The main concentration of the present paper is on the cost-bene t analysis of a cold standby system with the concept of priority, preventive maintenance and arrival time of the server. For, this purpose a stochastic model is designed in which one unit is operative initially and other unit is kept as cold standby. A single repair facility is provided which takes some time to arrive at the system to do PM and repair of the components as per the requirement of the system. Server does not do the preventive maintenance if there is no spare unit available for use. All random variables are statistically independent. The unit after repair and preventive maintenance is considered as good as new. All times distributions are exponential except the repair, arrival time of server and preventive maintenance time distributions which are considered as general. The expression for various important measures of system e ectiveness is obtained by using semi-Markov process and regenerative point technique. The numerical study of the results for mean time to system failure (MTSF), availability and pro t has also been made giving some particular values to various costs and parameters.