Maintenance Overtime Policy with Cumulative Damage

We propose an extended maintenance overtime policy for the cumulative damage model where an operating unit suffers some damage due to shocks. It is assumed that the total damage is additive, and the unit fails when the total damage has exceeded a prespecified damage level. It is supposed that we start to observe occurrence of shocks after time T, and the unit is replaced at Nth (N = 1, 2, ...) shock over time T or at failure, whichever occurs first. That is, we propose a new policy by extending maintenance overtime policy. One example is a rental of system such as industrial equipment with some reservations. For such systems, they should be maintained or replaced at a prespecified number of uses over a scheduled time. For such a model, we obtain the mean time to replacement and the expected costs rate. Further, we discuss about optimal number N and time T which minimizes the expected cost rate when shocks occur in a Poisson process. Finally, numerical examples are given, and suitable discussions are made. Keyword Overtime policy, Replacement policy, Shock model, Cumulative damage