Abstract In this paper, a n-unit cold-standby system with a single repair facility is analysed using two approximate methods namely, cutting and clustering the state space. It has been assumed that the failure rate is constant and the repair time is arbitrarily distributed. A mathematical model is developed using semi-regenerative phenomena and systems of convolution integral equations satisfied by various state probabilities corresponding to different initial conditions are obtained. Explicit expressions for the expected number of failures and expected number of repair completions in an interval [0, t] are obtained. An iterative numerical method is used to solve the systems of integral equations obtained and a comparative study has been carried out between exact and approximate solutions.