the mean residual lifetime of parallel systems with two exchangeable components under the generalized farlie-gumbel-morgenstern model

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 kendall’s tau correlation coefficient of generalized fgm bivariate copula.