Uncertainty in Industrial Practice

Editors: Etienne de Rocquigny, Electricite de France, R&D (Senior Research Fellow). Nicolas Devictor, Commissariat a l'Energie Atomique. Stefano Tarantola, J.R.C. Ispra. Authors: The 10 members of the Uncertainty Project Group, part of ESReDA: European Safety, Reliability and Data Association.

• Preface xiiiContributors and Acknowledgements xvIntroduction xviiNotation – Acronyms and abbreviations xxiPart I Common Methodological Framework 11 Introducing the common methodological framework 31.1 Quantitative uncertainty assessment in industrial practice: a wide variety of contexts 31.2 Key generic features, notation and concepts 41.2.1 Pre-existing model, variables of interest and uncertain/fixed inputs 41.2.2 Main goals of the uncertainty assessment 61.2.3 Measures of uncertainty and quantities of interest 71.2.4 Feedback process 91.2.5 Uncertainty modelling 101.2.6 Propagation and sensitivity analysis processes 101.3 The common conceptual framework 111.4 Using probabilistic frameworks in uncertainty quantification – preliminary comments 131.4.1 Standard probabilistic setting and interpretations 131.4.2 More elaborate level-2 settings and interpretations 141.5 Concluding remarks 17References 182 Positioning of the case studies 212.1 Main study characteristics to be specified in line with the common framework 212.2 Introducing the panel of case studies 212.3 Case study abstracts 27Part II Case Studies 333 CO2 emissions: estimating uncertainties in practice for power plants 353.1 Introduction and study context 353.2 The study model and methodology 363.2.1 Three metrological options: common features in the preexisting models 363.2.2 Differentiating elements of the fuel consumption models 383.3 Underlying framework of the uncertainty study 393.3.1 Specification of the uncertainty study 393.3.2 Description and modelling of the sources of uncertainty 403.3.3 Uncertainty propagation and sensitivity analysis 423.3.4 Feedback process 443.4 Practical implementation and results 443.5 Conclusions 47References 474 Hydrocarbon exploration: decision-support through uncertainty treatment 494.1 Introduction and study context 494.2 The study model and methodology 504.2.1 Basin and petroleum system modelling 504.3 Underlying framework of the uncertainty study 544.3.1 Specification of the uncertainty study 544.3.2 Description and modelling of the sources of uncertainty 564.3.3 Uncertainty propagation and sensitivity analysis 574.3.4 Feedback process 574.4 Practical implementation and results 594.4.1 Uncertainty analysis 594.4.2 Sensitivity analysis 624.5 Conclusions 63References 645 Determination of the risk due to personal electronic devices (PEDs) carried out on radio-navigation systems aboard aircraft 655.1 Introduction and study context 655.2 The study model and methodology 665.2.1 Electromagnetic compatibility modelling and analysis 665.2.2 Setting the EMC problem 675.2.3 A model-based approach 685.2.4 Regulatory and industrial stakes 695.3 Underlying framework of the uncertainty study 715.3.1 Specification of the uncertainty study 715.3.2 Description and modelling of the sources of uncertainty 725.3.3 Uncertainty propagation and sensitivity analysis 755.3.4 Feedback process 765.4 Practical implementation and results 765.4.1 Limitations of the results of the study 765.4.2 Scenario no.1: effects of one emitter in the aircraft on ILS antenna (realistic data-set) 765.4.3 Scenario no. 2: effects of one emitter in the aircraft on ILS antenna with penalized susceptibility 785.4.4 Scenario no. 3: 10 coherent emitters in the aircraft, ILS antenna with a realistic data set 795.4.5 Scenario no. 4: new model considering the effect of one emitter in the aircraft on ILS antenna and safety factors 795.5 Conclusions 80References 806 Safety assessment of a radioactive high-level waste repository – comparison of dose and peak dose 816.1 Introduction and study context 816.2 Study model and methodology 826.2.1 Source term model 836.2.2 Geosphere model 836.2.3 The biosphere model 846.3 Underlying framework of the uncertainty study 846.3.1 Specification of the uncertainty