Likelihood-Based Regression for Weibull Accelerated Life Testing Model Under Censored Data

TL;DR

This paper develops a likelihood-based regression approach for Weibull accelerated life testing models with censored data, incorporating stress variables and establishing estimator properties under complex censoring schemes.

Contribution

It introduces a two-step estimation framework linking Weibull parameters to stress variables under progressive hybrid censoring, with proven estimator properties.

Findings

Estimators are consistent and asymptotically normal.

Simulation results demonstrate good finite-sample performance.

Application shows practical relevance of the model.

Abstract

In this paper, we investigate accelerated life testing (ALT) models based on the Weibull distribution with stress-dependent shape and scale parameters. Temperature and voltage are treated as stress variables influencing the lifetime distribution. Data are assumed to be collected under Progressive Hybrid Censoring (PHC) and Adaptive Progressive Hybrid Censoring (APHC). A two-step estimation framework is developed. First, the Weibull parameters are estimated via maximum likelihood, and the consistency and asymptotic normality of the estimators are established under both censoring schemes. Second, the resulting parameter estimates are linked to the stress variables through a regression model to quantify the stress-lifetime relationship. Extensive simulations are conducted to examine finite-sample performance under a range of parameter settings, and a data illustration is also presented to showcase practical relevance. The proposed framework provides a flexible approach for modeling stress-dependent reliability behavior in ALT studies under complex censoring schemes.