Application of micro Markov models for quantitative safety assessment to determine safety integrity levels as defined by the IEC 61508 standard for functional safety

Knegtering, B.; Brombacher, AC Aarnout

doi:10.1016/s0951-8320(99)00034-4

Cited by 32 publications

(11 citation statements)

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“…Many scholars did lot of researches. The quantitative methods for safety analysis include micro-level Markov models (Knegtering and Broracher, 1999), computer-aided fault tree synthesis method (Wang et al, 2002), dynamic fault tree method (Čepin and Marko, 2002), and the decision tree method of incident management, and so on (Baumont et al, 2000). For example, safety technology investment model for assessing quantitatively the enterprise's risks and potential threats was put forward (Bojanc et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

The Calculation Method of Safety Degree and Its Application in Coal Mine Enterprises

Nie¹,

Huang²,

Wang³

et al. 2017

Proceedings of the 2nd Czech-China Scientific Conference 2016

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In order to evaluate the situation of safety production of coal mine enterprises efectively, quantitative analysis is necessary and very important. Safety degree of coal mine enterprises based on the concept of safety degree is deined and the method of calculating quantitatively the safety degree is put forward. The validity of this method is veriied by empirical research in view of micro-and macroanalyses. In view of micro analysis the safety degree is derived with the calculation method based on information of one coal mine. The safety degree of this coal mine went through rapid increase period, stable period, and slow increase period. Macroresearch results show that the situation of safety production of coal mine enterprises in China has signiicantly been improving and the level of safety degree also has been increasing year by year since 1979, the year when the policy of reform and opening began. The reasons are the advancement of technology, strengthening of safety management and education, increasing of safety investment, and perfection of policies, laws, and regulations. These achievements can provide quantitative method for assessing the status of coal mines.

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Section: Introductionmentioning

confidence: 99%

The Calculation Method of Safety Degree and Its Application in Coal Mine Enterprises

Nie¹,

Huang²,

Wang³

et al. 2017

Proceedings of the 2nd Czech-China Scientific Conference 2016

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“…The determination of these PFD or probability failure per hour, enables the quantitative determination of the safety integrity level (SIL), which the given SRS is able to provide. Analyses and comparisons of various calculation methods were carried out in several studies: Markov models [2][3][4] , fault tree analysis 5 , a method taking into account equipment failures, software and human errors (PDS) 6 , hybrid methods, preventive maintenance, and others 4,[7][8][9][10][11] . The authors of these studies mainly focused on improving the calculation methods, mathematical derivations and increased accuracy of parameters characteristic in the calculation methodology 3,12 . Zhang, Long, and Sato 3 defined downtime as t C1 and determined a more accurate value for it than the one given in the standard.…”

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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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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“…However, the DU failure can only be detected and repaired in the proof test. As the static unavailability is an important value in the reliability analysis for safety systems [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], this paper focuses on the static unavailability evaluation for koon systems with multiple failure modes.…”

Section: Introductionmentioning

confidence: 99%

“…There are many modeling techniques for unavailability analysis of koon systems with multiple failure modes, for example, simplified equations [9][10][11][12][13][14][15], reliability block diagram (RBD) [16], fault tree analysis (FTA) [17,18], and Markov analysis (MA) methods [19][20][21]. Rouvroye and Van den Bliek [22] compared these techniques and obtained the following conclusion: FTA and RBD are intuitive and easy to model; however, a new model has to be established for evaluating a new parameter by FTA and RBD.…”

Section: Introductionmentioning

confidence: 99%

“…MA covers most aspects that affect reliability and can describe the dynamic transitions among different system states. Therefore, the MA method has been widely used in the unavailability analysis of complex systems [19][20][21][22][23][24][25]. However, the states of Markov models increase explosively as the system becomes more complex, and it is fallible and time-consuming to create Markov models manually.…”

Section: Introductionmentioning

confidence: 99%

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Unavailability Analysis for k‐out‐of‐n:G Systems with Multiple Failure Modes Based on Micro‐Markov Models

Tang

Guo

Sun³

et al. 2014

Mathematical Problems in Engineering

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Markov models are commonly used for unavailability analysis of redundant systems. However, due to the exploding states of Markov models for redundant systems, the states need to be merged to simplify the computation, which is called micro-Markov models. However, how to derive the failure rates and repair rates of the newly developed micro-Markov models has not been studied thoroughly. Therefore, this paper proposes detailed explanations and rules to derive the static unavailability by the micro-Markov models for thek-out-of-n:G systems with multiple failure modes. Firstly, two properties about applying the Markov models to the repairable system with independent multiple failure modes are presented. Based on these two properties, two rules are proposed for implementing the micro-Markov models. The micro-Markov models provide the exact same results for the repairablek-out-of-n:G system with multiple independent failure modes and repair mechanisms and approximate results for systems with multiple hybrid failure modes. A case study of safety integrity verification for safety instrumented systems is provided to illustrate the application of the proposed method. The conceptual comparison and numerical examples demonstrate the reasonability and usefulness of the proposed micro-Markov models.

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Application of micro Markov models for quantitative safety assessment to determine safety integrity levels as defined by the IEC 61508 standard for functional safety

Cited by 32 publications

References 1 publication

The Calculation Method of Safety Degree and Its Application in Coal Mine Enterprises

The Calculation Method of Safety Degree and Its Application in Coal Mine Enterprises

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

Unavailability Analysis for k‐out‐of‐n:G Systems with Multiple Failure Modes Based on Micro‐Markov Models

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