The optimal replacement problem of a three-state system with preventive maintenance

In this paper, a three-state system with preventive maintenance is studied. Assume that the system have one working state and two different failure states. The preventive maintenance is performed as soon as the hazard rate reaches to the critical value r₀ before the system fails. The successive repair times form an increasing geometric process. A generalized replacement policy (r₀, N) is adopted. The explicit expression of the long-run expected cost per unit time is determined. Finally, a numerical example is given where the working time of the system yields a Weibull distribution. The corresponding optimal policy can be determined numerically. We also provide numerically some comparisons with two existing policies.