Abstract
A single-server n-unit system subject to random inspection and several failure modes has been investigated under the supposition that the failure time of a unit is distributed arbitrarily, while all the other time distributions involved are exponential. At any instant t, the system is characterized by the probabilities of its being in the “up” or “down” state. Integral equations are established for these probabilities by identifying the system at suitable regenerative epochs corresponding to different initial conditions. Various system parameters of significance, namely: 1.1.s-expected number of inspections in [O, t],2.2.s-expected number of repairs of different types in [O, t] and3.3.s-expected net gain per unit time in [O, t], habe been obtained.
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