Optimal Design for a Bivariate Step-Stress Accelerated Life Test with Alpha Power Exponential Distribution Based on Type-I Progressive Censored Samples

Abstract

We consider an optimization design for the alpha power exponential (APE) distribution as asymmetrical probability distributions under progressive type-I censoring for a step-stress accelerated life test. In this study, two stress variables are taken into account. To save the time and cost of lifetime testing, progressive censoring and accelerated life testing are utilized. The test units’ lifespans are supposed to follow an APE distribution. A cumulative exposure model is used to study the impact of varying stress levels. A log-linear relationship between the APE distribution’s scale parameter and stress is postulated. The maximum likelihood estimators, Bayesian estimators of the model parameters based on the symmetric loss function, approximate confidence intervals (CIs) and credible intervals are provided. Under normal operating conditions, an ideal test plan is designed by minimizing the asymptotic variance of the percentile life.