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 ( ( ) T A ) and the profit function ( ) PF of the system are compared. It was found that MTSF ,( ) PF are decreasing with the increase of the failure rate.