Optimal Acceptance Sampling Testing Plan With Pivotal Quantity for Log-Location-Scale Distributions

Abstract

Global market competition has led to manufacturers encountering a decision problem as the reliability of their products exceeds a given standard. Acceptance sampling tests (ASTs) can be expensive and time-consuming, especially for products with high reliability or quality. Thus, careful planning of the acceptance rule and determination of a suitable sample size for the test are important. In this article, an exact method for the optimal planning of ASTs is proposed for cases in which the product lifetimes follow a distribution in the general log-location-scale family of distributions. A novel procedure using the pivotal quantity is established based on the method-of-moments estimators of the model parameters, and the distribution of the reliability estimator is derived. An algorithm for obtaining the optimal sample size and the corresponding acceptability constant is presented in which the producer's and consumer's risks are constrained according to certain acceptance criteria. We apply the proposed method to a censored AST by generating censored observations with a quantile-filling method under Type-II censoring. The performance of the proposed AST with a complete or censored sample is studied and compared with an AST based on the maximum likelihood method. The robustness of the proposed AST is also examined under model misspecification. The results show that the proposed AST performs well under different scenarios.