Estimation in coherent reliability systems through copulas

The problem of estimating the parameter of a common distribution of components' lifetimes from system's lifetime data is of interest and importance in reliability engineering. The present paper deals with this problem when the common component distribution is exponential with mean μμ and the lifetimes of components have an exchangeable joint distribution which is constructed by the help of Archimedean copula. In particular we obtain moment estimator of μμ for Clayton and Ali-Mikhail-Haq copulas. We illustrate the findings of the paper for a special class of coherent systems called consecutive k-within-m-out-of-n:F system. A simulation study is performed to investigate the properties of the moment estimator. The method presented in this paper can be applied to all coherent systems.