Robust inference for nondestructive one‐shot device testing under step‐stress model with exponential lifetimes

Abstract

One‐shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one‐shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step‐stress tests allow the experimenter to increase the stress levels at prefixed times gradually during the life‐testing experiment. The cumulative exposure model is commonly assumed for step‐stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper, we develop robust estimators and Z‐type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for nondestructive one‐shot devices under the step‐stress ALTs with exponential lifetime distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and confidence intervals for different lifetime characteristic such as reliability, distribution quantiles, and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real‐life data sets are analyzed finally for illustrative purpose.

Robust Rao-Type Tests for Non-destructive One-Shot Device Testing Under Step-Stress Model with Exponential Lifetimes

“…Recent works on survival analysis and reliability have shown the advantage in terms of robustness, with a small loss of efficiency, of using divergence-based estimators. Balakrishnan et al (2023a) developed robust minimum density power divergence (DPD) estimators (MDPDEs) for non-destructive one-shot device data under step-stress model with exponential lifetimes, and later Balakrishnan et al (2022Balakrishnan et al ( , 2023c extended the theory to Weibull and gamma lifetime distributions. Further, Balakrishnan et al (2023b) developed restricted MDPDE (RMDPDE) for the step-stress model with exponential lifetimes, and derived robust Rao-type tests based the restricted estimators.…”