Reliability Inference for Bivariate Lifetimes With Odd Fréchet Half-Logistic Marginals Under Unified Hybrid Censoring

A bivariate lifetime model is proposed by coupling odd Fréchet half-logistic (OFHL) marginals with the Farlie–Gumbel–Morgenstern (FGM) copula under a unified hybrid censoring (UHC) scheme introducing UHC for bivariate lifetime models for the first time. We derive closed-form joint, marginal, and conditional distributions, product moments, the moment-generating function, and joint reliability and hazard functions. Inference for reliability is developed under both maximum likelihood and Bayesian paradigms, including point estimation and interval estimation for the joint reliability and hazard. Dependence is quantified via Kendall’s tau, Pearson’s copula correlation, and a copula-based median regression. A Monte Carlo study under UHC designs shows consistent estimators and that Bayesian procedures typically achieve lower bias, smaller mean squared error, and shorter intervals than classical methods. Five real data applications from medical and reliability/engineering domains demonstrate superior or competitive fits compared with established alternatives.