The quantification of reliability of systems has, for decades, been based on the structure function, which expresses functioning of a system given the states of its components. One problem of the structure function is that, in its simplest form, for a system with m components it must be specified for 2m combinations of component states, which is impossible for most practical systems and networks. Recently, the authors have introduced the survival signature, which is a summary of the structure function that is meaningful if the system’s components can be divided into groups with exchangeable failure times. The survival signature takes all the aspects of the system lay-out into account and is sufficient for a range of inferences, in particular, to derive the system’s failure time distribution given the components’ failure time distributions. In this paper, we provide a brief introductory overview of the survival signature, including recent advances. We then suggest a fundamental change to the nature of the structure function, namely from being a binary function to a probability, or even an imprecise probability. This provides a generalized tool for realistic quantification of system reliability and can straightforwardly be incorporated into the survival signature. We discuss opportunities these concepts provide for practical reliability assessment, and challenges for their application to real-world systems.
Coolen, F., & Coolen-Maturi, T. (2016). On the structure function and survival signature for system reliability. Safety and Reliability, 36(2), 77-87. https://doi.org/10.1080/09617353.2016.1219936