Decision diagram based methods and reliability analysis for k-out-of-n: G systems

Binary k-out-of-n systems are commonly used reliability models in engineering practice. Many authors have extended the concept of k-out-of-n system to multi-state k-out-of-n systems. This paper proposes a binary decision diagram (BDD) based approach for binary k-out-of-n: G system and a multi-state multi-valued decision diagram (MMDD) based approach for multi-state k-out-of-n: G system. BDD and MMDD have been extensively used for representing and manipulating logic functions in many areas, including reliability modeling and analysis. In this paper, patterns of BDD/MMDD for binary/multi-state k-out-of-n: G system are summarized and proved, a two-step algorithmic process is proposed for modeling the BDD/MMDD and three case studies are implemented to demonstrate the presented methods. Complexity analysis shows that the presented method is more computationally efficient than the traditional algorithms for k-out-of-n: G system.