This paper deals with the cost-benefit analysis of a system of two identical units-one is operative and the other is kept as cold standby. There is a single server who attends the system immediately whenever needed. The unit becomes degraded after repair. The server inspects the degraded unit at its failure to see the feasibility of repair. If the repair of the degraded unit is not feasible, it is replaced by new unit which gets priority in operation as well as in repair over the degraded unit. The system is considered in up-state if either of new/degraded unit is operative. The distributions of failure time of the units are taken as negative exponential while that of inspection and repair times are taken as arbitrary such as exponential distribution, Erlang distribution and Weibull distribution etc. Various reliability measures of system effectiveness are obtained by using semi-Markov process and regenerative point technique. The behavior of mean time to system failure (MTSF), availability and profit of the system have also been studied through graphs.