Optimal maintenance policies in random environments

Most devices are designed to function under different environmental conditions which vary in time. The deterioration and failure process depends on the environment so that the failure rate at any time is a function of the prevailing environmental state. This necessitates the use of the intrinsic age of a device, rather than the real age, in reliability and maintenance problems. The measurement of the age of a device with respect to an intrinsic clock which ticks differently in varying environments is a rather new approach with important implications on the optimal replacement and repair problems. We consider an attractive model where the underlying environmental process has a somewhat general semi-Markov structure. Under the usual assumption requiring increasing failure rate distribution functions in all environments and reasonable cost structures, we show that the control-limit type intrinsic age replacement and repair policies are still optimal.