A Novel Poisson–Weibull Model for Stress–Strength Reliability Analysis in Industrial Systems: Bayesian and Classical Approaches

Industrial systems often rely on specialized redundant systems to enhance reliability and prevent unexpected failures. This study introduces a novel three-parameter model, the Poisson–Weibull distribution (PWD), and discovers its various key properties. The primary focus of the study is to develop stress–strength (SS) model based on this newly developed distribution. Parameter estimation for both the PWD and SS models is carried out using maximum likelihood estimation (MLE) and Bayesian estimation techniques. Given the complexity of the proposed distribution, numerical approximation techniques are employed to obtain reliable parameter estimates. A comprehensive simulation study employing the Monte Carlo simulation (MCS) and Markov Chain Monte Carlo (MCMC) examines the behavior of the PWD and SS model parameters under various scenarios. The development of the SS model enhances understanding of the PWD’s dynamics while providing practical insights into its real-life applications and limitations. The effectiveness of the proposed distribution and the SS reliability measure is established through applications to real-life data sets.