Monte Carlo Analysis and Fuzzy Sets for Uncertainty Propagation in SIS Performance Assessment
The object of this work is the probabilistic performance evaluation of safety instrumented systems (SIS), i.e. the average probability of dangerous failure on demand (PFDavg) and the average frequency of failure (PFH), taking into account the uncertainties related to the different parameters that come into play: failure rate (λ), common cause failure proportion (β), diagnostic coverage (DC)... This leads to an accurate and safe assessment of the safety integrity level (SIL) inherent to the safety function performed by such systems. This aim is in keeping with the requirement of the IEC 61508 standard with respect to handling uncertainty. To do this, we propose an approach that combines (1) Monte Carlo simulation and (2) fuzzy sets. Indeed, the first method is appropriate where representative statistical data are available (using pdf of the relating parameters), while the latter applies in the case characterized by vague and subjective information (using membership function). The proposed approach is fully supported with a suitable computer code.
[1] IEC 61508 standard, Functional safety of electrical/electronic
/programmable electronic safety-related systems. Parts 1 to 7,
International Electrotechnical Commission, Geneva, Switzerland, 2010.
[2] Y. Dutuit, F. Innal, A. Rauzy, and J-P. Signoret, “Probabilistic
assessments in relationship with safety integrity levels by using fault
trees,” Reliability Engineering and System Safety, vol. 93, pp. 1867–
1876, 2008.
[3] F. Innal, “Contribution to modelling safety instrumented systems and to
assessing their performance-Critical analysis of IEC 61508 standard,”
Ph.D. dissertation, University of Bordeaux, France, 2008.
[4] M. Sallak, “Evaluation de paramètres de sûreté de fonctionnement en
présence d’incertitudes et aide à la conception: Application aux
Systèmes Instrumentés de Sécurité,” Ph.D. dissertation, Nancy
Université, Institut Nationnal Polytechnique de Lorraine, France, 2007.
[5] M. Sallak, C. Simon, and J.-F. Aubry, “A fuzzy probabilistic approach
for determining safety integrity level,” IEEE Transactions on Fuzzy
Systems, vol. 16 (1), pp. 239–248, 2008.
[6] U. Hauptmanns, “The impact of reliability data on probabilistic safety
calculations,” Journal of Loss Prevention in the Process Industries, vol.
21 (1), pp. 38–49, Jan. 2008.
[7] NASA, Probabilistic Risk Assessment Procedures Guide for NASA
Managers and Practitioners. NASA Office of Safety and Mission
Assurance,Washington, 2002.
[8] T. Aven. Foundations of Risk Analysis - A Knowledge and Decisionoriented
Perspective. Chichester: Wiley, 2003.
[9] IEC 61508 standard, Functional safety of electrical/electronic/
programmable electronic safety-related systems. Parts 1 to 7,
International Electrotechnical Commission, Geneva, Switzerland, 1998-
2000.
[10] J. L Rouvroye, “Enhanced Markov Analysis as a method to assess safety
in the process industry,” Ph.D. dissertation, Technische Universiteit,
Eindhoven, Netherlands, 2001. [11] W. Mechri, “Evaluation de la performance des Systèmes Instrumentés
de Sécurité à paramètres imprécis,” Ph.D. dissertation, Université de
Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, Tunisia, 2011.
[12] L. Zadeh, “Fuzzy sets,” Information and control, vol. 8, pp. 338–353,
1965.
[13] K. B Misra, and G. G Weber, “A new method for fuzzy fault tree
analysis” Microelectronics and Reliability, vol. 29(2), pp. 195–216,
1989.
[14] M. A. Lundteigen, “Safety instrumented systems in the oil and gas
industry,” Ph.D. dissertation, Department of Production and Quality
Engineering, Trondheim, Norway, 2009.
[15] T. Bedford, and R. Cooke, Probabilistic Risk Analysis: Foundations and
Methods. Cambridge University Press, Cambridge, 2003.
[16] C. E Kim, Y. J Ju, and M. Gens, “Multilevel fault tree analysis using
fuzzy numbers” Computers & Operations Research, vol. 23(7), pp. 695–
703, 1996.
[17] D. Dubois, L. Foulloy, G. Mauris, and H. Prade, “Probability-possibility
transformations, triangular fuzzy sets, and probabilistic inequalities,”
Reliable computing, vol. 10, pp. 273–297, 2004.
[1] IEC 61508 standard, Functional safety of electrical/electronic
/programmable electronic safety-related systems. Parts 1 to 7,
International Electrotechnical Commission, Geneva, Switzerland, 2010.
