Latest revision as of 13:25, 23 January 2026

Abstract

Long testing times are usually required for the life testing of very reliable products or materials. The testing process can be hastened by using accelerated life tests. The lifespan of the items that accelerated life tests inspect is reduced since they test products in more severe circumstances than those found in regular use scenarios. Data that was censored and disclosed the precise timings of failure may point to accelerated life tests where all units assigned to test are unknown, or where all units assigned to test have not failed for a few reasons, including challenges with technology, tools, costs, and schedules. The step-stress partially accelerated life test was examined in this work using the type-I progressive hybrid censoring scheme and the type-II progressive censoring scheme. The influence of the stress shift is explained using the tempered random variable model, where the failure times of the items are assumed to follow the alpha power Lomax distribution. The unknown parameters are estimated using the maximum likelihood estimation and Bayesian methods. The asymptotic theory of maximum likelihood estimation is also employed in the construction of the approximate confidence intervals. While the point estimates under two censoring schemes are compared in terms of absolute biases and root mean squared errors, approximate confidence intervals and coverage probabilities are compared in terms of their lengths and coverage probabilities. Additionally, three possible optimal test strategies are investigated using different optimal criteria. The performance of the estimators was evaluated and contrasted with two censoring techniques with various sample sizes using a simulation study. Finally, a numerical example for insulating fluid between electrodes data is presented to illustrate how the methods will work in real-world scenarios.OPEN ACCESS Received: 11/06/2025 Accepted: 29/07/2025 Published: 23/01/2026

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