CUMULATIVE OPERATING TIME DISTRIBUTIONS FOR A CLASS OF NON-MARKOVIAN SERIES SYSTEMS

Consider a series system with separately and independently maintained components. The failure and repair process of each component is assume d to be an alternating renewal process. It is supposed that, for each component, the failure time distribution is exponential whereas the re pair time distribution is general. We derive the Laplace-Stieltjes tra nsform of the distribution of U-c(T), the cumulative time that the ser ies system is operating in [c, c + T], for arbitrary c, T greater than or equal to 0, with respect to T, and obtain the asymptotic distribut ion of U-c(T) as c, T --> infinity.