study 846.3.2 Sources of uncertainty, model inputs and uncertainty model developed 856.3.3 Uncertainty propagation and sensitivity analysis 866.3.4 Feedback process 876.4 Practical implementation and results 876.4.1 Uncertainty analysis 876.4.2 Sensitivity analysis 916.5 Conclusions 95References 967 A cash flow statistical model for airframe accessory maintenance contracts 977.1 Introduction and study context 977.2 The study model and methodology 977.2.1 Generalities 977.2.2 Level-1 uncertainty 987.2.3 Computation 987.2.4 Stock size 1007.3 Underlying framework of the uncertainty study 1007.3.1 Specification of the uncertainty study 1007.3.2 Description and modelling of the sources of uncertainty 1017.3.3 Uncertainty propagation and sensitivity analysis 1037.3.4 Feedback process 1047.4 Practical implementation and results 1047.4.1 Design of experiments results 1057.4.2 Sobol’s sensitivity indices 1077.4.3 Comparison between DoE and Sobol’ methods 1087.5 Conclusions 108References 1098 Uncertainty and reliability study of a creep law to assess the fuel cladding behaviour of PWR spent fuel assemblies during interim dry storage 1118.1 Introduction and study context 1118.2 The study model and methodology 1128.2.1 Failure limit strain and margin 1138.2.2 The temperature scenario 1138.3 Underlying framework of the uncertainty study 1148.3.1 Specification of the uncertainty study 1148.3.2 Description and modelling of the sources of uncertainty 1158.3.3 Uncertainty propagation and sensitivity analysis 1168.3.4 Feedback process 1168.4 Practical implementation and results 1178.4.1 Dispersion of the minimal margin 1178.4.2 Sensitivity analysis 1198.4.3 Exceedance probability analysis 1208.5 Conclusions 121References 1229 Radiological protection and maintenance 1239.1 Introduction and study context 1239.2 The study model and methodology 1249.3 Underlying framework of the uncertainty study 1289.3.1 Specification of the uncertainty study 1289.3.2 Description and modelling of the sources of uncertainty 1299.3.3 Uncertainty propagation and sensitivity analysis 1319.3.4 Feedback process 1319.4 Practical implementation and results 1329.5 Conclusions 134References 13410 Partial safety factors to deal with uncertainties in slope stability of river dykes 13510.1 Introduction and study context 13510.2 The study model and methodology 13610.2.1 Slope stability models 13610.2.2 Incorporating slope stability in dyke design 13710.2.3 Uncertainties in design process 13810.3 Underlying framework of the uncertainty study 13810.3.1 Specification of the uncertainty study 13910.3.2 Description and modelling of the sources of uncertainty 14210.3.3 Uncertainty propagation and sensitivity analysis 14410.3.4 Feedback process 14910.4 Practical implementation and results 15010.5 Conclusions 153References 15311 Probabilistic assessment of fatigue life 15511.1 Introduction and study context 15511.2 The study model and methodology 15511.2.1 Fatigue criteria 15511.2.2 System model 15611.3 Underlying framework of the uncertainty study 15711.3.1 Outline of current practice in fatigue design 15711.3.2 Specification of the uncertainty study 15811.3.3 Description and modelling of the sources of uncertainty 16011.3.4 Uncertainty propagation and sensitivity analysis 16111.3.5 Feedback process 16111.4 Practical implementation and results 16211.4.1 Identification of the macro fatigue resistance β(N) 16211.4.2 Uncertainty analysis 16411.5 Conclusions 167References 16712 Reliability modelling in early design stages using the Dempster-Shafer Theory of Evidence 16912.1 Introduction and study context 16912.2 The study model and methodology 17012.2.1 The system 17012.2.2 The system fault tree model 17112.2.3 The IEC 61508 guideline: a framework for safety requirements 17212.3 Underlying framework of the uncertainty study 17312.3.1 Specification of the uncertainty study 17312.3.2 Description and modelling of the sources of uncertainty 17612.4 Practical implementation and results 17812.5 Conclusions 182References 182Part III Methodological Review and Recommendations 18513 What does uncertainty management mean in an industrial context? 