🤖 AI Summary
This study addresses a key limitation in traditional step-stress accelerated life testing (ALT) models, which assume product homogeneity and thus fail to capture heterogeneous aging behaviors that may emerge under high stress. The authors propose a hazard-rate-based heterogeneous step-stress ALT model that retains the homogeneity assumption at the initial stress level but introduces a finite mixture model at the second stress level to represent m latent subpopulations with distinct failure mechanisms. Parameter estimation under Type-II censoring is handled via the EM algorithm. Notably, this approach is the first to embed a finite mixture model within a hazard-rate framework, establishing an interpretable paradigm for heterogeneity modeling. The model rigorously reduces to the existing exponential heterogeneous model when the Weibull shape parameter equals one, confirming its theoretical generalizability. Simulations demonstrate that neglecting heterogeneity induces substantial bias in lifetime predictions across all quantiles, particularly at early failure quantiles.
📝 Abstract
Traditional step-stress accelerated life testing models assume that the test units originate from a homogeneous population. Recently, Lu and Kateri (2025) proposed a heterogeneous cumulative exposure based SSALT model to account for the inhomogeneous aging patterns among test units belonging to the same production batch. This paper introduces an alternative yet flexible failure-rate based heterogeneous simple SSALT model with Weibull-distributed Type-II censored failure times. The proposed model assumes homogeneous behavior of the test units at the initial stress level while allowing heterogeneity to emerge at the second stress level through a parametric finite mixture model formulation of m latent subgroups, each characterized by its own failure behavior. The expectation-maximization algorithm is developed for maximum likelihood estimation of the model parameters, exploiting the incomplete data structure arising from both unknown group membership and Type-II censoring. An extensive simulation study evaluates the finite-sample performance of the proposed estimators and demonstrates, through a quantile-based comparison, that ignoring population heterogeneity leads to systematic bias in lifetime predictions across the entire quantile range, with the most severe consequences at early failure quantiles of direct relevance to warranty period design. A special case comparison with the exponential heterogeneous SSALT model of Lu and Kateri (2025) under the cumulative exposure model confirms that the proposed Weibull failure-rate based formulation reduces to the existing model when the shape parameter equals unity, validating the proposed framework as a proper generalization. The practical application of the model is further illustrated through simulated data analysis examples.