Reliability Analysis of <i>k</i> ‐out‐of‐ <i>n</i> Systems With the Common‐Cause Failure Based on Dynamic Bayesian Network Method

ABSTRACT The k ‐out‐of‐ n systems are widely adopted to improve systems reliability. However, conventional reliability models tend to ignore the impact of common‐cause failure (CCF), resulting in potentially overestimated reliability predictions. To address this problem, this paper proposes the k ‐out‐of‐ n systems reliability analysis method based on dynamic Bayesian network (DBN). First, the CCF of the k ‐out‐of‐ n systems is described using the β ‐factor, and the state transfer relation is identified by Markov method. Secondly, each system is taken as the root node of the DBN, and the Markov state transition matrix is converted to the DBN state transition matrix by using matrix function e M t . Finally, the sensitivity analysis is performed using DBN to identify weak components. The feasibility and effectiveness of the proposed method are verified by a numerical example of an aircraft power system. This approach solves the complexity of DBN dealing with CCF modeling.