The present paper has been designed with an object to analyze and determine some reliability characteristics of a complex system of two non-identical units which is operative with different type of failure and rest period of repairman. The system consists of two units, one is main unit and other is supporting unit. The main unit passes through two types of failure i.e., partial failure mode and total failure mode whereas supporting unit fails directly. A single repairman is always available with the system for the repair a failed unit. The working efficiency of the repairman may reduce on the repairing of totally fail main unit and he needs rest after working some random period of time. The time to failure of the units and the time to which repairman goes for rest are exponentially distributed whereas the completion of rest time of repairman and repair time of the units are gamma distributed with different parameters. Using regenerative point technique, important measures of the system effectiveness are obtained. The graphical behaviours of Profit function have also been studied.