSL and ZUSL, finding the correspondingfraction defective estimates and Then, if + ≤ M, the lot will be accepted. ^ ^ pLSL pUSL ^ ^ pLSL pUSL

10. Designing a variables sampling plan with a specified OC curve • Let be the two points on the OC curve of interest. • are the levels of lot or process fraction nonconforming that correspond to acceptable and rejectable levels of quality, respectively. p1and p2

11. Designing a variables sampling plan with a specified OC curve • Example 1

12. Designing a variables sampling plan with a specified OC curve

13. Designing a variables sampling plan with a specified OC curve • Example 2 :Design a sampling plan using M-method

14. Designing a variables sampling plan with a specified OC curve

15. MIL STD 414 • There are five general levels of inspection, and level IV is designated as “normal”.

16. MIL STD 414 • As MIL STD 105E, sample size code letters are used, but the same code letter does not imply the same sample size in both standards. • Sample sizes are a function of the lot size and the inspection level. • All the sampling plans in the standards assume that the quality characteristic is normally distributed.

17. MIL STD 414 • Organization of MIL STD 414

18. MIL STD 414 • Example 3: Using MIL STD 414 Solution From table, if we use IV level, the sample size code letter is O. From a second table, we find n=100. For AQL of 1%, on normal inspection, k=2. For AQL of 1%, on tightened inspection, k=2.14

19. MIL STD 414

20. Plans to Control A Process Mean • Example 4 Solution Let XA be the value of the sample average below witch the lot will be accepted. If lots have 0.95 probability of acceptance, then P (X ≤ XA ) = 0.95 - -

21. Plans to Control A Process Mean P (Z≤ ) =0.95 =1.64 If lots have 0.1 probability of acceptance, then P (X ≤ XA ) = 0.1 p (Z ≤ ) = 0.1 = -1.28 These two equations can be solved for n and XA , giving n=9 and XA=0.356 - - -

22. Chain Sampling Plan • It is used for small sample size plans that have acceptance number of zero. • Lots should be produced under the same conditions, and be expected to be of the same quality. • There should be a good record of quality performance on the part of supplier. • The general procedure for ChSP-1: • For each lot, select the sample of size n and observe the defectives. • If sample has zero defectives, accept the lot . • If sample has two or more defectives, reject the lot. • If sample has 1 defective, accept the lot provided that there have been no defectives in the previous i lots.

23. Chain Sampling Plan • The effect of chain sampling on OC curve: • It is more difficult to reject lots with very small p with ChSp-1 Plan than it is with ordinary single Plan. • In practice, values of i vary between 3 and 5, since OC curves of such plans approximate OC curve for S-S plan. • The points on the OC curve of a ChSP-1 plan are given by:

24. Continuous Sampling Plan • Used when production is continuous. That is, the manufacturing operation do not result in the natural formation of lots. • It consists of altering sequences of sampling inspection and screening (100% inspection).

25. Continuous Sampling Plan • Procedure for CSP-1 plans

26. Continuous Sampling Plan • The average number of units inspected in a 100% screening is equal to , where q=1-p • The average number of units passed under the sampling inspection is • The average fraction of total manufactured units inspected in the long run is • The average fraction of manufactured units passed under the sampling procedure is

27. Continuous Sampling Plan • OC curves for various continuous sampling plans, CSP-1.