The joint survival signature of coherent systems with shared components

TL;DR

This paper introduces a joint survival signature for multiple systems with shared components, enabling reliability analysis over time and conditional probabilities, thus extending existing signatures to more complex, realistic scenarios.

Contribution

It generalizes the survival signature to multiple systems with shared components and different time points, facilitating advanced reliability assessments.

Findings

Defines a new joint survival signature for shared components.

Allows computation of conditional reliability probabilities.

Extends applicability to systems with multiple component types.

Abstract

The concept of joint bivariate signature, introduced by Navarro et al. (2013), is a useful tool for quantifying the reliability of two systems with shared components. As with the univariate system signature, introduced by Samaniego (2007), its applications are limited to systems with only one type of components, which restricts its practical use. Coolen and Coolen-Maturi (2012) introduced the survival signature, which generalizes Samaniego's signature and can be used for systems with multiple types of components. This paper introduces a joint survival signature for multiple systems with multiple types of components and with some components shared between systems. A particularly important feature is that the functioning of these systems can be considered at different times, enabling computation of relevant conditional probabilities with regard to a system's functioning conditional on the status of another system with which it shares components. Several opportunities for practical application and related challenges for further development of the presented concept are briefly discussed, setting out an important direction for future research.