Generalized analytical expressions for safety instrumented systems' performance measures: PFDavg and PFH

Chebila, Mourad; Innal, Fares

doi:10.1016/j.jlp.2015.02.002

Cited by 26 publications

(16 citation statements)

References 13 publications

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“…The results obtained according to Equation and reference allow the observation that the maximum difference is below 3.5%. More results presented in reference make the comparison more efficient. In this case, the maximum difference amounts to 11.3%.…”

Section: Numerical Example and Comparison Of Resultsmentioning

confidence: 99%

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Extending the Possibilities of Quantitative Determination of SIL - a Procedure Based on IEC 61508 and the Markov Model with Common Cause Failures

Pilch

2016

Qual. Reliab. Engng. Int.

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Generalized equations for calculating the probability of failure on demand (PFD) in accordance with the IEC 61508 standard and a model based on Markov processes, taking into account common cause failures, are proposed in this paper. The solutions presented in the standard and in many references concentrate on simple k‐out‐of‐n architectures. The equations proposed in the standard concern cases for n ≤ 3. In safety‐related systems applied in industry, architectures of a number of elements n larger than three often occur. For this reason, a generalized equation for calculating PFD was proposed. For cases presented in the standard, the proposed equation provides identical results. The presented simplified Markov model allows the determination of the system availability (A(t)) and unavailability (1–A(t)) as well as their values in the steady state (A and 1–A). This model can be an alternative method of PDF calculations for various k‐out‐of‐n architectures with self‐diagnostic elements. Calculations performed according to the proposed models provide very similar results. The developed models are suitable for practical implementations in calculations of the safety integrity level. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Numerical Example and Comparison Of Resultsmentioning

confidence: 99%

“…The generalized equations for k ‐out‐of‐ n ( k oo n ) architectures were also studied in . In , the generalized model for calculating PFD and probability failure per hour was presented. This model was developed for systems in which, during the proof‐test interval [0, T 1 ], the partial stroke test is additionally made.…”

Section: Introductionmentioning

confidence: 99%

Extending the Possibilities of Quantitative Determination of SIL - a Procedure Based on IEC 61508 and the Markov Model with Common Cause Failures

Pilch

2016

Qual. Reliab. Engng. Int.

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“…There have been many efforts related to generalized formula for PFH for M-out-of-N (MooN) architectures. The work proposed in [4] develops a set of generalized and simplified analytical expressions for MooN architectures by considering partial proof tests, while slightly taking the CCF contributions into account. In [11], probabilistic analysis of safety for MooN architectures is proposed when considering different degrees of uncertainty in some safety parameters such as failure rate, CCFs, and diagnostic coverage, by combining Monte Carlo sampling and fuzzy sets.…”

Section: Related Work and Motivationmentioning

confidence: 99%

Analysis of Design Parameters in Safety-Critical Computers

Ahangari

Atik

Ozkok

et al. 2020

IEEE Trans. Emerg. Topics Comput.

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Nowadays, safety-critical computers are extensively used in many civil domains like transportation including railways, avionics, and automotive. In evaluating these safety critical systems, previous studies considered different metrics, but some of safety design parameters like failure diagnostic coverage (C) or common cause failure (CCF) ratio have not been seriously taken into account. Moreover, in some cases safety has not been compared with standard safety integrity levels (IEC-61508: SIL1-SIL4) or even have not met them. Most often, it is not very clear that which part of the system is the Achilles heel and how design can be improved to reach standard safety levels. Motivated by such design ambiguities, we aim to study the effect of various design parameters on safety in some prevalent safety configurations, namely, 1oo2 and 2oo3, where 1oo1 is also used as a reference. By employing Markov modeling, we analyzed the sensitivity of safety to important parameters including: failure rate of processing element, failure diagnostic coverage, CCF ratio, test and repair rates. This study aims to provide a deeper understanding on the influence of variation in design parameters over safety. Consequently, to meet appropriate safety integrity level, instead of improving some parts of a system blindly, it will be possible to make an informed decision on more relevant parameters.

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“…The reliability related to random hardware failure is quantified based on failure rate, but systematic failure cannot be accurately estimated because of its deterministic nature, however, IEC61508 standard suggests, as a general rule, not to quantify systematic failure. If systematic failure is neglected the predicted unavailability will be of lower value and less conservative compared with actual unavailability, but its contribution is not completely ignored in reliability quantification [9,10]. However, PDS method uses the same classification as IEC61508, but gives a more detailed breakdown of the systematic failure as shown in figure 4.…”

Section: Common Cause Failurementioning

confidence: 99%

Average probability of failure on demand estimation for burner management systems

Okubanjo

Oyetola

Groot³

et al. 2018

Nig. J. Tech.

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Proper estimation of Safety Integrity Level (SIL) depends largely on accurate estimation of Safety performance in terms of average Probability of Failure on Demand, (PFDavg). For complex architectures of logic solvers, sensors, and valves, this can be calculated by distinguishing combinations of subsystems with basic (K-out-of-N) KooN approach for identical components. In the case of the typical configurations of valves for a burner management systems with non-identical subsystem configurations the KooN approach does not apply. Hence, it becomes an issues to calculate the correct safety performance since some of the established methods give too optimistic results due to lack of Common cause Failure information and data on non-identical components or sub-systems. This paper formulates a Markov model for determination of average probability of failure on demand for non-identical components and also proposes a more conservative lowest failure rate approach and maximum beta factor contrary to pragmatic minimum or average beta for correct estimation of average probability of failure on demand. It can be deduced that the measure of safety performance for components or subsystems with unequal failure rates depends largely on common cause failure, but a single beta factor is not appropriate to model the commonality of the failure. The result revealed that both geometric mean and lowest failure rate approaches result in different values with the lowest failure rate being the most conservative and optimistic result.

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Generalized analytical expressions for safety instrumented systems' performance measures: PFDavg and PFH

Cited by 26 publications

References 13 publications

Extending the Possibilities of Quantitative Determination of SIL - a Procedure Based on IEC 61508 and the Markov Model with Common Cause Failures

Extending the Possibilities of Quantitative Determination of SIL - a Procedure Based on IEC 61508 and the Markov Model with Common Cause Failures

Analysis of Design Parameters in Safety-Critical Computers

Average probability of failure on demand estimation for burner management systems

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