A geometric process model for deteriorating operating system with periodic and random inspections

In this paper, we consider a deteriorating operating system which executes a job with random working times. It is assumed that the working times form a geometric process. In Model 1, the system is checked at periodic times and also at every completion of working times to detect the failures. In Model 2, we extend Model 1 by further assuming that a preventive repair is taken when the failure is not found by periodic inspection. For both models, the explicit expressions of the total expected cost until the detection of the failure are obtained. The optimal periodic inspection policies are computed numerically.