Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T16:48:32.123Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  30 September 2014

Po Ting Lin ,
Yu-Cheng Chou ,
Yung Ting ,
Shian-Shing Shyu  and
Chang-Kuo Chen
Po Ting Lin
Affiliation:
Department of Mechanical Engineering, Research and Development Center for Microsystem Reliability, Center for Biomedical Technology, Chung Yuan Christian University, Chungli City, Taiwan
Yu-Cheng Chou*
Affiliation:
Institute of Undersea Technology, National Sun Yat-sen University, Kaohsiung City, Taiwan
Yung Ting
Affiliation:
Department of Mechanical Engineering, Chung Yuan Christian University, Chungli City, Taiwan
Shian-Shing Shyu
Affiliation:
Institute of Nuclear Energy Research, Atomic Energy Council, Chungli City, Taiwan
Chang-Kuo Chen
Affiliation:
Institute of Nuclear Energy Research, Atomic Energy Council, Chungli City, Taiwan
*
Reprint requests to: Yu-Cheng Chou, Institute of Undersea Technology, National Sun Yat-sen University, 70 Lienhai Road, Kaohsiung City 80424, Taiwan. E-mail: ycchou@mail.nsysu.edu.tw
Get access Rights & Permissions [Opens in a new window]

Abstract

This 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.

