Abstract
This paper summarizes the results of the basic model of Makabe and Morimura, in which a unit is replaced at k-th failure. The two generalized models are considered: A) A unit has two types of failures and is replaced at type 2 failure or k-th type I failure. B) A system has two types of units and is replaced at unit 2 failure or k-th unit I failure. The expected cost rates for each model are obtained, using the calculus method of probability. It is shown that the optimal numbers k* which minimize the cost rates are given by unique solutions of equations under certain conditions.
