This paper deals with life cycle benefit-cost analysis of a system, which has both repairable failures and non-repairable failures. The analysis involves the rewards generated by the system, the construction cost of the system, the inspection cost, the repair cost and the disposal cost during the life-time of the system. By using probability analysis, the supplementary variable technique, definite integral and the Laplace transform, this paper obtains the total profit function and the profit rate function based on the life cycle of the system. As an application of the profit rate function, the optimal inspection policy of the system is also studied.