A stochastic model for a system of two non-identical units is developed by considering the idea of repairman failure. Each unit has two modes: operative and complete failure. The units are non-identical in nature due to their different failure rates and so one is called the main unit and the other is duplicate unit. Initially, the main unit is operative and the duplicate unit is taken as spare in cold standby. The repairman is subjected to failure while repairing the main unit and so the failure is named as conditional failure. The failure time of the units and of the repairman follow negative exponential distribution whereas, the distributions of repair time of the units and treatment time of the repairman are taken as arbitrary with different probability density functions. The system is analyzed at different epochs by using semi-Markov process and regenerative point technique. The expressions for some significant reliability characteristics like mean time to system failure (MTSF), availability and finally for the profit function are derived in steady state. The graphical behavior of these measures has also been critically examined for arbitrary values of the parameters.