A simple recursive Markov chain model to determine the optimal replacement policies under general repairs

A repairable system (machine) is subject to failure. At each failure epoch, a general repair is performed. Such repairs return the system to a working condition somewhere between ‘good-as-new’ (a perfect repair) and ‘bad-as-old’ (a minimal repair). An important question for such systems is at what time should a major overhaul be conducted to return the unit to a ‘good-as-new’ state. Two policies are investigated in this research: (1) overhaul at fixed intervals and (2) overall at variable intervals by conducting each overhaul on the first failure following a predetermined time. We show in this research that both of these policies can be analyzed using a simple recursive Markov model thereby permitting the best of these policies to be identified in any particular situation. The Markov model is quite general, permitting a wide variety of structures to be investigated.