Reliability analysis for system with dependent components based on survival signature and copula theory

Recently, survival signature theory has been widely used in system reliability analysis. However, there are few studies that address the extension of survival signature theory to component-dependent systems. This study proposes a copula-based survival signature method to obtain an analytical solution for system reliability considering component dependence. It consists of two steps: constructing the dependence structure and utilizing the copula function to compute the analytical probability structure. The effectiveness of the Archimedean copula function in describing component dependence and its compliance with the exchangeability assumption in sur-vival signature theory are first derived. Then, using Sklar's theorem, the analytical solution for the probability structure is determined based on the inclusion-exclusion principle. Finally, the hierarchical Archimedean copula function is employed to build a more sophisticated dependent structure. It is demonstrated that the satisfaction of the exchangeability assumption under the hierarchical Archimedean copula structures depends only on whether the joint distribution probability function of the components in the same type is constructed by a unique Archimedean copula function. Three separate systems with imprecise dependent information are employed in the reliability analysis in order to show the validity of the proposed method. The findings show that given a straightforward series-parallel system with a single type of component, the system reliability initially drops and then rises as the dependence parameters in the copula function grow at each time point. Additionally, the approach is more precise and effective than the simulation method when it comes to the study of complex systems.