Optimum Age Replacement in the Bivariate Exponential Case

An age replacement policy is considered for pairs of units which operate in parallel and which have lifetimes displaying a bivariate exponential distribution. Both units are to be replaced at the same time. The limiting expected cost per unit time is the optimization criterion. The results state that no replacements should be made until at least one of the units in the pair fails. Both units shoould then be replaced either when one fails or when both fail, depending on which procedure involves the smaller limiting expected cost per unit time.