Robust inference for non-destructive 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 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, we 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.

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

“…𝒛 −1 = 𝒛 𝐿+1 = 0 and 𝑖 is the stress level at which the units are tested after the 𝑗−th inspection time. Then, the MDPDE verifies the estimating equations given by 𝑼 𝛽, 𝑁 ( 𝜽 𝛽 ) = 0 (see Balakrishnan et al (2022a) for more details).…”

“…Classical inferential methods for one-shot are based on the maximum likelihood estimator (MLE), which is very efficient by it lacks of robustness. To overcome the robustness drawback, Balakrishnan et al (2022a) proposed robust estimators for one-shot devices based on the popular density power divergence (DPD) under exponential lifetimes. They developed minimum DPD estimators (MDPDE) as well as Wald-type test based on them, and studied their asymptotic properties.…”

Non-destructive one-shot device testing under step-stress model with Weibull lifetime distributions

“…However, in the case of small samples, the interval limits may need to be truncated to satisfy some constraints, namely, positivity of the quantiles and mean lifetime and reliability lying between (0, 1). To avoid such truncation, Balakrishnan et al (2022) proposed transformed CIs based on the logit function (for the reliability) and logarithmic function (for the quantile and mean lifetime). The resulting asymptotic CIs for the reliability, quantile and mean lifetime are, respectively, given by…”