Construction of copulas for bivariate failure rates

This paper aims to develop a method to construct an asymmetric copula, based on which a closed form of the cumulative bivariate failure rate can be obtained. The construction method differs from existing ones. This new method can facilitate the derivation of some results such as the estimation of the expected number of occurrences for a system whose failure process is modelled by a bivariate stochastic process or the expected cost in optimisation of maintenance policies.