Utilizing unified progressive hybrid censored data in parametric inference under accelerated life tests

Progressive-stress accelerated life testing (PSALT) is a specialized experimental method that evaluates the longevity of a product under continuously fluctuating stress levels. Due to the constraints of testing equipment and expenses, the lifetime data collected by PSALT are typically censored. This paper introduces the PSALT model that utilizes Type-II unified progressive hybrid censoring to address this data characteristic, specifically when the lifespan of test units follows a truncated Cauchy power exponential (TCPE) distribution. The distribution's scale parameter follows the inverse power law, and the cumulative exposure model is relevant for the effects of differing stress levels. The estimation methods for the TCPE parameters and the acceleration factor are examined, including maximum likelihood and Bayesian estimation techniques. Bayesian estimates are generated using the Markov chain Monte Carlo technique based on symmetric and asymmetric loss functions. The highest posterior density intervals are assessed, as well as asymptotic confidence intervals. A simulation study is conducted to evaluate the efficacy of the proposed point and interval estimators. Ultimately, a real data set is applied to the TCPE distribution, and the proposed estimators are assessed.