Fuzzy metrics and cost optimization of a fault-tolerant system with vacationing and unreliable server

Abstract

A finite population fuzzy model for the fault-tolerant system (FTS) is studied by considering the general distributed repair time, server vacation, and server breakdown. The concept of imperfect recovery, along with reboot process, is considered for the evaluation of fuzzy performance indices of an FTS supported by warm standbys. If the faults in the system are not detected successfully, then FTS reconfigures itself automatically by rebooting. When the system becomes free from the assigned repair jobs, the idle server can take a vacation and returns from the vacation in case a machine fails and requires repair. The single failure-prone server can provide the repair of failed machines with a slower rate in the breakdown state also. The parametric non-linear programming approach is implemented for the evaluation of performance metrics in a fuzzified environment using system parameters as a trapezoidal fuzzy number. The supplementary variable and recursive approaches are employed to obtain the system size distribution of the M/G/1 model by taking remaining repair time as a supplementary variable. The cost analysis is performed in order to determine the suitable control parameters using harmony search approach. The impacts of the sensitive system parameters on the performance of FTS are explored by evaluating numerical results for specific distributions of repair time.