Multistage acceptance sampling under nonparametric dependent sampling designs

The evaluation of a set of objects, e.g. items of a production lot, in terms of a random measurement, such that the decision is statistically designed to control the probability of false decisions considered as a function of the fraction of measurements falling below a threshold, can be conducted by acceptance sampling procedures. These methods are typically studied for the quality control problem to accept or reject a lot of produced items. This paper provides an extension of the acceptance sampling methodology to a multi-stage framework where a lot is inspected at several time points and only accepted if it passes all stages. The resulting sampling plans allow to specify both the stage-wise and overall error probabilities and can be calculated before inspections start. Going beyond the case of independent random samples drawn at each inspection time, we consider a panel type design resulting in a dependent sampling scheme. Based on asymptotic approximations we provide explicit formulas for the proposed sampling plans and an effective recursive algorithm for their calculation. The theoretical results cover consistency and asymptotic optimality of the sampling plans as well as a central limit theorem. The statistical properties of the approach are studied by simulations. (C) 2018 Elsevier B.V. All rights reserved.