×

zbMATH — the first resource for mathematics

Mastering uncertainty in industry. I: A global methodological approach based on examples. (La maîtrise des incertitudes dans un contexte industriel. I. Une approche méthodologique globale basée sur des exemples.) (French. English summary) Zbl 1409.62256
Summary: An industrial decision process supported by quantitative modelling (safety and reliability, physical design of facilities or processes, economic optimisation, environmental impact, etc.) quickly faces a wide diversity of uncertainties, imprecisions, errors or randomness affecting all data or models. Through four introductory examples that summarise years of industrial practice in different sectors, this paper evidences that a generic and applied approach to uncertainty in industry can surpass a terminological heterogeneity that is largely explicable by the historical separation of the fields involved (such as metrology, reliability, statistics, numerical analysis, …). In relation with the applicable regulation and standards and a relevant decision criterion (step A), this approach involves in particular the proper identification of key steps such as: the quantification (or modelling) of the sources of uncertainty (step B), possibly involving an inverse approach (B’), their propagation through a pre-existing physical-industrial model (step C), the ranking of importance or sensitivity analysis (step C’) and sometimes a subsequent optimisation step. A review of the corresponding statistical, physical and numerical methods is the subject of a second part following the present paper. This approach is intended to be amenable to a variety of underlying epistemological choices, including the tricky choice of differentiating the modelling according to nature of uncertainty. It aims at giving a consistent and industrially-realistic framework for practical mathematical modelling, assumingly restricted to quantitative and quantifiable uncertainty, a domain of considerable recent interest from the industrial sector.

MSC:
62P30 Applications of statistics in engineering and industry; control charts
62-02 Research exposition (monographs, survey articles) pertaining to statistics
Software:
bootstrap
PDF BibTeX XML Cite
References:
[1] APOSTOLAKIS, G. (1999), The distinction between aleatory and epistemic uncertainties is important ; an example from the inclusion of aging effects in the PSA, PSA’99, Washington DC.
[2] AVEN, T. (2003), Foundations of Risk Analysis, Wiley. · Zbl 1039.91034
[3] BECK, M.B.(1987), Water Quality Modeling : A Review of the Analysis of Uncertainty, Wat. Res. Research, Vol. 23, n° 8.
[4] BEAUDOUIN, F., MUNIER, B., SERQUIN, Y. (1997), Multiattribute utility theory : Towards a more general framework, Proc. of the 1997 ESReDA seminar on decision analysis and its applications in safety and reliability. · Zbl 1012.90016
[5] BESTION, D. (2003), Final Report -§ 4.2 State of the Art on Uncertainty Evaluation, European Project for Future Advances in Sciences and Technology for Nuclear Engineering Thermal-Hydraulics (EUROFASTNET).
[6] BOYACK, B.E. (1990), Quantifying reactor safety margins-part I : an overview of the code scaling, applicability and uncertainty evaluation methodology, Nucl. Eng. Des. 119, 1-15.
[7] BUSSAC, R., BAILLY, P., THOMAS, Ph., de ROCQUIGNY, E. (2004), CO2 emissions : estimating uncertainties in practice for power plants, “Implementation of European Environmental Regulation in Fossil-Fired Power Plant” of EDF Group” Seminar Sep. 2004, Gdansk, Polska.
[8] CACUCI, D.G., et al. (1980), Sensitivity Theory for General Systems of Nonli-near Equations, Nucl. Sc. & Eng. 75.
[9] CAMBIER, S. (2000), Approche probabilité pour la prise en compte de la dispersion de paramètres mécaniques - Application à la fatigue vibratoire de réseaux de tuyauteries, Thèse ENSAM Paris.
[10] CAMBIER, S., GUIHOT, P., COFFIGNAL, G. (2002), Computational methods for accounting of structural uncertainties, applications to dynamic behavior prediction of piping systems. Structural Safety, 24 : 29-50.
[11] CORRE, B. (2003), Problématique des incertitudes en exploration-production pétrolière : application des plans d’expériences. Total Fina Elf, Séminaire «Plans d’Expériences Numériques», Ec. Mines St-Etienne.
[12] CUKIER, R.I., LEVINE, H.B., SCHULER, K.E. (1978). Non-linear sensitivity analysis of multi-parameter model systems. Journal of computational physics 26, p. 1-42. · Zbl 0369.65023
[13] DACUNHA-CASTELLE, D. (1996). Chemins de l’aléatoire. Le hasard et le risque dans la société moderne. Flammarion, Paris.
[14] DEMPSTER, A. P. (1967). Upper and lower probabilities induced by a multivalued mapping, Annals of Math. Statistics 38 : 325-339. · Zbl 0168.17501
[15] DE ROCQUIGNY, E. (2005), Couplage mécano-probabiliste pour la fiabilité des structures - un cas industriel où la robustesse d’une surface de réponse est démontrable. Actes du 17 ème Congrès Français de Mécanique. Troyes.
