Analysis of an n ‐unit cold‐standby system with general failure and repair time distributions

Analyses an n ‐unit cold‐standby system with a single repair facility under the assumption that the failure and repair times are arbitrarily distributed. Develops a mathematical model using semi‐regenerative processes. Obtains a system of integral equations satisfied by various state probabilities corresponding to different initial conditions. Obtains explicit expressions for the expected number of failures and expected number of visits to down state in a specified interval of time. Discusses two special cases when either the failure or repair rate is constant. Analyses numerically and compares particular cases with one, two and three units by assuming Weibull distribution for failure time and normal distribution for repair time.