Unification of Common Cause Failures’ Parametric Models Using a Generic Markovian Model

Chebila, Mourad; Innal, Fares

doi:10.1007/s11668-014-9828-0

Cited by 10 publications

(4 citation statements)

References 9 publications

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“…( 11)) is slightly different from that of Eq. (10). Regarding the possible values that could be attributed to the factor , we can validate the IEC formula for this second configuration that maintains the conservative aspect stated for the 1oo1 configuration.…”

Section: Markov Modelsupporting

confidence: 56%

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Consistency Checking of the IEC 61508 PFH Formulas and New Formulas Proposal Based on the Markovian Approach

Omeiri¹,

Innal²,

Liu³

2021

JESA

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Safety Instrumented Systems (SISs) are of prime importance in protecting people, assets and environment from hazardous events. Therefore, it is important to be able to assess accurately their performance indicators. For this end, IEC 61508 standard has provided two reliability metrics: the average failure probability of a SIS lowly demanded (PFDavg) and the average failure frequency of a SIS highly or continuously demanded (PFH). The aim of this paper is to investigate the IEC 61508 PFH formulas and to propose new ones based on the Markovian approach. Indeed, the new edition of IEC 61508 provides PFH formulas reflecting the possibility of automatic shutdown of the monitored process upon detection of a dangerous failure in the SIS. However, the IEC 61508 attempt remains incomplete and provide non-conservative results, which is dangerous from a safety point of view.

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Section: Markov Modelsupporting

confidence: 56%

“…The β-factor model [9,10] mentioned in the IEC 61508 is used in this verification to characterize CCFs. It considers that the partition of the total failure rate (λ) takes into account independent and dependent failures (dependent failures are denoted CCF).…”

Section: Common Cause Failures (Ccf)mentioning

confidence: 99%

Consistency Checking of the IEC 61508 PFH Formulas and New Formulas Proposal Based on the Markovian Approach

Omeiri¹,

Innal²,

Liu³

2021

JESA

Self Cite

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“…The start-up of the EUC after shutdown is performed within duration noted MTTR SD .(4)Common Cause Failures (CCF): CCF is the result of an event that simultaneously affects several or all the elements of a redundant system, resulting in the loss of the required function. The IEC 61508 standard uses the β -factor model (Hokstad and Rausand, 2008; Chebila and Innal, 2014) to characterize CCFs. According to this model, the failure rates (λDD and λDU) of a channel are split into two contributions: independent and dependent (CCF) (Figure 2).…”

Section: Used Concepts and Parametersmentioning

confidence: 99%

Verification of the IEC 61508 PFH formula for 2oo3 configuration using Markov chains and Petri nets

Omeiri

Hamaidi

Innal

et al. 2020

IJQRM

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PurposeThe purpose of this paper is to check the consistency of the IEC 61508 standard formula related to the average failure frequency (PFH: the probability of dangerous failure per hour) for a commonly used safety instrumented system (SIS) architecture in the process industry: 2-out-of-3 voting (2oo3), also known as Triple Modular Redundancy (TMR).Design/methodology/approachIEC 61508 standard provided PFH formulas for different SIS architectures, without explanations, assuming that the SIS puts the equipment under control into a safe state on the detection of dangerous failure. This assumption renders the use of classical reliability approaches such as fault trees and reliability block diagrams impractical for PFH calculation. That said, the consistency verification was performed thanks to a dynamic and flexible reliability approach, namely Markov chains following these steps: (1) developing the multi-phase Markov chains (MPMC) model for 2oo3 configuration, (2) deducing the related classical Markov chains (CMC) model and (3) deriving a new PFH formula for the 2oo3 architecture based on the CMC model and thoroughly comparing it to that given in the IEC 61508. Moreover, 2oo3 architecture has been modeled through Petri nets for numerical comparison purposes. That comparison has been carried out between the numerical results obtained from IEC 61508 formula, the newly derived formula, Markov chains and Petri nets models.FindingsThe newly obtained formula for 2oo3 configuration contains extra terms compared with the IEC 61508 one. Therefore, this latter formula induces an underestimated PFH results, which is dangerous from a safety point of view. This fact was corroborated by the numerical comparison.Research limitations/implicationsThis paper does not consider the different configurations given in IEC 61508.Originality/valueIn our knowledge, no verification works have been conducted before on the IEC 61508 PFH formulas with shutdown capability. Therefore, the nonaccuracy of the PFH formula related to the 2oo3 has not been stated before. This paper proposes a new and more accurate formula.

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“…In the operation of a redundant system, common-cause failure (CCF) can lead to severe reliability and safety degradation, which is one of the factors that cannot be ignored in reliability analysis. The current modeling methods of common-cause failure mainly include the α-factor model [29], [30], the beta factor model [31], the multiple beta factor (MBF) model [32], the multiple Greek letter (MGL) model [33], the basic parameter (BP) model [34], the binomial failure rate (BFR) model [35], and the multiple error shock (MESH) model [36] etc. In addition, Fan et al [37] developed a new model for CCFs considering components degradation based on Stochastic Hybrid System (SHS), the model can accurately describe the CCF effect on the reliability of a system with degrading components.…”

Section: Introductionmentioning

confidence: 99%

Reliability and Safety Modelling of the Electrical Control System of the Subsea Control Module Based on Markov and Multiple Beta Factor Model

et al. 2019

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Replacement of the subsea control module (SCM) and halting production caused by the failure of the SCM are costly, and the electrical control system plays a large role in the failure modes of the SCM. Hence, the analysis of its reliability and safety is important. Markov processes and the multiple beta factor model are used to model the reliability and safety for the electrical control system of the SCM that consider the effects of multiple factors, including the failure detection rate, common-cause failure, and the failure rate of each module, for evaluating system reliability and safety. The Morris screening method that is based on a large amount of random data with equal probability is applied to reliability and safety models that vary with time for quantifying the effect levels of each factor on the system reliability and safety in the time interval. The effect of each factor on the system and its interaction degree with other factors are evaluated in the time interval. Finally, the system model is simulated in MATLAB. The simulation demonstrates that the system reliability and safety gradually decrease and the effect of each factor on them increases over time; the reliability is most sensitive to the failure rates of the input, central processing unit, and output modules, whereas the safety is most sensitive to the failure detection rate. The common-cause failure and the comparator module have some effects on the reliability and safety of the system.

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Unification of Common Cause Failures’ Parametric Models Using a Generic Markovian Model

Cited by 10 publications

References 9 publications

Consistency Checking of the IEC 61508 PFH Formulas and New Formulas Proposal Based on the Markovian Approach

Consistency Checking of the IEC 61508 PFH Formulas and New Formulas Proposal Based on the Markovian Approach

Verification of the IEC 61508 PFH formula for 2oo3 configuration using Markov chains and Petri nets

Reliability and Safety Modelling of the Electrical Control System of the Subsea Control Module Based on Markov and Multiple Beta Factor Model

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