Effect of Approximate Probability Distributions on Single and Double Acceptance Sampling Plans for Attributes

An acceptance sampling plan is a statement of the sample size to be used and the associated acceptance or rejection criteria for sentencing individual lots. An important measure of the performance of an acceptance sampling plan, such as the operating characteristic curve, is related to probability distributions. This research investigates the effect of binomial, Poisson and normal approximations to single and double acceptance sampling plans for attributes. For single-sampling plans, type-A OC curves show that the binomial approximation tends to overestimate the probability of acceptance Pa of the true hypergeometric distribution when the lot size is at most 10 times the sample size. The single-sampling plan with type-B OC curve displays that the Pa from Poisson is a slight overestimate of the true Pa for the binomial distribution with small n and large p, moreover, the Pa from normal approximation can be a significant underestimation, exact value, or overestimation of the binomial, even with small p. On double-sampling plans, the Poisson approximation results in a tiny overestimation, while the normal approximation appears to be a major underestimation of the binomial. In rectifying inspection, the characteristics of AOQL are very similar to the sampling plan.