Optimal Variable Acceptance Sampling Plan under Progressive Type-II Censoring for the Mixture of Exponential-Rayleigh Distributions

Abstract

Mixture distributions are widely utilized in various practical problems, such as clinical experiments and electronic component life testing. Despite this, the literature does not extensively cover acceptance sampling plans associated with these distributions. In this paper, variable acceptance sampling plans are designed for a mixture of exponential-Rayleigh distributions using partially accelerated life tests. Under progressive Type-II censoring scheme, the maximum likelihood estimators of the unknown parameters of the mixture distribution are derived for Arrhenius and linear life-stress relationships. Based on these relationships, optimal variable sampling plans are formulated. The plan parameters are determined by solving corresponding optimization problems. The study presents numerical findings, a comparative analysis, and sensitivity assessments. Finally, the practical applicability and relevance of the proposed acceptance sampling plans are demonstrated using real-world datasets. These datasets include breast cancer patients' records and failure lifetime data from communication transmitter-receivers in a commercial aircraft.