Optimal replacement policy based on the effective age of the system for a deteriorating repairable system with multiple vacations

This paper aims to study the maintenance and replacement problem for a deteriorating repairable system with multiple vacations of one repairman. It proposes a new replacement policy and establishes corresponding replacement models.

It is assumed that the repair after the system failures is not “as good as new” and the repairman is in multiple vacations. The reaching of the effective age of the system is assumed to be mutually stochastic at working state, waiting state for repair and being repaired state. Under these assumptions, a replacement policy based on the effective age of the system is applied. The long-run expected downtime per unit time and the long-run expected profit per unit time as objective functions are chosen, respectively. By using geometric process theory and renewal process theory, the mathematic models have been established and the explicit expressions of the long-run expected downtime per unit time and the long-run expected profit per unit time are derived, respectively.

The optimal replacement policy can be calculated and determined by the computer to minimize the expected downtime or maximize the expected profit. The minimum expected downtime per unit time and maximum expected profit per unit time can also be determined.

This replacement policy and mathematic models can be used as reference to the failure system maintenance and replacement.