Simple Heterogeneous Step‐Stress Accelerated Life Testing Model Under Type II Censoring

ABSTRACT Common step‐stress accelerated life testing (SSALT) models assume that all testing items are sampled from a homogeneous population. However, this is often not the case in practice. Practitioners observe inhomogeneous aging patterns among items of the same production batch. This work proposes a simple SSALT model with exponentially distributed, Type II censored lifetimes that accounts for underlying heterogeneity in aging. To capture the inhomogeneity, a mixture model is introduced and an expectation–maximization (EM) algorithm for censored data is constructed for approximating the maximum likelihood estimates of the model's parameters. The validity of the suggested model and its advantage over the SSALT model in the presence of heterogeneity are demonstrated via simulation studies. Additionally, the log‐link function, used to extrapolate the inferential results to normal operating condition (NOC), is adjusted to accommodate the heterogeneous setup. For log‐link models, it is demonstrated that in presence of heterogeneity, the common model always overestimates the lifetime under NOC. In contrast, the proposed model, accounting for heterogeneity, reduces the bias in estimation and extrapolation.