Statistical inference and optimal design for step-stress accelerated life testing with hybrid group censoring for non-destructive one-shot devices

Abstract

Step-stress accelerated life tests (SSALTs) have attracted increasing attention from both industry and academia as effective methods for inducing rapid product failures and collecting extensive failure data for reliability analysis. This paper explores the analysis and optimal design of SSALTs utilizing a hybrid group censoring scheme, which provides a decision rule for practitioners on when to terminate the experiment based on the number of failures observed. We propose an approach to determine the optimal stopping threshold for an SSALT experiment, aiming to minimize the asymptotic variance of the maximum likelihood estimator (MLE) for the mean lifetime under normal operating conditions, assuming an exponential lifetime distribution. This study aims to introduce a new framework for optimizing the design of SSALTs with hybrid group censoring specifically for non-destructive one-shot devices, all while adhering to budget and time constraints. The findings demonstrate that this framework is a valuable tool for designing effective SSALTs, enabling the evaluation of mean lifetimes in a cost-effective manner for non-destructive one-shot devices. Illustrative examples including a Monte Carlo simulation study are presented to validate the proposed inference procedure and optimal SSALT design.