Optimal design of multivariate acceptance sampling plans by variables

Abstract

Quality-control via acceptance sampling is a technique well established for monitoring the quality of production by lots. The design of acceptance sampling plans for univariate characteristics that follow the Gaussian distribution is reported in various references. Formulations for finding statistically and economically optimal acceptance sampling plans have been consistently proposed. Contrarily, the extension of acceptance sampling to multivariate characteristics has limited applications and the methods available to design plans are still elusive as they involve complex numerical computation procedures. We propose optimization-based formulations to design acceptance sampling plans by variables for multivariate characteristics. First, we consider the independence of characteristics and address plans that satisfy all the controlled quality levels of each one. A Mixed Integer Nonlinear Programming formulation is introduced for such a purpose. Then, we extend the analysis to dependent characteristics and use Surrogate-based optimization to handle the problem. The formulations are demonstrated with simulated scenarios and an industrial case of practical interest.