Inspection interval optimization for a k-out-of-n load sharing system under a hybrid mixed redundancy strategy

In this paper, we optimize the periodic inspection interval for a k-out-of-n load sharing system with a mixed redundancy strategy in which the components are identical. The system is inspected at fixed intervals. If the system has any failed components, they will be detected at the end of the inspection interval. The components will be sent for repair at the beginning of the next inspection interval and will be available at the end of the interval. We assume the component's repair time is less than the inspection interval. Similarly, if the system fails to work during an inspection interval, it will be detected at the end of the interval. In the proposed hybrid mixed redundancy strategy, the system starts working with any number of components between k and n, depending on the number of the available components at the beginning of the inspection interval. We consider replacing the failed component with a new one from the standby queue using an imperfect discrete switch. Moreover, after a component's failure, its load will be shared among the remaining components, which causes an increase in their failure rates. The presented work aims to find the optimal total expected system cost per unit time by determining the number of working components at the beginning of each time interval and the inspection interval. The expected total system cost consists of the system's inspection cost, components' repair cost, system's downtime cost, and repair cost. The presented problem is solved with a full enumeration method and a new heuristic algorithm. The results show the superiority of the presented mixed redundancy strategy in comparison with the traditional strategies. Moreover, the proposed heuristic algorithm performs better in terms of computational time (up to one percent) compared to the full enumeration techniques.