Component selection for optimal reliability of a repairable load-sharing system

This study determines the number of components in each subsystem that maximizes the reliability of a load-sharing [Formula: see text] out of [Formula: see text] system when repair is performed at the subsystem level. Previous studies have obtained the system availability given that repair is performed for each component failure. We explain how the statistical flowgraph model is used for computing system reliability under the assumption of an inverse Gaussian distribution for the repair of each subsystem and an exponential distribution for the lifetime of a component operating at a fixed load. A closed-form expression is derived for the transition probability between the system states and the moment generating function of the corresponding waiting time distribution conditional on the transition. By comparing the reliability of systems using different numbers of components in subsystems, we explain how the optimal solution is affected by the repair process and the component homogeneity among subsystems. We discover that, if repair is not considered, it is optimal to use a single subsystem that has the maximum reliability across different operating loads, whereas the use of multiple subsystems is beneficial if repair is performed for a subsystem with a small number of components.