A robust system reliability analysis using partitioning and parallel processing of Markov chain

2014 ◽  
Vol 28 (4) ◽  
pp. 311-322 ◽  
Author(s):  
Po Ting Lin ◽  
Yu-Cheng Chou ◽  
Yung Ting ◽  
Shian-Shing Shyu ◽  
Chang-Kuo Chen
Keyword(s):  
Markov Chain ◽  
Parallel Processing ◽  
Reliability Analysis ◽  
System Reliability ◽  
Large Scale ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Processing Unit ◽  
Central Processing ◽  
System Reliability Analysis

AbstractThis paper presents a robust reliability analysis method for systems of multimodular redundant (MMR) controllers using the method of partitioning and parallel processing of a Markov chain (PPMC). A Markov chain is formulated to represent the N distinct states of the MMR controllers. Such a Markov chain has N2 directed edges, and each edge corresponds to a transition probability between a pair of start and end states. Because N can be easily increased substantially, the system reliability analysis may require large computational resources, such as the central processing unit usage and memory occupation. By the PPMC, a Markov chain's transition probability matrix can be partitioned and reordered, such that the system reliability can be evaluated through only the diagonal submatrices of the transition probability matrix. In addition, calculations regarding the submatrices are independent of each other and thus can be conducted in parallel to assure the efficiency. The simulation results show that, compared with the sequential method applied to an intact Markov chain, the proposed PPMC can improve the performance and produce allowable accuracy for the reliability analysis on large-scale systems of MMR controllers.

System reliability analysis in spatially variable slopes using coupled Markov chain and MARS

2020 ◽  
Vol 13 (20) ◽  
Author(s):  
Dehui Kong ◽  
Qiang Luo ◽  
Wensheng Zhang ◽  
Liangwei Jiang ◽  
Liang Zhang
Keyword(s):  
Markov Chain ◽  
Reliability Analysis ◽  
System Reliability ◽  
System Reliability Analysis

Complementary Interaction Method (CIM) for System Reliability Analysis

2007 ◽  
Author(s):  
Byeng D. Youn ◽  
Pingfeng Wang ◽  
Zhimin Xi ◽  
David J. Gorsich
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Large Scale ◽  
Higher Order ◽  
Interaction Method ◽  
Reliability Based Design ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Eigenvector Dimension Reduction ◽  
Reliability Methods

Researchers desire to evaluate system reliability uniquely and efficiently. Despite years of research, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. For system reliability bounds, the probabilities of the second or higher order joint events are assumed to be known exactly although there is no numerical method to evaluate them effectively. Two primary challenges in system reliability analysis are how to evaluate the probabilities of the second or higher order joint events and how to uniquely obtain the system reliability so that the system reliability can be used for Reliability-Based Design Optimization (RBDO). This paper proposes the Complementary Interaction Method (CIM) to define system reliability in terms of the probabilities of the component events, Ei = (X |Gi ≤ 0), and the complementary interaction events, Eij = (X |Gi*Gj ≤ 0). For large-scale systems, the probabilities of the component and complementary interaction events can be conveniently written in the CI-matrix. In this paper, three different reliability methods will be used to construct the CI-matrix numerically: First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM), and the Eigenvector Dimension Reduction (EDR) method. Two examples will be employed to demonstrate that the CIM with the EDR method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

Investigation of Numerical Performance of Partitioning and Parallel Processing of Markov Chain (PPMC) for Complex Design Problems

2014 ◽  
Author(s):  
Po Ting Lin ◽  
Yu-Cheng Chou ◽  
Mark Christian E. Manuel ◽  
Kuan Sung Hsu
Keyword(s):  
Markov Chain ◽  
Parallel Processing ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Divide And Conquer ◽  
Threshold Parameter ◽  
Network Systems ◽  
Numerical Efficiency ◽  
Numerical Performance

Divide-and-conquer strategies have been utilized to perform evaluation calculations of complex network systems, such as reliability analysis of a Markov chain. This paper focuses on partitioning of Markov chain for a multi-modular redundant system and the fast calculation using parallel processing. The complexity of Markov chain is first reduced by eliminating the connections with low transition probabilities associated with a threshold parameter. The transition probability matrix is then reordered and partitioned such that a worse-case reliability is evaluated through the calculations in only the diagonal sub-matrices of the transition probability matrix. Since the calculations of the sub-matrices are independent to each other, the numerical efficiency can be greatly improved using parallel computing. The numerical results showed the selection of threshold parameter is a key factor to numerical efficiency. In this paper, the sensitivity of the numerical performance of Partitioning and Parallel-processing of Markov Chain (PPMC) to the threshold parameter has been investigated and discussed.

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