Comparison of Different Level Sampling Plans in Z1.4 The following operating characteristic curves show the effect of using different Special or General Inspection Level sampling plans in Z1.4. The set of operating characteristic curves, shown below, represent all normal inspection sampling plans available in Z1.4 for an AQL value of 1%. There are 9 such plans with sample size code letters E, H, J, K, L, M, N, P, and Q. As you can see by comparing these operating characteristic curves for various sample size code letters, there is very little loss of statistical power for values of quality (%defective) in the neighborhood of the AQL or better (as it should be since plans being compared all have the same specified AQL). The only issue would be if the slight loss of statistical power for quality levels worse than the AQL would justify staying with the larger sample size plans. When you look at the operating characteristic curves being compare for each case, you will note that each plan will accept good quality equally well and each plan will reject very poor quality (quality levels at the maximum RQL for all plans) equally well. The only measurable differences exist for quality levels between the AQL and maximum RQL. Sample Sample Maximum %Defective Where Size Code Size (n) #(c) Probability of Acceptance Letter Defectives Equals 50% E 13 0 5.19 H 50 1 3.33 J 80 2 3.33 K 125 3 2.94 L 200 5 2.84 M 315 7 2.43 N 500 10 2.13 P 800 14 1.83 Q 1250 21 1.73 In order to compare the operating characteristic curves for several of the inspection levels [S-3, S-4, I, and II (the current level being used)] for various lot sizes in Z1.4, the operating characteristic curves for the appropriate sampling plans are presented below. LOT SIZE: 1.2K - 3.2K LEVEL S-3, S-4, I, and II SAMPLE SIZE CODE LETTER: E, G(converts to H), H, and K As reflected above, the level II plan (K: n=125, c=3) has a 50% probability of accepting quality levels around 2.94% defective, the level S-4 and I plan (H: n=50, c=1) have a 50% probability of accepting quality levels around 3.33% defective, and the level S-3 plan (E: n=13, c=0) has a 50% probability of accepting quality levels around 5.19% defectives. There is certainly very little variation in statistical power between the level I, II, and S-4 plans above and very little difference from the level S-3 plan. LOT SIZE: 3.2K - 10K LEVEL S-3, S-4, I, and II SAMPLE SIZE CODE LETTER: F(converts to E), G(converts to H), J, and L As reflected above, the level II plan (L: n=200, c=5) has a 50% probability of accepting quality levels around 2.84% defective, the level I plan (J: n=80, c=2) has a 50% probability of accepting quality levels around 3.33% defective, the level S-4 plan (H: n=50, c=1) has a 50% probability of accepting quality levels around 3.33% defective and the level S-3 plan (E: n=13, c=0) has a 50% probability of accepting quality levels around 5.19% defectives. There is certainly very little variation in statistical power between the level I, II, and S-4 plans above and not a major difference from the level S-3 plan. LOT SIZE: 10K - 35K LEVEL S-3, S-4, I, and II SAMPLE SIZE CODE LETTER: F(converts to E), H, K, and M As reflected above, the level II plan (M: n=315, c=7) has a 50% probability of accepting quality levels around 2.43% defective, the level I plan (K: n=125, c=3) has a 50% probability of accepting quality levels around 2.94% defective, the level S-4 plan (H: n=50, c=1) has a 50% probability of accepting quality levels around 3.33% defective and the level S-3 plan (E: n=13, c=0) has a 50% probability of accepting quality levels around 5.19% defectives. There is certainly very little variation in statistical power between the level I, II, and S-4 plans above and not a major difference from the level S-3 plan. LOT SIZE: 35K – 150K LEVEL S-3, S-4, I, and II SAMPLE SIZE CODE LETTER: G(converts to H), J, L, and N As reflected above, the level II plan (N: n=500, c=10) has a 50% probability of accepting quality levels around 2.13% defective, the level I plan (L: n=200, c=5) has a 50% probability of accepting quality levels around 2.84% defective, the level S-4 plan (J: n=80, c=2) has a 50% probability of accepting quality levels around 3.33% defective and the level S-3 plan (H: n=50, c=1) also has a 50% probability of