Decision diagram based methods and reliability analysis for k -out-of- n : G systems
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DOI 10.1007/s12206-014-0902-z
Decision diagram based methods and reliability analysis for k-out-of-n: G systems† Shumin Li, Shudong Sun, Shubin Si*, Shuai Zhang and Hongyan Dui School of Mechanical,Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China (Manuscript Received January 14, 2014; Revised March 27, 2014; Accepted April 23, 2014) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract 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 kout-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 kout-of- n: G system. Keywords: Binary decision diagrams; Multi-state multi-valued decision diagram; k-out-of-n: G systems; Multi-state system ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction In a binary reliability system, the system and its components have only two possible states: either working or failed. In a multi-state system, both the system and its components may have more than two states, for example, completely working, partially working, and completely failed. In the binary context, a k-out-of-n: G/F system with n components works/fails if and only if at least k components work/fail. Both series and parallel systems are special cases of the k-out-of-n: G/F systems [1]. A series system is an n-outof-n: G system, while a parallel system is a 1-out-of-n: G system. In other words, a series system is a 1-out-of-n: F system, while a parallel system is an n-out-of-n: F system. Wu and Chen [2] generalized the binary k-out-of-n system model into the binary weighted k-out-of-n model. The definitions of binary systems have been extended to the multi-state cases by allowing both the system and its components to have more than two possible states [3-5]. The state of a multi-state k-out-of-n: G system was defined to b
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