Vacation Policy for k-out-of-n Redundant System with Reboot Delay

Abstract

Redundancy is a well-known concept for system resilience; k-out-of-n redundancy stipulates that a minimum number of functional components must be present for the system to function. Introducing a reboot delay acknowledges the temporal complexities of system recovery after a failure. A dynamic component is added by the vacation policy, which introduces strategic downtime for system components. This work predicts the performance measures of a multi-state system consisting of two subsystems A and B. Subsystem A follows the k-out-of-n: F policy and subsystem B has m working units and s warm standby units. The system is under the consideration of a single unreliable repairman who may go allow for vacation. There are two possibilities for a repairman’s vacation: if the system failed and the repairman is on vacation, in that case, if the repairman immediately returns from vacation, he/ she repairs the system but if the repairman does not return immediately from vacation, then the system takes a reboot action and when the repairman available, he/ she repairs the system. Failure and repair time of the units are expected to pursue an exponential distribution. In addition, the vacation time and reboot time regarding the failure of the units also pursue an exponential distribution. The concept of reboot and repairman’s vacation are incorporated to make the model more practical and versatile. The expressions for several performance measures such as availability, reliability, and MTTF are obtained with the help of the Markov process. Likewise, sensitivity analysis is done to study the impact of various parameters on system performance measures. The results are explained by taking numerical illustrations.