Multistage Replacement Strategies

In a system containing a large number of a certain unreliable item the replacement cost per unit may be different because of inaccessibility or unusual expense associated with the failure of certain units. For such a system a generalized theory of multistage strategies is developed showing the exact conditions under which it is more economical than the simple replacement policy. This theory is based on the grouping of units according to replacement cost and on the replacement of failures and of vacancies caused by the transfer of units operating in one stage to the preceding stage. The economy is brought in by transfer of failure rates from groups where replacement cost per unit is large to those where it is comparatively small. Procedure for quick computation of savings is also shown. The method of finding the optimum number of stages for multistage strategies is indicated. In the literature two-stage strategies are available; however, they are of limited advantage and multistage strategies will be more economical in many practical cases. Further, only with the aid of multistage strategies is it possible to arrive at the optimum number of stages. As an illustration, three-stage strategies for certain distributions are worked out and they are found to be more economical than the two-stage strategies described in the literature. Finally, some possible fields of applications are indicated.