Abstract
The paper deals with a single-server n-unit system subject to random inspection and several failure modes. It is assumed that the life-time of a unit is exponentially distributed while all the other time distributions involved are arbitrary. At any instant t, 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 corresponding to different initial conditions. Analysis is developed for several service strategies. Various system characteristics of practical significance, namely, 1. (1) s-expected number of idle inspections in [0, t], 2. (2) s-expected number of actual inspections in [0, t] and 3. (3) s-expected number of repairs of type i (1 ≤ i ≤ r) in [0, t], have been explicitly obtained. A cost-benefit analysis of the system is developed by making use of the above obtained system characteristics. An economics-related measure of system-effectiveness, namely, s-expected net gain per unit time in [0, t] has been obtained.
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