Abstract
The stochastic behaviour of a single-server two-unit system subject to random inspection and two 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. Further, it is assumed that there is a single service facility which serves the dual purpose of inspection and repair. The system is characterized by the probabilities of its being in the “up” or “down” state. Integral equations are set up for these probabilities by identifying the system at suitable regenerative epochs. Laplace-transform technique is adopted to solve these equations. Various system parameters of vital significance, namely: 1.(1) point-wise availability of the system at instant t,2.(2) s-expected up-time of the system in [0, t],3.(3) s-expected inspection-time of the server in [0, t],4.(4) s-expected repair-time of type i (i = 1,2) in [0, t],5.(5) s-expected net gain per unit time in [0, t] and6.(6) steady-state availability of the system have been obtained explicitly.
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