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Affine arithmetic for assessing the uncertainty propagation on steady-state probabilities of Markov models owing to uncertainties in transition rates

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  • Claudio M Rocco S

Abstract

This article proposes the use of affine arithmetic as an alternative approach for assessing the effects of uncertainties of transition rates on the steady-state probabilities for each possible state of a system represented by a Markov model. Affine arithmetic is an extension of interval arithmetic, able to track “the dependency between variables throughout calculations†and to provide strict bounds. Several examples illustrate the proposed approach. Results are compared with other approaches, such as interval arithmetic, Monte Carlo simulation or solving linear systems of simultaneous equations.

Suggested Citation

  • Claudio M Rocco S, 2013. "Affine arithmetic for assessing the uncertainty propagation on steady-state probabilities of Markov models owing to uncertainties in transition rates," Journal of Risk and Reliability, , vol. 227(5), pages 523-533, October.
    • Handle: RePEc:sae:risrel:v:227:y:2013:i:5:p:523-533
    DOI: 10.1177/1748006X13485189
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    References listed on IDEAS

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    1. 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.
    2. 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:

    1. 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.

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