Enhancing System Reliability Under Extremes: A Multi–Stress–Strength Analysis Using Frequentist and Bayesian Approaches

ABSTRACT Many real‐world systems have performance degradation when operating in extreme environments. While previous research often focuses on system failures under specific stress conditions, there remain critical gaps in understanding and minimizing risks associated with systems operating in a wide range of extreme conditions. This paper addresses this critical need by examining the reliability of systems subjected to multiple stresses, where both stress and strength are independent random variables that follow the Burr III distribution. They have different first‐shape parameters but the same second‐shape parameter. To improve the efficiency and cost‐effectiveness of reliability assessment, we use a progressive Type‐II censoring scheme. This study is the first to estimate the multi–stress–strength reliability using this scheme, employing both Bayesian and frequentist statistical methods. We derive the system reliability estimators and use different loss functions to obtain Bayesian estimates with gamma priors. Additionally, we construct asymptotic confidence intervals based on the Fisher information matrix and generate credible intervals with the highest posterior density. Comprehensive Monte Carlo simulations are used to evaluate the performance of the proposed approaches, and real data sets are used for validation. Overall, the simulation experiments show that Bayesian approaches provide better point and interval estimates than conventional approaches under all censoring conditions, which is evaluated using accuracy metrics. Our results provide useful insights for improving the design, performance, and maintenance of systems operating in challenging environments.