Reliability estimation for the multicomponent stress-strength model based on objective Bayesian method

Abstract

The multicomponent stress-strength model has many important applications in reliability analysis. Most existing studies assume that stress and strength follow the same distribution and employ maximum likelihood (ML) estimation for reliability inference. However, this assumption restricts the model’s applicability, as there is often no physical rationale for requiring identical distributions for stress and strength. Hence, this paper discusses the reliability inference of a multicomponent stress-strength model under the assumption that the strength and stress variables belong to different distributions. An objective Bayesian method (OBM) framework is applied to infer the model parameters and system reliability based on derived Jeffreys and two reference priors. To ensure the validity of reliability inference, the proper properties of posterior distributions of the model parameters are proved and a Gibbs sampling algorithm is developed. Simulations are implemented to compare the OBM with the considered methods and the results show the superiority of the proposed OBM for the small sample size case. Finally, one real example is analyzed for illustrative purposes.