A repair and replacement policy for repairable systems based on probability and mean of profits

In the optimization of maintenance policies, when a repairable system fails, an important question that arises is whether the system should be repaired or replaced by a new system. This paper deals with this problem and presents a policy to decide between repairing or replacing a system that has failed. Upon taking into account the costs involved, an optimal policy is developed that maximizes the benefit per unit time for repair and replacement. It is assumed that preventive maintenance is performed periodically thus increasing the lifetime of the system, and as a result delaying its failure. Perfect and imperfect repairs are considered to find the solution. Numerical computations are given to study the effect of model parameters on the optimal solutions. The proposed plan is used on a real data set containing failure times and repair times.