Component Importance Based on Dependence Measures

TL;DR

This paper introduces new component importance measures for reliability systems based on dependence measures like covariance and mutual information, applicable in both time-dependent and continuous time scenarios.

Contribution

It develops importance measures derived from stochastic dependence measures and analyzes their properties and ordering in reliability systems.

Findings

Properties of the importance measures are established.

Results on the ordering of component importance are obtained.

Applicability to both time-dependent and continuous time models is demonstrated.

Abstract

We discuss the construction of component importance measures for binary coherent reliability systems from known stochastic dependence measures by measuring the dependence between system and component failures. We treat both the time-dependent case in which the system and its components are described by binary random variables at a fixed instant as well as the continuous time case where the system and component life times are random variables. As dependence measures we discuss covariance and mutual information, the latter being based on Shannon entropy. We prove some basic properties of the resulting importance measures and obtain results on importance ordering of components.