In this paper, we discussed a two unit cold standby system with the concepts of degradation, inspection, priority and preventive maintenance (PM) where all random variables follow general distribution. A single repairman is provided to the system who visits the system immediately whenever needed and is capable to do all repair activities. The repairman inspects the failed degraded unit to see the feasibility of repair. Degraded unit is replaced by new unit if its repair is not feasible. PM will be provided to the system to increase the performance of the system when both the units are degraded and available for use. Priority for repair is provided to the new unit over degraded unit. Regenerative point graphical technique (RPGT) is adopted to obtain the various reliability characteristics such as mean time to system failure (MTSF), availability, busy period of the repairman, expected number of visits by the repairman and profit of the system. For particular case, numerical results are derived for MTSF, availability and profit of the system by considering exponential, Rayleigh and Weibull distributions for all random variables.