A versatile stochastic maintenance model with reserve and super-reserve machines (Q1397230)

The authors consider a class of stochastic reliability systems with three groups of machines, main working, reserve, and `super-reserve'. Main working machines are subject to exponential failures and the repair times are generally distributed. As soon as a main machine breaks down, it is immediately replaced by an available reserve machine. If the main facility is restored to its original quantity, the repair facility leaves on routine maintenance and renewals come from the super-reserve group until the latter becomes exhausted. Then, the busy period is regenerated. The authors analyze the random process describing the number of main and reserve machines using two-variate Markov and semi-regenerative processes, and a duality principle. This model is applicable to computer networking, human resources, and manufacturing processes.