This paper analyzed a parallel system of two identical units which work simultaneously. Each unit has direct complete failure from normal mode. The system is considered in up-state if at least one unit is operative. There is a single server who visits the system immediately for doing repair of the unit. If repair of the failed unit is not possible in a pre-specific time (called maximum repair time), it is replaced by new one giving some replacement time. The time to failure of the unit and repair time taken by the server follow negative exponential distribution while the distributions of repair and replacement times the unit are considered as arbitrary with different probability density functions. The expressions for some important reliability and economic measures are derived by using Semi-Markov process and regenerative point technique. The graphical study of the results obtained for a particular case has also been made.