A generalized multi-standby multi-failure mode system with various repair facilities

Abstract We consider a system of ( m + 1) non-identical units—one functioning and m standby. Each unit of the system has the following states: normal, N types of partial failures and corresponding to them N types of total failures. There are k distinct major repair facilities and one on the spot repairman. One unit can pass from one state to another with known probability and then the time of staying in this state has a general distribution. The system starts to work at t = 0 and fails when the ( m + 1)th unit after a total failure is finally rejected. Using semi-Markov techniques we obtain Laplace transforms of transition probabilities. Considering particular cases we derive known results for systems which have been defined in the past.