Essentially ML ASN-Minimax double sampling plans

TL;DR

This paper develops ASN-Minimax double sampling plans for normally distributed quality characteristics with unknown standard deviation, optimizing sample size while maintaining quality control standards.

Contribution

It introduces AM-double sampling plans based on the ML estimator p* for the fraction defective, minimizing maximum ASN under classical OC constraints.

Findings

AM-double sampling plans are optimal in ASN minimization.

Plans are based on the ML estimator p* for fraction defective.

The approach ensures classical OC conditions are satisfied.

Abstract

Subject of this paper is ASN-Minimax (AM) double sampling plans by variables for a normally distributed quality characteristic with unknown standard deviation and two-sided specification limits. Based on the estimator p* of the fraction defective p, which is essentially the Maximum-Likelihood (ML) estimator, AM-double sampling plans are calculated by using the random variables p*_1 and p*_p relating to the first and pooled samples, respectively. Given p_1, p_2, {\alpha}, and {\beta}, no other AM-double sampling plans based on the same estimator feature a lower maximum of the average sample number (ASN) while fulfilling the classical two-point condition on the corresponding operation characteristic (OC).