Inference for stress–strength reliability of multi-state system with dependent stresses and strengths using improved generalized survival signature

Multi-state systems are widely used in engineering field, which usually contain complex internal structures and variable external environmental stresses. Discussing the reliability of such system has theoretical significance and application values. In this paper, a new stress–strength model for multi-state system consisting of multi-type multi-state components is introduced. Each type of components has two dependent strengths, which is suffered from two dependent stresses in working environment, while the strengths and stresses are independent. We discuss inferential procedures for stress–strength reliability of the multi-state system using the proposed improved generalized survival signature in the case of all types of components exposed to common pair of dependent stresses. Based on the assumption that strength variables follow Weibull and exponential distributions, as well as the stress variables, the expressions of stress–strength reliability of such multi-state system in different states are derived by using Gumbel and Clayton copulas. The pseudo maximum likelihood estimation is employed to estimate the dependence parameters and maximum likelihood estimation, asymptotic confidence interval, parametric bootstrap confidence interval and transformation-based confidence interval to make inference for stress–strength reliability. Monte Carlo simulations are carried out to compare the performances of the proposed estimation methods. Finally, a real data analysis is presented to illustrate the developed model and inferential procedures.