MUT of a one out of two system with preventive maintenance

We are interested in the MUT (Mean Up Time) of a one out of two system in cold standby with preventive maintenance: a preventive maintenance occurs when the working unit reaches a given age. We study in details the stationary distribution of the Markov chain describing the state of the system at the beginning of its working periods. We give exact analytical formulas from which we derive a way to compute the MUT and we compare the results with those of Smith and Decker [M.A.J. Smith, R. Decker, Preventive maintenance in a 1 out of n system: The uptime, downtime and costs, European Journal of Operational Research 99 (1997) 565–583] which are based on approximations. We also investigate some discontinuities problems.