A parallel system of two identical units has been analyzed stochastically using the ideas of preventive maintenance, replacement and priority in repair disciplines. The unit has two modes-operative and complete failure. A single server attends the system immediately to repair the snags whenever occur during operation of the system. Server conducts preventive maintenance of the system after a maximum operation time‘t’ up-to which no failure occurs. However, repair of the unit is done at its complete failure. And, the failed unit is replaced by new one in case its repair is not completed by the server in a given maximum repair time. Priority to repair is given to one unit over preventive maintenance of the other unit. The unit works as new after preventive maintenance and repair. The random variables associated with failure, preventive maintenance, repair and replacement times are statistically independent. The failure time and time by which unit under goes for preventive maintenance and replacement follow negative exponential distribution while the distributions for preventive maintenance, repair and replacement rates are assumed as arbitrary with different probability density functions. The semi-Markov process and regenerative point technique are adopted to drive the expressions for some reliability measures of vital significance. The behavior of mean time to system failure (MTSF), availability and profit functions have been observed graphically.