Reliability analysis of a multi-component machining system with service interruption, imperfect coverage, and reboot

In this study, the reliability and queueing characteristics of the fault-tolerant system (FTS) with unreliable server, vacation, and working breakdown are investigated. The performance metrics of FTS having L on-line and W warm standby machines are derived by incorporating the impact of recovery failure along with reboot process. If the failures/faults in the system are not covered successfully due to imperfect switching, the system reconfigures automatically by rebooting to clear the faults. It is assumed that when there is no failed machine in the system, the idle server can take a vacation and return as soon as a unit fails and requires repair. The failed units of FTS are repaired by a single failure-prone operator who can provide the repair with a slower rate in the partially failed state also. To develop Markov model, Chapman-Kolmogorov equations are framed for the system states, and transient probabilities are obtained by computing eigenvalues of transition matrix and using a spectral method. The queueing and reliability metrics are established to explore the redundancy and maintainability issues for the up-gradation of system design. By taking an illustration, numerical results for performance metrics and cost optimization are presented to examine the variation in system parameters.