Emperical Tests of Acceptance Sampling Plans

Acceptance sampling is a quality control procedure applied as an alternative to 100% inspection. A random sample of items is drawn from a lot to determine the fraction of items which have a required quality characteristic. Both the number of items to be inspected and the criterion for determining conformance of the lot to the requirement are given by an appropriate sampling plan with specified risks of Type I and Type II sampling errors. In this paper, we present the results of empirical tests of the accuracy of selected sampling plans reported in the literature. These plans are for measureable quality characteristics which are known have either binomial, exponential, normal, gamma, Weibull, inverse Gaussian, or Poisson distributions. In the main, results support the accepted wisdom that variables acceptance plans are superior to attributes (binomial) acceptance plans, in the sense that these provide comparable protection against risks at reduced sampling cost. For the Gaussian and Weibull plans, however, there are ranges of the shape parameters for which the required sample sizes are in fact larger than the corresponding attributes plans, dramatically so for instances of large skew. Tests further confirm that the published inverse-Gaussian (IG) plan is flawed, as reported by White and Johnson (2011).