Statistical Inference Under Step Stress Partially Accelerated Life Testing for Adaptive Type-II Progressive Hybrid Censored Data

Accelerated life tests (ALTs) are designed to investigate the lifetime of extraordinarily reliable things by exposing them to increased stress levels of stressors such as temperature, voltage, pressure, and so on, in order to cause early breakdowns. The Nadarajah-Haghighi (NH) distribution is of tremendous importance and practical relevance in many real-life scenarios due to its attractive qualities such as its density function always has a zero mode and its hazard rate function can be increasing, decreasing, or constant. In this article, the NH distribution is considered as a lifetime distribution under the step stress partially accelerated life testing (SSPALT) model with adaptive type II progressively hybrid censored samples. The unknown model parameters and acceleration factors are estimated using maximum likelihood estimation (MLE) method assuming that the impact of stress change in SSPALT is explained by a tampered random variable (TRV) model. The Fisher information matrix, which is based on large sample theory, is also constructed and used to produce the approximate confidence intervals (ACIs). Furthermore, two potential optimum test strategies based on the A and D optimality criteria are evaluated. To investigate the performance of the proposed methodologies and statistical assumptions established in this article, extensive simulations using R software have been conducted. Finally, to further illustrate the suggested approach, a real-world example based on the times between breakdowns for a repairable system has been provided.