The main aim of the present paper is to examine the changes in the values of reliabilitymeasures of a computer system with hardware redundancy in cold standby and priority tosoftware up-gradation over hardware repair. A single server is called immediately to conducthardware repair and software up-gradation as and when required. The repair and up-gradationactivities performed by the server are perfect.The random variables associated with time tofailure, hardware repair and software up-gradation is statistically independent. The time tohardware and software failures follows negative exponential distribution, whereas thedistributions of hardware repair and software up-gradation times are taken as arbitrary withdifferent probability density functions. The expressions for various reliability and economicmeasures are derived in steady state using semi-Markov process and regenerative pointtechnique. The trends of some important measures of system effectiveness have been observedfor arbitrary values of the parameters. The profit of the present model has also been comparedwith that of the model as discussed in Malik and Munday [5].