The mean residual lifetime of parallel systems with two exchangeable components under the Generalized Farlie-Gumbel-Morgenstern model

Hashemi-Bosra, Seyed Shahrokh; Salehi, Ebrahim

doi:10.22103/jmmrc.2016.1305

The mean residual lifetime of parallel systems with two exchangeable components under the Generalized Farlie-Gumbel-Morgenstern model

Document Type : Research Paper

Authors

Seyed Shahrokh Hashemi-Bosra

Ebrahim Salehi

Department of Basic Science, Birjand University of Technology, Birjand, Iran

10.22103/jmmrc.2016.1305

Abstract

The parallel systems are special important types of coherent structures and have many applications in various areas. In this paper we consider a two-exchangeable-component parallel system for the Generalized Farlie-Gumbel-Morgenstern (Generalized FGM) distribution. We study the reliability properties of the residual lifetime of the system under the condition that both components of the system are operating at time $t$, and obtain an explicit expression for the mean residual lifetime (MRL) for such system. The asymptotic behavior of the proposed MRL function of the system is also investigated when the exchangeable lifetimes of components have a Generalized FGM bivariate exponential. Finally, we present some results for the correlation coefficient Kendall's Tau of Generalized FGM bivariate copula.

Keywords

mean residual lifetime

copula

exponential distribution

reliability