Profit Evaluation of a Repairable System with Three-Stage Deterioration

This paper deals with the cost analysis of a repairable system subject to deterioration. The system works in three different modes: the normal, deterioration and failure. The deterioration can be minor, medium or major. The failure can be type I in which the system is perfectly repair or type II in which the system is minimally repaired. We analyzed the system using linear first order differential equations and developed explicit expressions for availability, busy period due to failure, busy period due to minor deterioration, busy period due to major deterioration and profit function for the system. Based on assumed numerical values given to the system parameters, some particular cases have also been discussed graphically to see the effect of deterioration, failure and repair rates on profit. The results have indicated that deterioration and failure rates decrease the profit while repair, minor and major maintenance rates increase the profit.