Statistical Inference of Stress–Strength Reliability for Multi-State System Based on Exponentiated Pareto Distribution Using Generalized Survival Signature

The stress–strength reliability model is widely applied in various fields such as mechanical engineering, materials science, and aerospace engineering to identify weak links in systems and thereby improve system reliability. This paper analyzes the stress–strength reliability for multi-state systems composed of multi-state components. One of the main contributions is the derivation of a multi-state stress–strength reliability model under combined stresses based on the generalized survival signature theory. In the model analysis, it is assumed that each component of the system is subjected to two different stresses corresponding to two different strengths, and that the stress variables and strength variables are mutually independent and all follow the exponentiated Pareto distribution with the common second shape parameter. Another contribution is the use of maximum likelihood estimation, empirical Bayesian estimation, and weakly informative Bayesian estimation to estimate the variable parameters and the stress–strength reliability under the progressive first-failure censoring scheme. In addition, the asymptotic confidence intervals for the stress–strength reliability model are derived, and the Bayesian credible intervals are constructed based on MCMC sampling. Finally, through MCMC simulation of a three-state consecutive 3-out-of-5: G system, the accuracy of the variable parameters and the stress–strength reliability under the aforementioned point estimation and interval estimation methods is analyzed, and the performance of these estimation methods is compared under different sample sizes. In addition, sensitivity analyses were conducted on the common shape parameter and the hyperparameters of the weakly informative prior distributions. Furthermore, a real data set is applied to illustrate the proposed procedures.