Here, we describe the stochastic analysis of a repairable system consisting two non-identical units called the main unit and the other is a duplicate unit. The units have direct complete failure from the operative state. A single repairman has been engaged to carry out the repair activities that can be failed while performing his jobs with the main unit. The repairman does repair activities of the duplicate unit without any problem. Priority for operation and repair to the duplicate unit is given over the main unit. The repairman performs with full efficiency after getting treatment. The distribution for failure rates of the units has been considered as negative exponential while arbitrary distributions have been taken for repair and treatment rates. The use of semi-Markov process and regenerative point technique has been made to study the probabilistic behavior of the system in different possible transition states. The reliability characteristics of the system model have been examined numerically and graphically for particular values of the parameters. The profit of the system has also been analyzed for some fixed values of the repair and other maintenance costs.