Fuzzy modelling and cost optimization of fault-tolerant system with service interruption

Redundancy and maintainability-supported fault-tolerant machining systems are used in many industries to achieve pre-specified reliability and system capability. In this investigation, a non-Markov model for the machining system has been developed by involving the concepts of server vacation, server breakdown, and reboot process. The server may fail and undergo primary repair which may be unsuccessful in recovering the server. In case of imperfect server repair, an additional repair is also performed to bring the server back into functional mode. By using the supplementary variable for the residual repair, we obtain the analytic solution of the finite population M/G/1 queueing model for the performance prediction of FTMS. The method of parametric non-linear programming has been implemented to evaluate the performance measures in both crisp and fuzzy environments. The meta-heuristic approaches PSO, GA and classical optimization technique quasi-Newton method are employed to determine the optimal design descriptors by minimizing the total cost. The sensitivity of performance indices with respect to system parameters has been examined for the specific repair time distributions by taking illustrations.