STOCHASTIC MODELING AND PERFORMANCE ANALYSIS OF A 2(K)-OUT-OF-3(N) SYSTEMWITH INSPECTION SUBJECT TO OPERATIONAL RESTRICTION

In repairable redundant systems the failed units can either be repaired or replaced byidentical standby to reduce the system down time. The failed units are inspected forrepair/replacement. In this paper, two stochastic models for 2(k)-out-of-3(n) redundant system ofidentical units with repair and inspection are examined stochastically. The system is consideredin up-state only if 2(k)-out-of-3(n) units are operative in both the models. Normally, the servereither attends the system promptly or may take some time, after failure. The system is studiedunder an operational restriction on the inspection i.e. in case when system has only one unit inoperational mode the server has to attend the system for inspection. Semi-Markov processes andRegenerative point technique is adopted to obtain the expressions for measures of systemeffectiveness such as transition probabilities, mean sojourn times, mean time to system failure,steady state availabilities, busy periods, expected number of visits etc. Cost-analysis is alsocarried out for the system models.