The restricted minimum density power divergence estimator for non-destructive one-shot device testing the under step-stress model with exponential lifetimes

TL;DR

This paper introduces robust restricted estimators based on density power divergence for non-destructive one-shot devices under step-stress accelerated life tests with exponential lifetimes, improving parameter estimation robustness.

Contribution

It develops a novel robust estimation method using DPD for non-destructive one-shot devices under step-stress ALTs with exponential lifetimes, with theoretical and empirical validation.

Findings

The proposed estimators are robust against outliers.

The estimators have desirable asymptotic properties.

Simulation confirms improved robustness and accuracy.

Abstract

One-shot devices data represent an extreme case of interval censoring.Some kind of one-shot units do not get destroyed when tested, and so, survival units can continue within the test providing extra information about their lifetime. Moreover, one-shot devices may last for long times under normal operating conditions, and so accelerated life tests (ALTs) may be used for inference. ALTs relate the lifetime distribution of an unit with the stress level at which it is tested via log-linear relationship.Then, mean lifetime of the devices are reduced during the test by increasing the stress level and inference results on increased stress levels can be easily extrapolated to normal operating conditions. In particular, the step-stress ALT model increases the stress level at pre-fixed times gradually during the life-testing experiment, which may be specially advantageous for non-destructive one-shot devices. However, when the number of units under test are few, outlying data may greatly influence the parameter estimation. In this paper, we develop robust restricted estimators based on the density power divergence (DPD) under linearly restricted subspaces, for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distributions. We theoretically study the asymptotic and robustness properties of the restricted estimators and we empirically illustrate such properties through a simulation study.