Reliability modeling of modular k-out-of-n systems with functional dependency: A case study of radar transmitter systems

The k-out-of-n systems are among the most important redundancy structures in engineering practices, and their reliability assessment has been extensively studied in the past decades. However, components in a k-out-of-n structure are often subject to functional dependency (FDEP), in which component states are affected by other components’ states in the system. In this article, we study a new system structure, namely modular k-out-of-n system with FDEP. In such a system, the failure of some specific components will disable some components in the k-out-of-n structure. Bayesian network (BN) models are used to construct the structure function of modular k-out-of-n systems. The parameters encoded in the graphical structure of the modular k-out-of-n system are automatically generated by a customized algorithm. Furthermore, a dynamic BN (DBN) is developed to update the reliability of modular k-out-of-n system dynamically when observation data are collected from either component or system level. The Birnbaum importance measure of the different types of components in the modular k-out-of-n system is also evaluated by the DBN model via inserting evidence of the components’ states overtime. A real-world case of a radar transmitter system in the space launch site is studied to demonstrate the effectiveness of the proposed method.