Parameter Estimation in Step Stress Partially Accelerated Life Testing under Different Types of Censored Data

Abstract

A long testing period is usually required for the life testing of high-reliability products or materials. It is possible to shorten the testing process by using ALTs (accelerated life tests). Due to the fact that ALTs test products in harsher settings than are typical use conditions, the life expectancy of the objects they evaluate is reduced. Censored data in which the specific failure timings of all units assigned to test are not known, or all units assigned to test have not failed, may arise in ALTs for a variety of reasons, including operational failure, device malfunction, expense, and time restrictions. In this paper, we have considered the step stress partially accelerated life test (SSPALT) under two different censoring schemes, namely the type-I progressive hybrid censoring scheme (type-I PHCS) and the type-II progressive censorship scheme (type-II PCS). The failure times of the items are assumed to follow NH distribution, while the tampered random variable (TRV) model is used to explain the effect of stress change. In order to obtain the estimates of the unknown parameters, the maximum likelihood estimation (MLE) approach is adopted. Furthermore, based on the asymptotic theory of MLEs, the approximate confidence intervals (ACIs) are also constructed. The point estimates under two censoring schemes are compared in terms of root mean squared errors (RMSEs) and relative absolute biases (RABs), while ACIs are compared in terms of their lengths and coverage probabilities (CPs). The performance of the estimators has been evaluated and compared under two censoring schemes with various sample sizes through a simulation study. Simulation results show that estimates with type-I PHCS outperform estimates with type-II PCS in terms of RMSEs, RABs, lengths, and CPs. Finally, a real-world numerical example of insulating fluid failure times is presented to show how the approaches will work in reality.

Sensitivity of step‐stress accelerated fatigue‐life tests on type I censored data—An engineering perspective

“…In contrast, Balakrishnan et al 16 and Mahto et al 17 do address the functional relationship N ( S ) with unknown model parameters, although the article from Mahto et al 17 deals with a progressive step‐stress test and not the SSALT. Some articles have also been published in which approaches with different PDFs than the Weibull function are presented, yet the functional relationship between the time‐to‐failure and the stress level is again not addressed explicitly (see, e.g., Moala and Chagas 18 ; Riad et al 19 ; or Kamal et al 20 ). The common characteristic of all the mentioned references is that they are based on similar mathematical principles, but they do not show how the engineering proof of concept from Figure 1 can be achieved.…”