Robust statistical inference for accelerated life-tests with one-shot devices under log-logistic distributions

TL;DR

This paper develops robust statistical methods using weighted minimum density power divergence estimators for analyzing accelerated life tests of one-shot devices under log-logistic distributions, accounting for censoring and multiple stress levels.

Contribution

It introduces robust WMDPDE-based inference procedures specifically tailored for one-shot devices tested under accelerated conditions with log-logistic lifetimes, including explicit formulas and asymptotic properties.

Findings

WMDPDE estimators show robustness in simulations.

Explicit estimating equations derived for practical use.

Simulation results demonstrate estimator effectiveness.

Abstract

A one-shot device is a unit that operates only once, after which it is either destroyed or needs to be rebuilt. For this type of device, the operational status can only be assessed at a specific inspection time, determining whether failure occurred before or after it. Consequently, lifetimes are subject to left- or right-censoring. One-shot devices are usually highly reliables. To analyze the reliability of such products, an accelerated life test (ALT) plan is typically employed by subjecting the devices to increased levels of stress factors, thus allowing life characteristics observed under high-stress conditions to be extrapolated to normal operating conditions. By accelerating the degradation process, ALT significantly reduces both the time required for testing and the associated experimental costs. Recently, robust inferential methods have gained considerable interest in statistical analysis. Among them, weighted minimum density power divergence estimators (WMDPDEs) are widely recognized for their robust statistical properties with small loss of efficiency. In this work, robust WMDPDE and associated statistical tests are developed under a log-logistic lifetime distribution with multiple stresses. Explicit expressions for the estimating equations and asymptotic distribution of the estimators are obtained. Further, a Monte Carlo simulation study is presented to evaluate the performance of the WMDPDE in practical applications.