### Mixture representations for the joint distribution of lifetimes of two coherent systems with shared components

#### Abstract

The signature of a system is defined as the vector whose ith element is the probability that the system fails concurrently with the ith component failure. The signature vector is known to be a distribution-free measure and a representation of the system's survival function has been developed in terms of the system's signature. The present work is devoted to the study of the joint distribution of lifetimes of pairs of systems with shared components. Here, a new distribution-free measure, the 'joint bivariate signature', of a pair of systems with shared components is defined, and a new representation theorem for the joint survival function of the system lifetimes is established. The theorem is shown to facilitate the study of the dependence between systems and the comparative performance of two pairs of such systems.

#### Article information

Source
Adv. in Appl. Probab., Volume 45, Number 4 (2013), 1011-1027.

Dates
First available in Project Euclid: 12 December 2013

https://projecteuclid.org/euclid.aap/1386857855

Digital Object Identifier
doi:10.1239/aap/1386857855

Mathematical Reviews number (MathSciNet)
MR3161294

Zentralblatt MATH identifier
1288.60118

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60K10: Applications (reliability, demand theory, etc.)

#### Citation

Navarro, Jorge; Samaniego, Francisco J.; Balakrishnan, N. Mixture representations for the joint distribution of lifetimes of two coherent systems with shared components. Adv. in Appl. Probab. 45 (2013), no. 4, 1011--1027. doi:10.1239/aap/1386857855. https://projecteuclid.org/euclid.aap/1386857855

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