Bivariate lifetime distributions and optimal replacement

The assumption that components which are part of a technical system work independently seems not appropriate in a number of applications. A lot of multivariate extensions of the univariate exponential distribution have been suggested as lifetime distributions. But only the models of J.E. Freund and of A.W. Marshall and I. Olkin seem to be physically motivated. A combination of these approaches yields a bivariate lifetime distribution which is investigated in some detail. Applications of this bivariate lifetime model are considered in preventive maintenance. In a two-component parallel system the optimal replacement time shall be determined with respect to the total expected discounted cost criterion. Results of the theory of stochastic processes are used to obtain the optimal strategy for different information levels. Some numerical examples based on a two-component parallel system with dependent component lifetimes show how the optimal replacement policy depends on the different information levels and on the degree of dependence of the components.