Analysis of multiple step-stress dependent competing risks under proportional hazard model

In real-life situations, the cause-specific failure time distribution often does not exhibit a constant failure rate. To model dependent competing risk scenarios under multiple step stress conditions, distributions with non-constant failure marginals are required. This paper presents a cumulative exposure-based modeling approach for analyzing multiple step-stress accelerated life testing (SSALT) data using a progressive Type-I censoring plan. The time-to-failure distributions associated with specific causes are categorized within a class of proportional hazard distributions that can accommodate both monotonic and non-monotonic failure rate patterns. The interdependence among competing causes is modeled by assuming that the time-to-failure distributions for each stress follow the Marshall-Olkin bivariate distribution. The power law model is employed to characterize the acceleration factor. Maximum likelihood estimation is used to derive point estimates for model parameters, with interval estimates computed based on asymptotic normality. The proposed model can estimate parameters even when no failures occur at a particular stress level. The effectiveness of the approach is evaluated through extensive simulation studies, which yield satisfactory results. Additionally, the model’s applicability is validated using a real-world dataset of aerospace electrical connectors.