Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal

Abstract Uncertainty and sensitivity analysis techniques for use in performance assessments for radioactive waste disposal are reviewed. Summaries are given for the following techniques: differential analysis, Monte Carlo analysis, response surface methodology, and Fourier amplitude sensitivity test. Of these techniques, Monte Carlo analysis is felt to be the most widely applicable for use in performance assessment. Monte Carlo analysis involves five steps: (1) selection of a range and distribution for each input variable; (2) generation of a sample from the input variables; (3) propagation of the sample through the model under consideration; (4) performance of uncertainty analysis; and (5) performance of sensitivity analysis. These steps are discussed and illustrated with an analysis performed as part of a preliminary performance assessment for the Waste Isolation Pilot Plant (WIPP).

[1]  W. V. Loscutoff,et al.  General sensitivity theory , 1972 .

[2]  James E. Campbell,et al.  An Approach to Sensitivity Analysis of Computer Models: Part I—Introduction, Input Variable Selection and Preliminary Variable Assessment , 1981 .

[3]  Jon C. Helton,et al.  An uncertainty/sensitivity study for the station blackout sequence at a Mark I boiling water reactor , 1989 .

[4]  Yih-Tsuen Wu Demonstration of a new, fast probability integration method for reliability analysis , 1987 .

[5]  R Mead,et al.  A review of response surface methodology from a biometric viewpoint. , 1975, Biometrics.

[6]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[7]  M. Granger Morgan,et al.  Graphical Communication of Uncertain Quantities to Nontechnical People , 1987 .

[8]  T. Cruse,et al.  Advanced probabilistic structural analysis method for implicit performance functions , 1990 .

[9]  M. D. McKay,et al.  Monte Carlo estimation under different distributions using the same simulation , 1987 .

[10]  E Ackerman,et al.  Latin hypercube sampling and the sensitivity analysis of a Monte Carlo epidemic model. , 1988, International journal of bio-medical computing.

[11]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[12]  F. G. Pin,et al.  An automated sensitivity analysis procedure for the performance assessment of nuclear waste isolation systems , 1986 .

[13]  H. Steinberg GENERALIZED QUOTA SAMPLING , 1963 .

[14]  M. Eslami,et al.  Introduction to System Sensitivity Theory , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  G. Parry On the meaning of probability in probabilistic safety assessment , 1988 .

[16]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[17]  Ronald L. Iman,et al.  A Modern Approach To Statistics , 1983 .

[18]  E. Oblow,et al.  Sensitivity Theory for General Systems of Nonlinear Equations , 1980 .

[19]  Gordon Woo A quitting rule for Monte Carlo simulation of extreme risks , 1991 .

[20]  T. D. Brown,et al.  Evaluation of severe accident risks: Quantification of major input parameters , 1992 .

[21]  R. Iman,et al.  Rank correlation plots for use with correlated input variables , 1982 .

[22]  Jon C. Helton,et al.  Integration of the NUREG-1150 analyses: Calculation of risk and propagation of uncertainties , 1987 .

[23]  B. Silverman Density estimation for statistics and data analysis , 1986 .

[24]  R. L. Iman,et al.  Overview of methods for uncertainty analysis and sensitivity analysis in probabilistic risk assessment , 1984 .

[25]  R. L. Iman,et al.  Sensitivity-analysis techniques: self-teaching curriculum , 1982 .

[26]  M. S. Tierney Combining scenarios in a calculation of the overall probability distribution of cumulative releases of radioactivity from the Waste Isolation Pilot Plant, southeastern New Mexico , 1991 .

[27]  D. C. Cox,et al.  Methods for Uncertainty Analysis: A Comparative Survey , 1981 .

[28]  Ronald L. Iman,et al.  Expert opinion in risk analysis: the NUREG-1150 methodology , 1989 .

[29]  J. Friedman Multivariate adaptive regression splines , 1990 .