[16] DE ROCQUIGNY, E. (2004), Tutoriel Incertitudes, présenté dans la Conférence Lambda-Mu 14, Bourges, Octobre 2004.
[17] DEVICTOR, N. (2004), Intérêt des méthodes statistiques pour la prise en compte des incertitudes dans les processus de décision, Phoebus N°31.
[18] DEVICTOR, N. (1996), Fiabilité et mécanique : méthodes FORM/SORM et couplages avec des codes d’éléments finis par surfaces de réponse adaptative. PhD Université Blaise Pascal, Clermont-Ferrand.
[19] DEVICTOR, N., BOLADO LAVIN, R. (eds) (2005), Proc. of the Workshop on the Use of Expert Judgment in Decision-Making, CEA & Eur. Comm. JRC Petten, Aix-en-Provence.
[20] Directive 2003/87/EC of the European Parliament and of the Council of 13 October 2003 establishing a scheme for greenhouse gas emission allowance trading within the Community & Commission - Decision of 29 January 2004 (C(2004) 130) establishing guidelines for the monitoring and reporting of greenhouse gas émissions pursuant to Directive 2003/87/EC.
[21] DITLEVSEN, O. & MADSEN, H.O. (1996), Structural reliability Methods, John Wiley & Sons.
[22] DUBOIS, D., PRADE, H. (1988), Possibility theory : an approach to computerized processing of uncertainty, New York, Plenum Press. · Zbl 0703.68004
[23] DUCKSTEIN, L., PARENT, E. (1994), Engineering Risk in Natural Resources Management, NATO ASI Series.
[24] DUTFOY, A. (2000), Uncertainty propagation in radionuclide transport modelling for performance assessment of a nuclear waste repository, Proc. of PSAM5, Japan.
[25] DUTFOY, A., RITZ, J.B. (2001), Uncertainty propagation in a 3D thermal code for performance assessment of a nuclear waste disposal, Proceedings of the SIAM’6 Conference on Mathematical and Computational Issues in the Geosciences, Boulder, Colorado.
[26] EFRON, B., TIBSHIRANI, R.J. (1993), An introduction to the Bootstrap, Chapman & Hall. · Zbl 0835.62038
[27] EKELAND, I. (1991), Au Hasard - La chance, la science et le monde, Seuil.
[28] FREY, H.C., RHODES, D.S. (2005), Quantitative Analysis of Variability and Uncertainty in with Known Measurement Error : Methodology and Case Study, Risk Analysis Vol. 25, No3.
[29] GRANGER MORGAN, M., HENRION, M. (1990), Uncertainty - A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge University Press.
[30] HELTON, J. (1993), Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal, Rel. Eng. & Syst. Saf., 42, 327-367.
[31] HELTON, J.C., BURMASTER, D.E. et al. (1996), Treatment of Aleatory and Epistemic Uncertainty, Special Issue of Rel. Eng. & Syst. Saf., vol. 54 n°2 et 3.
[32] HELTON, J.C., OBERKAMPF, W.L. (2004), Alternative Representations of Epistemic Uncertainty, Special Issue of Rel. Eng. & Syst. Saf., vol. 85 n°1-3.
[33] HOFFMAN, F.O., HAMMONDS, J.S. (1994), Propagation of Uncertainty in Risk Assessments : the Need to Distinguish between Uncertainty Due to Lack of Knowledge and Uncertainty due to Variability, Risk Analysis, Vol 14. n°5.
[34] INTERGOVERNMENTAL PANEL ON CLIMATE CHANGE (IPCC) 2000, Good practice guidance and Uncertainty Management in National Greenhouse Gas Inventories.
[35] KENDALL, MG. & STUART ( 1943-1979), A, The Advanced Theory of Statistics (2 vol), Griffin & Co., London. · Zbl 0249.62003
[36] KNIGHT, F.H. (1921), Risk, Uncertainty and Profit, Hart, Schaffner & Marx.
[37] KUSCHEL, N., RACKWITZ, R. (2000), Optimal design under time-variant reliability constraints, Structural Safety, Volume 22, Issue 2, p. 113-127. · Zbl 0972.90019
[38] LANNOY, A., et al. (1994), Méthodes avancées d’analyse des bases de données du retour d’expérience industriel, Coll. D.E.R.EDF, n°86, Eyrolles.
[39] LEBRUN, R. (2006), Modelling dependency with copulas in reliability analysis, a new approach to the FORM and SORM methods, submitted to 8 PSAM Conference.