accepting quality levels around 3.33% defectives. In this case there is very little variation in statistical power between the level I, S-3, and S-4 plans above and not a major difference from the level I plan. LOT SIZE: 150K – 500K LEVEL S-3, S-4, I, and II SAMPLE SIZE CODE LETTER: G(converts to H), J, M, and P As reflected above, the level II plan (P: n=800, c=14) has a 50% probability of accepting quality levels around 1.83% defective, the level I plan (M: n=315, c=7) has a 50% probability of accepting quality levels around 2.43% defective, the level S-4 plan (J: n=80, c=2) has a 50% probability of accepting quality levels around 3.33% defective and the level S-3 plan (H: n=50, c=1) has a 50% probability of accepting quality levels around 3.33% defectives. In this case there is almost no variation in statistical power between the S-3 and S-4 plans above and not a major difference from the level I and level II plans. LOT SIZE: > 500K LEVEL S-3, S-4, I, and II SAMPLE SIZE CODE LETTER: H, K, N, and Q As reflected above, the level II plan (Q: n=1250, c=21) has a 50% probability of accepting quality levels around 1.73% defective, the level I plan (N: n=500, c=10) has a 50% probability of accepting quality levels around 2.13% defective, the level S-4 plan (K: n=125, c=3) has a 50% probability of accepting quality levels around 2.94% defective and the level S-3 plan (H: n=50, c=1) has a 50% probability of accepting quality levels around 3.33% defectives. In this case there is very little variation in statistical power between the S-3 and S-4 plans , very little difference between the level I and II plans and not a major difference between all four. SUMMARY: When one has a choice of inspection level, the decision should be based on a combination of things such as (a) the sampling cost, (b) the level, power, of protection afforded by the sampling plan, (c) the marginal increase in power associated with a larger sample size plan, (d) the current defect rate being produced by the process, (e) the historical stability of the process, (f) the effectiveness of process controls during production, and (g) the seriousness of accepting lots with “marginal” quality. While all of the available sampling plans will protect you against accepting lots with marginal quality, my recommendation would be to allocate your quality resources to process control activities and use your sampling plans to detect serious breakdowns in the lot quality, in the event your process controls fail to detect this breakdown. The following table for plans with an AQL of 1% summarizes the lot quality for inspection levels S-3, S-4, I, and II where the probability of accepting a lot is 50%. INSPECTION LEVEL LOT SIZE S-3 S-4 I II 1.2K - 3.2k 5.19 3.33 3.33 2.94 3.2K - 10k 5.19 3.33 3.33 2.84 10K - 35K 5.19 3.33 2.94 2.43 35K - 150K 3.33 3.33 2.84 2.13 150K - 500K 3.33 3.33 2.43 1.83 >500K 3.33 2.94 2.13 1.73 LOT QUALITY - % Defective where Probability of Acceptance Equals 50% Based on the results presented above, it is my opinion that you gain very little additional power by using inspection level II plans. Indeed, I would suggest that inspection level S-4 or maybe even S-3 plans, coupled with effective process controls would afford you adequate protection and insure release of quality products. In the event you chose to use inspection level S-4 plans, for lot sizes greater that 1.2k, you would end up at one of three possible sampling plans (H: n=50, c=1), (J: n=80, c=2) or (K: n=125, c=3) depending on your lot size. The operating characteristic curves for these three plans are given below. If these plans afford you with the protection you feel is necessary, given effective process controls, it would seem logical to select inspection level S-4. In the event you chose to use inspection level S-3 plans, for lot sizes greater that 1.2k, you would end up at one of two possible sampling plans (F: n=13, c=0), or (H: n=50, c=1) depending on your lot size. The operating characteristic curves for these two plans are given below. If these plans afford you with the protection you feel is necessary, given effective process controls, it would seem logical to select inspection level S-3. You will note that the c=0 plan is far weaker than the other plan recommended, as are all c=0 sampling plans.