Keywords

Fault ToleranceMarkov ChainM-PartitioningParallel ProcessingReliability Analysis
Type
Special Issue Articles
Information
AI EDAM , Volume 28 , Issue 4: Design of Complex Engineered Systems , November 2014 , pp. 311 - 322
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aldemir, T., Miller, D., Stovsky, M., Kirschenbaum, J., & Buccim, P. (2006). Current State of Reliability Modeling Methodologies for Digital Systems and Their Acceptance Criteria for Nuclear Power Plant Assessments. Washington, DC: US Nuclear Regulatory Commission.Google Scholar
Bhaduri, D., Shukla, S.K., Graham, P.S., & Gokhale, M.B. (2007). Reliability analysis of large circuits using scalable techniques and tools. IEEE Transactions on Circuits and Systems I 54(11), 2447–2460.Google Scholar
Cai, B., Liu, Y., Liu, Z., Tian, X., Li, H., & Ren, C. (2012). Reliability analysis of subsea blowout preventer control systems subjected to multiple error shocks. Journal of Loss Prevention in the Process Industries 25, 1044–1054.Google Scholar
Cannon, L.E. (1969). A cellular computer to implement the Kalman filter algorithm. PhD Thesis. Montana State University.Google Scholar
Chou, Y.-C., & Lin, P.T. (2014). An efficient and robust design optimization of multi-state flow network for multiple commodities using generalized reliability evaluation algorithm and edge reduction method. International Journal of Systems Science. Advance online publication. doi:10.1080/00207721.2013.879228Google Scholar
Dominguez-Garcia, A.D., Kassakian, J.G., & Schindall, J.E. (2006). Reliability evaluation of the power supply of an electrical power net for safety-relevant applications. Reliability Engineering & System Safety 91(5), 505–514.Google Scholar
Grama, A., Gupta, A., Karypis, G., & Kumar, V. (2004). Introduction to Parallel Computing. Essex: Pearson Education.Google Scholar
Gropp, W. (2002). MPICH2: A new start for MPI implementations. Proc. 9th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface.Google Scholar
Gropp, W., Huss-Lederman, S., Lumsdaine, A., Lusk, E., Nitzberg, B., Saphir, W., & Snir, M. (1998). MPI: The Complete Reference—The MPI-2 Extensions. Cambridge, MA: MIT Press.Google Scholar
Guo, H., & Yang, X. (2008). Automatic creation of Markov models for reliability assessment of safety instrumented systems. Reliability Engineering & System Safety 93(6), 829–837.Google Scholar
Han, J., Gao, J., Jonker, P., Qi, Y., & Fortes, J.A. (2005). Toward hardware-redundant, fault-tolerant logic for nanoelectronics. IEEE Design & Test of Computers 22(4), 328–339.Google Scholar
Kim, H., Lee, H., & Lee, K. (2005). The design and analysis of AVTMR (all voting triple modular redundancy) and dual-duplex system. Reliability Engineering & System Safety 88(3), 291–300.Google Scholar
Lin, P.T., Chou, Y.-C., Manuel, M.C.E., & Hsu, K.S. (2014). Investigation of numerical performance of partitioning and parallel processing of Markov chain (PPMC) for complex design problems. Proc. ASME 2014 Int. Design & Engineering Technical Confs. and Computers & Information in Engineering Conf., IDETC/CIE 2014, Paper No. DETC2014-34652, Buffalo, NY.Google Scholar
Lisnianski, A., Elmakias, D., Laredo, D., & Ben Haim, H. (2012). A multi-state Markov model for a short-term reliability analysis of a power generating unit. Reliability Engineering & System Safety 98(1), 1–6.Google Scholar
Liu, Y., & Rausand, M. (2011). Reliability assessment of safety instrumented systems subject to different demand modes. Journal of Loss Prevention in the Process Industries 24(1), 49–56.Google Scholar
Liu, Z., Liu, Y., Cai, B., Liu, X., Li, J., Tian, X., & Ji, R. (2013). RAMS analysis of hybrid redundancy system of subsea blowout preventer based on stochastic Petri nets. International Journal of Security and Its Applications 7(4), 159–166.Google Scholar
Liu, Z., Ni, X., Liu, Y., Song, Q., & Wang, Y. (2011). Gastric esophageal surgery risk analysis with a fault tree and Markov integrated model. Reliability Engineering & System Safety 96(12), 1591–1600.Google Scholar
Matthews, P., & Philip, A. (2012). Bayesian project diagnosis for the construction design process. Artificial Intelligence for Engineering Design, Analysis and Manufacturing 26(4), 375–391.Google Scholar
Mutha, C., Jensen, D., Tumer, I., & Smidts, C. (2013). An integrated multidomain functional failure and propagation analysis approach for safe system design. Artificial Intelligence for Engineering Design, Analysis and Manufacturing 27(4), 317–347.Google Scholar
Parashar, B., & Taneja, G. (2007). Reliability and profit evaluation of a PLC hot standby system based on a master-slave concept and two types of repair facilities. IEEE Transactions on Reliability 56(3), 534–539.Google Scholar
Snir, M., Otto, S., Huss-Lederman, S., Walker, D., & Dongarra, J. (1998). MPI: The Complete Reference—The MPI Core. Cambridge, MA: MIT Press.Google Scholar
Soro, I.W., Nourelfath, M., & Ait-Kadi, D. (2010). Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance. Reliability Engineering & System Safety 95(2), 65–69.Google Scholar
Stewart, W.J. (2009). Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton, NJ: Princeton University Press.Google Scholar
Wang, S., Ji, Y., Dong, W., & Yang, S. (2007). Design and RAMS analysis of a fault-tolerant computer control system. Tsinghua Science & Technology 12(Suppl. 1), 116–121.Google Scholar
Yu, H., Chu, C., Châtelet, Ė., & Yalaoui, F. (2007). Reliability optimization of a redundant system with failure dependencies. Reliability Engineering & System Safety 92(12), 1627–1634.Google Scholar
Zhang, C.W., Zhang, T., Chen, N., & Jin, T. (2013). Reliability modeling and analysis for a novel design of modular converter system of wind turbines. Reliability Engineering & System Safety 111, 86–94.CrossRefGoogle Scholar
Zhang, T., Long, W., & Sato, Y. (2003). Availability of systems with self-diagnostic components-applying Markov model to IEC 61508-6. Reliability Engineering & System Safety 80(2), 133–141.Google Scholar