Reliability is an important area that is receiving attention globally. This paper studies reliability analysis of a two-dissimilar-unit cold standby system with three modes using Kolmogorov forward equation’s method, in which its reliability and availability analysis are evaluated. This proposed system has been investigated under three modes: normal, partial failure, total failure. The failure and the repair time are assumed to have exponential distribution. The effect of failure rate on meantime to system failure (MTSF ), steady state availability ( AT (∞) ) and the profit function PF(∞) of the system are compared. It was found thatMTSF , AT (∞) , and PF(∞) are decreasing with the increase of the failure rate.Keywords: Cost analysis, Meantime to System Failure, Steady State Availability and Kolmogorov forward equation.