Reliability analysis for dependent stress-strength reliability of multi-state system using improved generalized survival signature

In this paper, a new multi-state stress-strength model is introduced, where the system consists of multi-type multi-state components. Each type of components has two dependent strengths and is subjected to two dependent stresses in working environment. Using the proposed improved generalized survival signature, the inferences for stress-strength reliability of the multi-state system are deduced in the case that different types of components are exposed to different pairs of dependent stresses. By assuming the stress(strerngth) variables are Weibull and exponential variables, the exact expressions of the multi-state system reliability are obtained by using Gumbel copula in different states. Then the dependence parameters and maximum likelihood estimation of the stress-strength reliability are computed by adopting the pseudo maximum likelihood estimation method. In addition, the asymptotic confidence interval, parametric bootstrap confidence interval and transformation-based confidence interval for the stress-strength reliability are given. Finally, the Monte-Carlo simulation and a real data analysis are provided for illustrative purpose.