In this paper, a cold standby system of two non-identical units (original & duplicate) has been analyzed stochastically with the concept of preventive maintenance. Initially, the original unit is operative and duplicate unit is kept as spare in cold standby. The original unit undergoes for preventive maintenance after a maximum operation time. There is a single server who visits immediately to the system for conducting repair activities. The random variables associated with failure time, preventive maintenance time, and repair time are statistically independent. The distribution for failure time and the rate by which unit under goes for preventive maintenance after a maximum operation time are exponentially distributed while the distributions for preventive maintenance time and repair time are assumed as arbitrary with different probability density function. The expressions for various reliability measures of the system model have been derived in study state by using regenerative point technique. Graphs are plotted for mean time to system failure (MTSF), availability and profit of system model for particular values of the parameters and costs.