[2] Y. Dutuit, F. Innal, A. Rauzy, and J-P. Signoret, “Probabilistic
assessments in relationship with safety integrity levels by using fault
trees,” Reliability Engineering and System Safety, vol. 93, pp. 1867–
1876, 2008.
[3] F. Innal, “Contribution to modelling safety instrumented systems and to
assessing their performance-Critical analysis of IEC 61508 standard,”
Ph.D. dissertation, University of Bordeaux, France, 2008.
[4] M. Sallak, “Evaluation de paramètres de sûreté de fonctionnement en
présence d’incertitudes et aide à la conception: Application aux
Systèmes Instrumentés de Sécurité,” Ph.D. dissertation, Nancy
Université, Institut Nationnal Polytechnique de Lorraine, France, 2007.
[5] M. Sallak, C. Simon, and J.-F. Aubry, “A fuzzy probabilistic approach
for determining safety integrity level,” IEEE Transactions on Fuzzy
Systems, vol. 16 (1), pp. 239–248, 2008.
[6] U. Hauptmanns, “The impact of reliability data on probabilistic safety
calculations,” Journal of Loss Prevention in the Process Industries, vol.
21 (1), pp. 38–49, Jan. 2008.
[7] NASA, Probabilistic Risk Assessment Procedures Guide for NASA
Managers and Practitioners. NASA Office of Safety and Mission
Assurance,Washington, 2002.
[8] T. Aven. Foundations of Risk Analysis - A Knowledge and Decisionoriented
Perspective. Chichester: Wiley, 2003.
[9] IEC 61508 standard, Functional safety of electrical/electronic/
programmable electronic safety-related systems. Parts 1 to 7,
International Electrotechnical Commission, Geneva, Switzerland, 1998-
2000.
[10] J. L Rouvroye, “Enhanced Markov Analysis as a method to assess safety
in the process industry,” Ph.D. dissertation, Technische Universiteit,
Eindhoven, Netherlands, 2001. [11] W. Mechri, “Evaluation de la performance des Systèmes Instrumentés
de Sécurité à paramètres imprécis,” Ph.D. dissertation, Université de
Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, Tunisia, 2011.
[12] L. Zadeh, “Fuzzy sets,” Information and control, vol. 8, pp. 338–353,
1965.
[13] K. B Misra, and G. G Weber, “A new method for fuzzy fault tree
analysis” Microelectronics and Reliability, vol. 29(2), pp. 195–216,
1989.
[14] M. A. Lundteigen, “Safety instrumented systems in the oil and gas
industry,” Ph.D. dissertation, Department of Production and Quality
Engineering, Trondheim, Norway, 2009.
[15] T. Bedford, and R. Cooke, Probabilistic Risk Analysis: Foundations and
Methods. Cambridge University Press, Cambridge, 2003.
[16] C. E Kim, Y. J Ju, and M. Gens, “Multilevel fault tree analysis using
fuzzy numbers” Computers & Operations Research, vol. 23(7), pp. 695–
703, 1996.
[17] D. Dubois, L. Foulloy, G. Mauris, and H. Prade, “Probability-possibility
transformations, triangular fuzzy sets, and probabilistic inequalities,”
Reliable computing, vol. 10, pp. 273–297, 2004.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62995", author = "Fares Innal and Yves Dutuit and Mourad Chebila", title = "Monte Carlo Analysis and Fuzzy Sets for Uncertainty Propagation in SIS Performance Assessment", abstract = "The object of this work is the probabilistic performance evaluation of safety instrumented systems (SIS), i.e. the average probability of dangerous failure on demand (PFDavg) and the average frequency of failure (PFH), taking into account the uncertainties related to the different parameters that come into play: failure rate (λ), common cause failure proportion (β), diagnostic coverage (DC)... This leads to an accurate and safe assessment of the safety integrity level (SIL) inherent to the safety function performed by such systems. This aim is in keeping with the requirement of the IEC 61508 standard with respect to handling uncertainty. To do this, we propose an approach that combines (1) Monte Carlo simulation and (2) fuzzy sets. Indeed, the first method is appropriate where representative statistical data are available (using pdf of the relating parameters), while the latter applies in the case characterized by vague and subjective information (using membership function). The proposed approach is fully supported with a suitable computer code.
", keywords = "Fuzzy sets, Monte Carlo simulation, Safety instrumented system, Safety integrity level.", volume = "7", number = "11", pages = "1557-9", }
