STOCHASTIC BEHAVIOR OF A 2-UNIT STANDBY SYSTEM WITH CONTACT FAILURE AND INTERMITTENTLY AVAILABLE REPAIR FACILITY

A two-unit standby redundant system with exponential failure-time distribution is considered. It is assumed that system must keep good contact with other systems otherwise its operation is just futile. Contact ceases at an exponential rate. A switch is used to switch in standby unit to operate and it is successful with a known probability. Repair facility is available at the time of failure of a unit with a known probability. If it is available, repair starts, otherwise the unit waits for repair. Repair facility can be made available by paying extra cost. Times to restore contact and time for which repair facility is preoccupied are also general. The system is analysed by studying the underlying semi-Markov process and a large number of system parameters are obtained viz. MTSF, steady-state availability, expected number of visits to a state, absorption probabilities. Some of the parameters have been studied for their behaviour. In the sequence Howard’s reward structure has been superimposed on the above semi-Markov process to obtain expected profit. Discounting is also mentioned at the end. Two optimization problems are posed treating mean-time to repair, mean time to preoccupation, etc., as decision variables and expected profit as the criterion. Several earlier models are included as special cases. © 1979 Taylor & Francis Group, LLC.