[40] LEMMER, J.F., KANAL, L.N. (eds) (1986), Uncertainty in Artificial Intelligence, Elsevier. · Zbl 0595.00024
[41] LENCASTRE, A. (1999), Hydraulique générale, Eyrolles.
[42] McKAY, M.D. (1996), Application of Variance-Based Methods to NUREG-1150 Uncertainty Analyses, USNRC 1996.
[43] McKONE, T.E. (1994), Uncertainty and Variability in Human Exposures to Soil Contaminants Through Home-Grown Food : A Monte-Carlo Assessment, Risk Analysis Vol 14, No4.
[44] MERRICK, J.R., et al. (2005), Assessing uncertainty in Simulation-Based Maritime Assessment, Risk Analysis Vol. 25, No3.
[45] MIQUEL, J. (1984), Guide pratique d’estimation des probabilités de crues, Eyrolles.
[46] NELSEN, R.B. (1999), An introduction to copulas, SPRINGER. · Zbl 0909.62052
[47] NILSEN, T.-, AVEN, T. (2003), Models and model uncertainty in the context of risk analysis, Rel. Eng. Sys. Safe. 79, 309-317.
[48] Norme AFNOR XP X 07-020 (1996) : Normes Fondamentales : Guide pour l’expression de l’incertitude de mesure - AFNOR ( 1999) : Guide pour l’expression de l’incertitude de mesure, NF ENV 13005.
[49] OBERKAMPF, W.L. et al. (2002), Error and uncertainty in modelling and simulation, Rel. Eng. &; Sys. Saf., 75.
[50] PATÉ-CORNELL, M.E. (1996), Uncertainty in risk analysis : six levels of treatment, Rel. Eng. & Syst. Saf. 54 (2-3), 95-111.
[51] PENDOLA, M. (2000), Fiabilité des Structures en contexte d’incertitudes statistiques et d’écarts de modélisation, Thèse de l’Université Clermont II.
[52] PERSOZ, M., HUGONNARD-BRUYÈRE, S., VENTURINI, V., MEISTER, E. (2000), Deterministic and probabilistic assessments of the reactor pressure vessel structural integrity with user-friendly software, ASME Press. Vess. &; Piping.
[53] PROCACCIA, H., MORILHAT, P. (1996), Fiabilité des structures des installations industrielles, Coll. D.E.R. EDF, n°94, Eyrolles.
[54] QUIGGIN, J. (1982), A theory of anticipated utility, Journal of Economic Behavior and Organization, vol 3, pp. 323-343.
[55] RABL, A., SPADARO, J.V. (1999), Damages and Costs of Air Pollution : an Analysis of Uncertainties, Environment International Vol 25(1), 29-46.
[56] RASMUSSEN et al. (1975), Reactor Safety Study : An Assessment of Accident Risks in U.S. Commercial Nuclear Power Plants, Nuclear Regulatory Commission, NUREG-75/014 (WASH-1400), Washington D.C.
[57] REISS, R.D., THOMAS, M. (2001), Statistical Analysis of Extreme Values, Ed. Birkhauser. · Zbl 1002.62002
[58] RELCON, A.B., Risk Spectrum - Theory Manual.
[59] ROYSET, J.O., DER KIUREGHIAN, A., and POLAK, E. (2001), Reliability-based optimal structural design by the decoupling approach, Rel. Eng. Sz Syst. Saf., Vol. 73, Issue 3, P. 213-221.
[60] ROWE, W.D. (1994), Understanding Uncertainty, Risk Analysis, Vol 14. n°5.
[61] SAVAGE, L.H. ( 1954 & 1972), The Foundations of Statistics, Dover, New York. · Zbl 0276.62006
[62] SHANNON, C.E., (1948), A mathematical theory of communication, Bell Systems Technical Journal 27. · Zbl 1154.94303
[63] SOURGET, F., et al. (2004), Protection de la ligne TGV-Méditerranée face aux vents traversiers, Actes de la Conf. Lambda-Mu 14, Bourges.
[64] SUDRET, B., DEFAUX, G., PENDOLA, M. (2005), Time-variant finite element reliability analysis - Application to the durability of cooling towers, Structural Safety, Vol. 27, pp. 93-112.
[65] SUDRET, B., GUÉDÉ, Z., LEMAIRE, M. (2005), Probabilistic assessment of thermal fatigue in nuclear components, Nucl. Eng. Des., Vol. 235, pp. 219-235.
[66] VON NEUMANN, J., MORGENSTERN, O., (1944), Theory of games and economic behavior, Princeton University Press. · Zbl 0063.05930
[67] WALLEY, P. (1991), Statistical Reasoning with Imprecise Probabilities, London, Chapman and Hall. · Zbl 0732.62004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.