A robust multi-risk model and its reliability relevance: A Bayes study with Hamiltonian Monte Carlo methodology

This paper proposes a robust model that describes complex time-to-failure and competing risk datasets found with bathtub curve hazard rate (BCHR). The resulting model, named the flexible Dhillon–Weibull competing risk (FDWCR) model, hybridized the Weibull and flexible Dhillon distributions. It is built with the assumptions of competing risk data characterized by monotone and non-monotone hazard rates. In contrast to most recent additive or competing risk models, the FDWCR model can analyze not only time-to-failure datasets identified with increasing hazard rates and BCHR but also effectively describe time-to-failure data associated with decreasing, upside-down bathtub and modified bathtub hazard rates. Several reliability and structural properties of the model are discussed. We present a complete Bayesian paradigm for FDWCR and suggest employing the Hamiltonian Monte Carlo (HMC) algorithm to enhance precision and expedite inference. The maximum likelihood estimators are also presented. We evaluate the appropriateness of the proposed estimators via simulation experiments, considering both techniques. We offer three case studies to demonstrate the practical utility of the proposed model. The results outperform those produced by other alternative models, indicating a reliable approach for modeling diverse competing risk problems, particularly in the context of engineering reliability studies or other domains of quantitative research.