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Assessment of the transition-rates importance of Markovian systems at steady state using the unscented transformation

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  • Rocco S., Claudio M.
  • Emmanuel Ramirez-Marquez, José

Abstract

The Unscented Transformation (UT) is a technique to understand and compute how the uncertainty of a set of random variables, with known mean and variance is propagated on the outputs of a model, through a reduced set of model evaluations as compared with other approaches (e.g., Monte Carlo). This computational effort reduction along with the definition of a proper UT model allows proposing an alternative approach to quantify the transition rates (TR) having the highest contribution to the variance of the steady-state probability, for each possible state of a system represented by a Markov model. The so called “main effects†of each transition rate, as well as high order component interactions are efficiently derived from the solution of only (2n+1) linear system of simultaneous equations, being n the number of transition rates in the model.

Suggested Citation

  • Rocco S., Claudio M. & Emmanuel Ramirez-Marquez, José, 2015. "Assessment of the transition-rates importance of Markovian systems at steady state using the unscented transformation," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 212-220.
    • Handle: RePEc:eee:reensy:v:142:y:2015:i:c:p:212-220
    DOI: 10.1016/j.ress.2015.05.019
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    References listed on IDEAS

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    1. Li, Junye, 2013. "An unscented Kalman smoother for volatility extraction: Evidence from stock prices and options," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 15-26.
    2. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2008. "Reliability importance analysis of Markovian systems at steady state using perturbation analysis," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1605-1615.
    3. Badea, Anca Costescu & Rocco S., Claudio M. & Tarantola, Stefano & Bolado, Ricardo, 2011. "Composite indicators for security of energy supply using ordered weighted averaging," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 651-662.
    4. Rocco Sanseverino, Claudio M. & Ramirez-Marquez, José Emmanuel, 2014. "Uncertainty propagation and sensitivity analysis in system reliability assessment via unscented transformation," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 176-185.
    5. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2010. "From differential to difference importance measures for Markov reliability models," European Journal of Operational Research, Elsevier, vol. 204(3), pages 513-521, August.
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    Cited by:

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    3. Yeh, Wei-Chang, 2023. "QB-II for evaluating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    4. Yeh, Wei-Chang & Tan, Shi-Yi & Forghani-elahabad, Majid & Khadiri, Mohamed El & Jiang, Yunzhi & Lin, Chen-Shiun, 2022. "New binary-addition tree algorithm for the all-multiterminal binary-state network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    5. Yeh, Wei-Chang & Tan, Shi-Yi & Zhu, Wenbo & Huang, Chia-Ling & Yang, Guang-yi, 2022. "Novel binary addition tree algorithm (BAT) for calculating the direct lower-bound of the highly reliable binary-state network reliability," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    6. Yeh, Wei-Chang, 2022. "Novel self-adaptive Monte Carlo simulation based on binary-addition-tree algorithm for binary-state network reliability approximation," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    7. Lin, Yan-Hui & Yam, Richard C.M., 2017. "Uncertainty importance measures of dependent transition rates for transient and steady state probabilities," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 402-409.
    8. Yeh, Wei-Chang, 2021. "Novel Algorithm for Computing All-Pairs Homogeneity-Arc Binary-State Undirected Network Reliability," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

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