A Contribution to the Evaluation of Imprecise Availability of Complex Systems Using Markov Models

Akrouche, Joanna; Sallak, Mohamed; Châtelet, Éric; Abdallah, Fahed; Chehade, Hiba Haj

doi:10.7712/120217.5383.16866

Cited by 2 publications

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“…In this work, we propose the use of imprecise Markov models for the calculation of the availability of an MMS. In a previous paper [7], we have some preliminary work about this subject.…”

Section: Introductionmentioning

confidence: 99%

New method for availability computing of complex systems using imprecise Markov models

Akrouche

Sallak

Châtelet³

et al. 2018

Proceedings of the 10th IMA International Conference on Modelling in Industrial Maintenance and Reliability

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The system availability is defined as the probability that the system is operational at a given time. To compute the availability of a multi-states system (the system and its components could have multi-states), we have to sum over all the probabilities of the components working states, therefore these probability precise values are required. In some cases (rare event failures, new components, ...), it isn't possible to obtain the working probabilities precisely because of the lack of data. In this work, we propose to apply imprecise continuous Markov chain where the failure and repair rates are imprecise. Only few works were developed using this concept. The precise initial distributions are replaced by intervals, which represents the unknown initial probabilities and the unknown transition matrix. The interval constraint propagation method is exploited for the first time, in availability modeling, to compute the imprecise multi-states system availability. The probability interval bounds associated to real variables are contracted, without removing any value that may be consistent with the set of constraints. The proposed methodology is guaranteed, and different examples of complex systems with some properties (convergence, ergodicity, ...) are studied. All the numerical examples and results will be discussed in the paper.

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“…In this work, we propose the use of imprecise Markov models for the calculation of the availability of an MMS. In a previous paper [7], we have some preliminary work about this subject.…”

Section: Introductionmentioning

confidence: 99%

New method for availability computing of complex systems using imprecise Markov models

Akrouche

Sallak

Châtelet³

et al. 2018

Proceedings of the 10th IMA International Conference on Modelling in Industrial Maintenance and Reliability

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“…To our knowledge, the combination of a Markovian approach with interval contraction methods has not been investigated. Note that a preliminary work concerning our approach was briefly presented in our short conference papers [39,40]. Apart from the novelty of our proposed work, we can note many reasons to justify why such an extension is appealing:…”

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confidence: 99%

Methodology for the Assessment of Imprecise Multi-State System Availability

et al. 2022

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Most existing studies of a system’s availability in the presence of epistemic uncertainties assume that the system is binary. In this paper, a new methodology for the estimation of the availability of multi-state systems is developed, taking into consideration epistemic uncertainties. This paper formulates a combined approach, based on continuous Markov chains and interval contraction methods, to address the problem of computing the availability of multi-state systems with imprecise failure and repair rates. The interval constraint propagation method, which we refer to as the forward–backward propagation (FBP) contraction method, allows us to contract the probability intervals, keeping all the values that may be consistent with the set of constraints. This methodology is guaranteed, and several numerical examples of systems with complex architectures are studied.

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A Contribution to the Evaluation of Imprecise Availability of Complex Systems Using Markov Models

Abstract: Abstract. When using classical methods for the availability assessment of a multi-state

Cited by 2 publications

References 7 publications

New method for availability computing of complex systems using imprecise Markov models

New method for availability computing of complex systems using imprecise Markov models

Methodology for the Assessment of Imprecise Multi-State System Availability

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