Optimal random replacement policies

It would be practical and useful to replace systems, adjusting to their successive processing times when they work for jobs. This paper proposes the extended replacement models where a system is replaced at both periodic times and at the same times as its working times. The expected cost rates of a system is obtained, when its working times are random times. In particular, when the random times are exponential, optimal policies which minimize the expected costs are analytically discussed. Finally, numerical examples are given and optimal replacement times are computed.