A stochastic model for a cold standby system of non-identical units has been developed by introducing the idea of priority to preventive maintenance over replacement. There are two units in the system- one is original (called main unit) and the other unit is its duplicate. The system starts its operation with original unit and the duplicate unit is taken as spare in cold standby. A single repair facility is provided immediately to rectify the faults which occur in the system. The main unit under goes for preventive maintenance after a pre specific operation time with some constant rate. The unit at its complete failure under goes for repair while the duplicate unit is replaced by new one at its failure. Priority is given to maintenance of the main unit over replacement of the duplicate unit. The random variables associated to failure, preventive maintenance, repair and replacement times are statistically independent. The distributions for failure time and the rate by which main unit under goes for preventive maintenance are taken as exponential while that of repair time, preventive maintenance time and replacement time are assumed as arbitrary with different probability density functions. The expressions for some important reliability measures are derived in steady state by using semi-Markov process and regenerative point technique. The behavior of mean time to system failure (MTSF), availability and profit function has been observed with respect to arbitrary values of repair rate and other parameters