Stochastic Modeling and Performance Analysis of a 2(k)-out-of-3(n) System with Inspection Subject to Operational Restriction

In repairable redundant systems the failed units can either be repaired or replaced by identical standby to reduce the system down time. The failed units are inspected for repair/replacement. In this paper, two stochastic models for 2(k)-out-of-3(n) redundant system of identical units with repair and inspection are examined stochastically. The system is considered in up-state only if 2(k)-out-of-3(n) units are operative in both the models. Normally, the server either attends the system promptly or may take some time, after failure. The system is studied under an operational restriction on the inspection i.e. in case when system has only one unit in operational mode the server has to attend the system for inspection. Semi-Markov processes and Regenerative point technique is adopted to obtain the expressions for measures of system effectiveness 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 also carried out for the system models.