Stress-strength reliability inference of multi-state system with multi-type components based on copula theory

This article considers a multi-state system which is composed by several multi-type components, it is assumed that any type of components has two strengths which is suffered from two stresses. Further, assume that two strengths have dependent relationship, as well as the two stresses, but there are no relationship among strengths and stresses for different types of components. By extending the applied scenarios, a new survival signature, that is named by improved generalized survival signature, is introduced and is used to analyze the system reliability. When stress (strength) variables follow the distributions of Weibull and exponential, the Clayton copulas are employed to depict the dependence structure of system, then the inferences of system reliability are obtained by a two-stage method. In the first stage, the dependent parameters are achieved by adopting the pseudo maximum likelihood estimation method. The second stage, the maximum likelihood estimation, two confidence intervals based on parametric bootstrap method and transformation-based method for system reliability are deduced. At last, the numerical study and real data application are conducted to illustrate the proposed methodologies.