Mani Sharifi - Department of Information Systems & Analytics, Farmer School of Business, Miami University, Oxford, Ohio, United States of America

In this paper, we study a redundancy allocation problem. The investigated problem has a system with s serially connected subsystems, which are under periodic inspection. In each subsystem, component failures are diagnosed by a perfect switching system, and the first component on the standby queue starts working as a replacement for the failed component. . The failures of the components are detected at inspection. The failed component(s) will be repaired during the next inspection interval and added to the standby queue. The subsystems can be in different states depending on their working component and the order of the components on the standby queue. We present an approach to calculate the subsystems-states transition probabilities. We used a two-phase approach to minimize the system cost. In the first phase, we minimize the subsystem's expected total cost by determining the optimal number of components and the optimal subsystem's inspection intervals. The expected total cost consists of downtime, repair, and inspection costs of the subsystems per unit time. Then, in the second phase, we determine the optimum allocated components to each subsystem under some constraints to find the optimal system inspection cost per unit time

Redundancy allocation problem, Periodic inspection, Inspection interval, Transition probabilities, Standby configuration, Markov theory