A redundant system of two-identical units has been analyzed stochastically in detail by considering server failure while performing jobs. Initially one unit is operative and other is kept as spare in cold standby. There is a single server who takes some time to arrive at the system with the condition that he has to attend the system immediately at its complete failure. The failed server undergoes for treatment and resumes jobs with full efficiency after treatment. The random variables associated with the failure rate of the unit and server, repair rate of the unit, treatment rate and arrival rate of the server are statistically independent. The distributions for failure time of the unit and the server are taken as negative exponential while that of repair rate, treatment rate and arrival time of the server are arbitrary with different probability density functions. The semi-Markov process and regenerative point technique are adopted to derive the expressions for some measures of system effectiveness in steady state. Graphs are drawn to depict the graphical behavior of some important performance measures for arbitrary values of various parameters and costs.