Replacement policies with interval of dual system for system transition

Abstract

This study considers optimal replacement policies in which the system operates as a dual system from the beginning of new unit to the stopping of old unit. Especially, when a new unit begins to operate, it is in initial failure period. Then, the old unit is in random failure period or wearout failure period. When the system fails, minimal repair is done. Introducing the loss cost for a minimal repair and maintenance, we obtain the expected cost for a interval that the new unit is in initial failure period, and derive analytically optimal times of stopping of old unit. Numerical examples are given when the failure distribution of new unit is Weibull distribution and ones of old unit are exponential and Weibull distributions. © 2011 Springer-Verlag.