Sampling inspection by variables

Abstract

A classic statistical problem is the optimal construction of sampling plans to accept or reject a lot based on a small sample. We propose a new asymptotically optimal solution for the acceptance sampling by variables setting where we allow for an arbitrary unknown underlying distribution. In the course of this, we assume that additional sampling information is available, which is often the case in real applications. That information is given by additional measurements which may be affected by a calibration error. Our results show that, firstly, the proposed decision rule is asymptotically valid under fairly general assumptions. Secondly, the estimated optimal sample size is asymptotically normal. Further, we illustrate our method by a real data analysis and we investigate to some extent its finite sample properties and the sharpness of our assumptions by simulations.