The survival signature has recently been presented as an attractive concept to aid quantification of system reliability. It has similar characteristics as the system signature, which is well established, but contrary to the latter it is easily applicable to systems with multiple types of components. We present an introductory overview of the survival signature together with new results to aid computation. We develop nonparametric predictive inference for system reliability using the survival signature. The focus is on the failure time of a system, given failure times of tested components of the same types as used in the system.

Mean residual life is a useful dynamic characteristic to study reliability of a system. It has been widely considered in the literature not only for single unit systems but also for coherent systems. This article is concerned with the study of mean residual life for a coherent system that consists of multiple types of dependent components. In particular, the survival signature based generalized mixture representation is obtained for the survival function of a coherent system and it is used to evaluate the mean residual life function. Furthermore, two mean residual life functions under different conditional events on components’ lifetimes are also defined and studied.

Reliability importance which serves to quantify the influence of each component (or each type of components) in each phase on the reliability of a phased mission system (PMS) plays an important role in security assessment and risk management. In this paper, we present a new and efficient method for reliability importance analysis of PMSs using the theory of survival signature. A new kind of survival signature is applied to assess the reliability of PMS with multiple types of components. A closed-form formula is derived to predict reliability importance of the PMS with respect to each type of components in each phase. The Birnbaum importance model is further extended to calculate the reliability importance of the PMS with respect to each component in each phase. Finally, two numerical examples are used to demonstrate the validity and effectiveness of the proposed approaches.