A cold standby repairable system of two identical units has been analysed stochastically in detail by considering the idea of rest of the server after each repair (called repair wise) rest. The preventive maintenance of the system is conducted after a specific period of operation. And, server does not need any rest after preventive maintenance.  The unit either remains in operation or in the failed state. The random variables associated with repair and rest times of the server follow arbitrary distributions while the failure rate of the unit is considered as constant. The semi-Markov process and regenerative point technique are used to derive the reliability characteristics which include mean time to system failure (MTSF), availability, and busy period of the server due to repair, busy period of the server due to preventive maintenance, expected number of repairs, expected number of preventive maintenances of the unit and profit function. The profit analysis of the system model has been carried out for particular values of the parameters. The profit of the system model has also been observed for change in the revenue per unit time, change in the costs for which server is busy due to repair and preventive maintenance and change in the cost per repair and preventive maintenance per unit time.