Statistical inference for dependent stress–strength reliability of multi-state system using generalized survival signature

In reliability analysis of the stress–strength models, it is generally assumed that an individual only has one type of strength. However, in some situation, an individual, which has several types of independent or dependent strengths, is subjected several types of independent stresses in the working environment. Hence, we define a new multi-state stress–strength model for multi-state system consisting of n multi-state components with several types of strengths. In this paper, we discuss inferential procedures for stress–strength reliability of such multi-state system using generalized survival signature in two cases, viz., independent strengths and dependent strengths. Based on the assumption that the strengths and stresses variables follow exponential distributions, the exact expressions for stress–strength reliability of system in different states are derived in case of independent strengths. When the strengths are dependent, we utilize the Gumbel copula to depict the dependence structure of strengths. Additionally, two semiparametric methods, viz., method-of-moment and maximum pseudo-likelihood estimation, are used to estimate the dependence parameter. Then, maximum likelihood estimation, asymptotic confidence interval estimation and bootstrap percentile confidence interval estimation based on the aforementioned two semiparametric methods for the dependence parameter are provided, separately, to estimate the stress–strength reliability of system in different states. Monte Carlo simulations are performed to compare the performances of the proposed estimation methods. Finally, a real data analysis is provided to illustrate the proposed procedures.