Subsignatures of systems

TL;DR

This paper introduces the concept of subsignatures in semicoherent systems, providing a new class of indexes that generalize existing importance measures and offer explicit formulas for failure probabilities.

Contribution

It defines the M-signature for subsets of components, linking system structure and component lifetime distributions, and explores special cases like exchangeable lifetimes and modular sets.

Findings

Derived explicit linear formulas for M-signatures.

Analyzed the case of exchangeable component lifetimes.

Examined subsignatures for modular component sets.

Abstract

We introduce the concept of subsignature for semicoherent systems as a class of indexes that range from the system signature to the Barlow-Proschan importance index. Specifically, given a nonempty subset M of the set of components of a system, we define the M-signature of the system as the |M|-tuple whose k-th coordinate is the probability that the k-th failure among the components in M causes the system to fail. We give various explicit linear expressions for this probability in terms of the structure function and the distribution of the component lifetimes. We also examine the case of exchangeable lifetimes and the special case when M is a modular set.