Reliability Evaluation of Reconfigurable NMR Architecture Supported with Hot Standby Spare: Markov Modeling and Formulation
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The document discusses the reliability evaluation of reconfigurable non-modular redundancy (NMR) architectures with hot standby spares using Markov modeling. It outlines the basic concepts of fault tolerance, redundancy types, and provides numerical results for various system configurations. The study culminates in a parametric formula for reliability evaluation, which aids in system optimization and mean time to failure calculations.
Reliability Evaluation of Reconfigurable NMR Architecture Supported with Hot Standby Spare: Markov Modeling and Formulation
- 1. 1 Reliability Evaluation of Reconfigurable NMR Architecture Supported with Hot Standby Spare: Markov Modelling and Formulation Koorosh Aslansefat, Gholamreza Latif-Shabgahi and Mehrdad Mohammadi Email: k.aslansefat-2018@hull.ac.uk
- 2. 2 Table of Content What we are going to discuss Introduction Introduction, Fault Tolerance and Redundancy Markov Modelling Models, Assumptions, Basic Concepts Reliability Evaluation Reliability Evaluation of Reconfigurable NMR supported with Hot Standby Spares Numerical Results and Conclusion Numerical reliability evaluation of Reconfigurable NMR architectures and Conclusion
- 3. 3 Introduction Redundancy ActivePassive Hybrid Fault tolerance is the property that enables a system to continue operating properly in the event of the failure of (or one or more faults within) some of its components.
- 5. 5 Introduction Active Redundancy ساختارTMR ساختارNMR Cold Standby HOT Standby
- 7. 7 Introduction Hybrid Redundancy ساختارTMR ساختارNMR 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(6), 1044-1054.
- 9. 9 Markov Modelling Assumptions In the beginning the system is healthy. There is no common cause failure. There is no repair or maintenance available for the system. All modules have the same failure rate with the exponential distribution. Upon the failure of each module the spare replaces it immediately. All modules are performing the same computation with the same inputs.
- 14. 14 Markov Modelling 𝑅 𝑇𝑀𝑅_1𝑆 𝑡 = 𝑒−4𝜆𝑡 2 −6𝑐2 + 12𝑐 + 𝑒−3𝜆𝑡 6𝑐2 − 12𝑐 − 2 + 𝑒−2𝜆𝑡 2 −6𝑐2 + 12𝑐 + 6 𝑅5𝑀𝑅_1𝑆 𝑡 = − 𝑒−6𝜆𝑡 6 60𝑐3 − 180𝑐2 + 180𝑐 + 𝑒−5𝜆𝑡 2 60𝑐3 − 180𝑐2 + 180𝑐 + 12 − 𝑒−4𝜆𝑡 2 60𝑐3 − 180𝑐2 + 180𝑐 + 30 + 𝑒−3𝜆𝑡 6 60𝑐3 − 180𝑐2 + 180𝑐 + 60 𝑅7𝑀𝑅_1𝑆 𝑡 = − 𝑒−8𝜆𝑡 24 840𝑐4 − 3360𝑐3 + 5040𝑐2 − 3360𝑐 + 𝑒−7𝜆𝑡 6 840𝑐4 − 3360𝑐3 + 5040𝑐2 − 3360𝑐 − 140 − 𝑒−6𝜆𝑡 4 840𝑐4 − 3360𝑐3 + 5040𝑐2 − 3360𝑐 − 280 + 𝑒−5𝜆𝑡 6 840𝑐4 − 3360𝑐3 + 5040𝑐2 − 3360𝑐 − 504 − 𝑒−4𝜆𝑡 24 840𝑐4 − 3360𝑐3 + 5040𝑐2 − 3360𝑐 − 840
- 15. 15 Markov Modelling 𝑅 𝑁𝑀𝑅_1𝑆 𝑡 = 𝑘= 𝑁+1 2 𝑁+1 𝛼 + 𝛽 𝑁 + 1 − 𝑘 𝑒−𝑘𝜆𝑡 𝑁 + 1 2 ! 𝑁 + 1 2 𝑘 − 𝑁 + 1 2 𝛼 = 𝛥 𝑗=0 𝑁−1 2 𝑁 + 1 2 𝑗 𝑖= 𝑁+1 2 𝑁 𝑖 𝑐 𝑁+1 2 −𝑗 −1 𝑗+1 𝛽 𝑘 = 𝛥 0 𝑘 = 𝑁 + 1 2 𝑘 + 𝑁 + 1 2 𝑁 − 3 2 𝑁 + 1 2 𝑁 + 1 2 𝑂. 𝑊.
- 17. 17 Numerical Results System Type c = 0.3 c = 0.5 c = 0.8 c = 1 Simple TMR 0.75 0.75 0.75 0.75 TMR + HSP 0.83 0.86 0.88 0.90 Simple 5MR 0.80 0.80 0.80 0.80 5MR + HSP 0.87 0.89 0.90 0.91 Simple 7MR 0.85 0.85 0.85 0.85 7MR + HSP 0.91 0.92 0.92 0.92 0.001 at time = 40
- 20. 20 Conclusion What will be the final conclusion A Systematic Markov Model Construction for Reconfigurable NMR supported with Hot Standby Spares has been explained. A parametric formula for reliability evaluation of Reconfigurable NMR architecture supported with one hot standby spare has been obtained that can be used for system optimization. From the parametric equation other factors like Mean Time To Failure can be easily calculated.
- 21. 21 References Selected References • Z. Liu, Y. Liu, B. Cai, X. Liu, J. Li, X. Tian and R. Ji, "RAMS Analysis of Hybrid Redundancy System of Subsea Blowout Preventer Based on Stochastic Petri Nets," International Journal of Security & Its Applications, vol. 7, no. 4, pp. 159-166, 2013. • B. Cai, Y. Liu, Z. Liu, X. Tian, H. Li and C. Ren, "Reliability Analysis of Subsea Blowout Preventer Control Systems Subjected to Multiple Error Shocks," Journal of Loss Prevention in the Process Industries, vol. 25, no. 6, pp. 1044-1054, 2012. • S. Distefano, F. Longo and K. S. Trivedi, "Investigating Dynamic Reliability and Availability through State– Space Models," Computers & Mathematics with Applications, vol. 64, no. 12, pp. 3701-3716, 2012. • F. P. Mathur and A. Avižienis, "Reliability Analysis and Architecture of a Hybrid-redundant Digital System: Generalized Triple Modular Redundancy with Self-repair," in Spring Joint Computer Conference, ACM, 1969. • K. Zhang, G. Bedette and R. F. DeMara, "Triple Modular Redundancy with Standby (TMRSB) Supporting Dynamic Resource Reconfiguration," in IEEE Autotestcon, Anaheim, CA, 2006. • Z. Zhe, L. Daxin, W. Zhengxian and S. Changsong, "Research on Triple Modular Redundancy Dynamic Fault-Tolerant System Model," in First International Multi-Symposiums on Computer and Computational Sciences. IMSCCS, Hanzhou, Zhejiang, 2006.
- 22. 22 Thanks for Your Attention If you have any question, please feel free to ask