Inference on stress-strength reliability from censored data using the asymmetric generalized Poisson Lomax model

This paper investigated the estimation of the stress-strength reliability parameter $R=P(X>Y)$, where the random variables $X$ (strength) and $Y$ (stress) were independently modeled by the generalized Poisson Lomax distribution (GPLD). The analysis was conducted under a progressive Type II censoring scheme, which provided greater flexibility in practical life-testing experiments by allowing for staggered removal of surviving units. Assuming shared scale and shape parameters, both maximum likelihood estimators (MLEs) and Bayesian estimators of $R$ were derived. Due to the absence of closed-form solutions, numerical optimization techniques were applied for MLEs, while Bayesian estimates were obtained under squared error and LINEX loss functions using Markov chain Monte Carlo methods with importance sampling. Asymptotic confidence intervals and highest posterior density credible intervals were constructed to assess uncertainty. A comprehensive simulation study was performed to evaluate the efficiency and robustness of the proposed estimators under varying sample sizes and censoring schemes. Furthermore, two real data applications were analyzed that show survival times of melanoma patients and failure times of high-voltage insulating fluids to illustrate the practical utility of the methodology. The results demonstrated that Bayesian approaches, particularly under asymmetric loss functions, yielded superior performance compared to their frequentist counterparts.