Reliability inference of a multicomponent stress-strength model for exponentiated Pareto distribution based on progressive first failure censored samples

Multicomponent stress-strength (MC-SS) analysis is crucial for risk management and decision-making in various fields such as engineering, manufacturing, and quality control. It helps in identifying vulnerable components and areas where improvements can enhance overall system reliability. A primary contribution of this research is the implementation of the progressive first-Failure censored (PFIF-C) scheme. This scheme offers a novel and efficient approach to time and cost censoring, surpassing many existing censoring schemes found in the literature. The current study investigates the issue of MC-SS reliability inference under PFIF-C from the exponentiated Pareto distribution. The reliability of the MC-SS system is considered under the condition that both stress and strength follow an exponentiated Pareto distribution with a common second shape parameter. The parameter estimates and reliability estimate of the MC-SS system is produced using the maximum likelihood and Bayesian procedures. The asymptotic confidence intervals and highest posterior density credible intervals for the MC-SS system reliability are produced. Bayesian estimates are yielded using Markov Chain Monte Carlo under both informative and non-informative priors, considering symmetric and asymmetric loss functions. In order to assess the efficacy of the suggested methodology, simulation analyses are conducted. According to the simulation data Bayesian estimates of the MC-SS reliability, employing both symmetric and asymmetric loss functions, consistently outperform maximum likelihood estimates in terms of estimated risks. In general, Bayesian estimates based on asymmetric loss function perform better than the other competing loss function. The procedure is further shown with one real-world data example about failure times of a specific software model to show how the recommended approach may be applied to assess the strength and stress of a multicomponent model.