Robust inference for non-destructive one-shot device testing under step-stress model with exponential lifetimes

TL;DR

This paper develops robust statistical methods for analyzing non-destructive one-shot device reliability under step-stress accelerated life testing with exponential lifetimes, improving inference accuracy and robustness.

Contribution

It introduces density power divergence-based estimators and tests for non-destructive one-shot devices under step-stress models, with theoretical and practical validation.

Findings

Robust estimators outperform traditional methods in simulations.

The proposed tests maintain accuracy under model deviations.

Application to real data demonstrates practical utility.

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 pre-fixed 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,vwe develop robust estimators and Z-type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive 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.