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

Abstract

One-shot devices are product or equipment that can be used only once, so they get destroyed when tested. However, the destructiveness assumption may not be necessary in many practical applications such as assessing the effect of temperature on some electronic components, yielding to the so called non-destructive one-shot devices. Further, one-shot devices generally have large mean lifetime to failure, and so accelerated life tests (ALTs) must be performed for inference. The step-stress ALT shorten the lifetime of the products by increasing the stress level at which units are subjected to progressively at pre-specified times. Then, the non-destructive devices are tested at certain inspection times and surviving units can continue within the experiment providing extra information. Classical estimation methods based on the maximum likelihood estimator (MLE) enjoy suitable asymptotic properties but they lack of robustness. In this paper, we develop robust inferential methods for non-destructive one-shot devices based on the popular density power divergence (DPD) for estimating and testing under the step-stress model with Weibull lifetime distributions. We theoretically and empirically examine the asymptotic and robustness properties of the minimum DPD estimators and Wald-type test statistics based on them. Moreover, we develop robust estimators and confidence intervals for some important lifetime characteristics, namely reliability at certain mission times, distribution quantiles and mean lifetime of a device. Finally, we analyze the effect of temperature in three electronic components, solar lights, medium power silicon bipolar transistors and LED lights using real data arising from an step-stress ALT.

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

“…Setting λ β = 0 r in Equation ( 7) yields the same estimating equations of the (unrestricted) MDPDE obtained in Balakrishnan et al (2022), and the function…”

“…Then, studying the boundedness of the IF in its classical approach only makes sense for these continuous covariates. Balakrishnan et al (2022) proved the boundedness of the IF of the MDPDE for large stress levels and inspection times. On the other hand, since the multinomial variable has a finite support, multinomial samples can only take values in a finite set.…”

“…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.…”