Bivariate and multivariate lifetime distributions are important tools to describe the stochastic behaviour of complex: systems in reliability and life testing. As a consequence of the fact that the assumption that all the components of a technical system work independently is not true in many applications several authors describe models including a dependence structure of the lifetimes of the components which lead to extensions of the one-dimensional exponential distribution. But only the models of Freund and Marshall/Olkin seem to have technical applications. A combination of these two models is presented which allows for further applications. Such a bivariate lifetime distribution is combined with the possibility of preventive replacements. The optimal stopping (replacement) time In a two-component parallel system is determined with respect to the total expected discounted cost criterion for different information levels. [References: 7]
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