Joint reliability importance analysis of components in uncertain Boolean system

Joint reliability importance is a measure of interaction of two or more system components for their contribution to the reliability of a system. Boolean system is a system with binary states and all of its components also have binary states. Here, binary states mean working or failing. Considering the limitation of resources used to maintain system, we should allocate resources according to the joint reliability importance of components and fully utilize resources in the most important set of components of the system to optimize system performance. Hence, joint reliability importance is valuable for system optimization. In this paper, we proposed the concept of uncertain joint reliability importance of components in a Boolean system where the component and the system is modeled by uncertain variable. Then some formulae are proved to compute uncertain joint reliability importance of a pair or groups of components. Finally, the results are applied into some special systems, such as series system, parallel system as well as k-out-of-n system. Also, we give some examples to show how calculate the uncertain two-component and multi-component joint reliability importance. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.