18713.1 Introduction 18713.2 A basic distinction between ‘design’ and ‘in-service operations’ in an industrial estate 18813.2.1 Design phases 18813.2.2 In-service operations 18913.3 Failure-driven risk management and option-exploring approaches at company level 19013.4 Survey of the main trends and popular concepts in industry 19113.5 Links between uncertainty management studies and a global industrial context 19213.5.1 Internal/endogenous context 19313.5.2 External/exogenous uncertainty 19413.5.3 Layers of uncertainty 19513.6 Developing a strategy to deal with uncertainties 195References 19714 Uncertainty settings and natures of uncertainty 19914.1 A classical distinction 19914.2 Theoretical distinctions, difficulties and controversies in practical applications 20214.3 Various settings deemed acceptable in practice 205References 21015 Overall approach 21315.1 Recalling the common methodological framework 21315.2 Introducing the mathematical formulation and key steps of a study 21415.2.1 The specification step – measure of uncertainty, quantities of interest and setting 21415.2.2 The uncertainty modelling (or source quantification) step 21515.2.3 The uncertainty propagation step 21815.2.4 The sensitivity analysis step, or importance ranking 21915.3 Links between final goals, study steps and feedback process 22015.4 Comparison with applied system identification or command/control classics 22115.5 Pre-existing or system model validation and model uncertainty 22215.6 Links between decision theory and the criteria of the overall framework  223References 22416 Uncertainty modelling methods 22516.1 Objectives of uncertainty modelling and important issues 22516.2 Recommendations in a standard probabilistic setting 22716.2.1 The case of independent variables 22816.2.2 Building an univariate probability distribution via expert/engineering judgement 22916.2.3 The case of dependent uncertain model inputs 23416.3 Comments on level-2 probabilistic settings 236References 23717 Uncertainty propagation methods 23917.1 Recommendations per quantity of interest 24017.1.1 Variance, moments 24017.1.2 Probability density function 24317.1.3 Quantiles 24517.1.4 Exceedance probability 24717.2 Meta-models 25017.2.1 Building a meta-model 25117.2.2 Validation of a meta-model 25217.3 Summary 253References 25618 Sensitivity analysis methods 25918.1 The role of sensitivity analysis in quantitative uncertainty assessment 26018.1.1 Understanding influence and ranking importance of uncertainties (goal U) 26118.1.2 Calibrating, simplifying and validating a numerical model (goal A) 26218.1.3 Comparing relative performances and decision support (goal S) 26318.1.4 Demonstrating compliance with a criterion or a regulatory threshold (goal C) 26418.2 Towards the choice of an appropriate Sensitivity Analysis framework 26418.3 Scope, potential and limitations of the various techniques 26918.3.1 Differential methods 26918.3.2 Approximate reliability methods 27018.3.3 Regression/correlation 27118.3.4 Screening methods 27318.3.5 Variance analysis of Monte Carlo simulations 27418.3.6 Non-variance analysis of Monte Carlo simulations 27618.3.7 Graphical methods 27818.4 Conclusions 280References 28119 Presentation in a deterministic format 28519.1 How to present in a deterministic format? 28619.1.1 (Partial) safety factors in a deterministic approach 28619.1.2 Safety factors in a probabilistic approach 28719.2 On the reliability target 29019.3 Final comments 291References 29220 Recommendations on the overall process in practice 29320.1 Recommendations on the key specification step 29320.1.1 Choice of the system model 29420.1.2 Choice of the uncertainty setting 29420.1.3 Choice of the quantity of interest 29620.1.4 Choice of the model input representation (‘x’ and ‘d’) 29720.2 Final comments regarding dissemination challenges 297References 298Conclusion 299Appendices 303Appendix A A selection of codes and standards 305Appendix B A selection of tools and websites 307Appendix C Towards non-probabilistic settings: promises and industrial challenges 313Index 329

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