A computer system is analyzed stochastically byconsidering the idea of priority and failure of service facility. The concept of unit wise redundancy (one more computer system in cold standby) is used to develop the system model. The service facility fails during s/w up-gradation. The system undergoes for repair when there is a h/w failure while it undergoes for up-gradation in case s/w fails to follow the instructions specified for the proper functioning of the system. The repair activities are perfectly handled by the service facility after getting treatment. The priority to h/w repair is given over the s/w up-gradation. The h/w and s/w components exhibit constant failure rates while an arbitrary distribution is taken up for h/w repair time, s/w up-gradation time and treatment time of the server. The profit function based on revenue per unit up time (availability), cost incurred due to repair activities, expenditure made due to no. of repair activities carried out for proper functioning of the system and expenditure made on treatment for  recovering the service facility after failure. The use of SMP and RPT has been made to drive the expressions for various reliability indices in steady state. To highlight the significance of study, graphs of MTCSF, availability and profit function have been drawn for arbitrary values of the parameters.