In this paper a reliability model for a computer system has been developedby providing cold standby redundancy to hardware. The hardware and software work together and so constitutes a unit of the system. A single service facility is used to upgrade the software and to repair the hardware whenever required. The failure of the components is considered as independent. Priority to software up-gradation is given over the hardware repair. The service facility undergoes for treatment when it fails to perform the jobs adequately. The random variables associated with failure times of components and service facility are taken as constant while the treatment time of the server,  up-gradation and repair times of the components follow arbitrary distributions with different probability density functions. The expressions for some reliability measures including mean time to system failure (MTSF), steady state availability,busy period of the server due to hardware repair,expected numbers of software up-gradations, expected numbers of the treatments given to the service facilityand profit analysis are derived stochastically by using semi-Markov process and regenerative point technique. The graphical behavior of some important measures of system effectiveness has been observed for arbitrary values of the parameters.