The concentration of this paper is on the stochastic analysis of a parallel system of two identical units with a single service facility (called server) which is subjected to failure while performing jobs. The service facility takes some time to arrive at the system for carring out repair activities. The unit is repaired at its complete failure. Treatment is given to the failed service facility in order to resumes the jobs as usual. The unit and service facility works as new after repair and treatment respectively. The random variable associated with failure time, treatment time of the server and repair time of the units are statistically independent. The failure time and the time by which server undergoes for treatment follow negative exponential whereas the distributions for treatment time of the server, arrival time and repair time of the unit are taken as arbitrary with different probability density functions. The expressions for some reliability characteristics are derived in steady state by using semi-Markov process and regenerative point technique. Graphs are drawn to depict the behavior of mean time to system failure, availability and profit function with respect to treatment rate of the service facility for arbitrary values of others parameters.