[30]  G. J. Hahn,et al.  Statistical models in engineering , 1967 .

[31]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[32]  F. O. Hoffman,et al.  Imprecision of dose predictions for radionuclides released to the environment: An application of a Monte Carlo simulation technique , 1980 .

[33]  Ronald L. Iman,et al.  FORTRAN 77 program and user's guide for the calculation of partial correlation and standardized regression coefficients , 1985 .

[34]  T. W. Anderson An Introduction to Multivariate Statistical Analysis , 1959 .

[35]  K. Rose,et al.  A Simulation Comparison and Evaluation of Parameter Sensitivity Methods Applicable to Large Models , 1983 .

[36]  George Apostolakis,et al.  Assessment of the uncertainties associated with the core uncovery time in TMI-type accidents , 1984 .

[37]  T. A. Wheeler,et al.  Use of expert judgment in NUREG--1150 , 1991 .

[38]  Jack C. Parker,et al.  Effects of parameter uncertainty on predictions of unsaturated flow , 1989 .

[39]  S. Kaplan,et al.  On The Quantitative Definition of Risk , 1981 .

[40]  J. C. Helton,et al.  A COMPARISON OF UNCERTAINTY AND SENSITIVITY ANALYSIS TECHNIQUES FOR COMPUTER MODELS , 1985 .

[41]  Jon C. Helton,et al.  Risk, Uncertainty in Risk, and the EPA Release Limits for Radioactive Waste Disposal , 1993 .

[42]  A. Saltelli,et al.  Non-parametric statistics in sensitivity analysis for model output: A comparison of selected techniques , 1990 .

[43]  D. Teichroew A History of Distribution Sampling Prior to the Era of the Computer and its Relevance to Simulation , 1965 .

[44]  M. G. Marietta,et al.  Preliminary comparison with 40 CFR Part 191, Subpart B for the Waste Isolation Pilot Plant, December 1990 , 1990 .

[45]  Evaristo J. Bonano,et al.  Treatment of uncertainties in the performance assessment of geologic high-level radioactive waste repositories , 1988 .

[46]  G. Stephanopoulos,et al.  Development and global sensitivity analysis of a closed ecosystem model , 1985 .

[47]  M. Mazumdar,et al.  Propagation of uncertainties in problems of structural reliability , 1978 .

[48]  Jon C. Helton,et al.  Evaluation of severe accident risks: Surry Unit 1 , 1990 .

[49]  J. W. Gorman,et al.  Fitting Equations to Data. , 1973 .

[50]  John W Tukey THE PROPAGATION OF ERRORS, FLUCTUATIONS AND TOLERANCES, SUPPLEMENTARY FORMULAS , 1957 .

[51]  G. Yule Why do we Sometimes get Nonsense-Correlations between Time-Series?--A Study in Sampling and the Nature of Time-Series , 1926 .

[52]  D. Rubin,et al.  A Research Agenda for Assessment and Propagation of Model Uncertainty , 1987 .

[53]  N. R. Ortiz,et al.  Risk methodology for geologic disposal of radioactive waste: Final report , 1987 .

[54]  R. H. Myers Classical and modern regression with applications , 1986 .

[55]  Ronald L. Iman,et al.  Risk methodology for geologic disposal of radioactive waste: small sample sensitivity analysis techniques for computer models, with an application to risk assessment , 1980 .

[56]  W. J. Conover,et al.  Practical Nonparametric Statistics , 1972 .

[57]  Jon C. Helton,et al.  Calculation of reactor accident safety goals , 1993 .

[58]  James R. Burns Error Analysis of Nonlinear Simulations: Applications to World Dynamics , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[59]  John H. Seinfeld,et al.  Global sensitivity analysis—a computational implementation of the Fourier Amplitude Sensitivity Test (FAST) , 1982 .

[60]  F. G. Pin,et al.  Sensitivity analysis using computer calculus: A nuclear waste isolation application , 1986 .

[61]  J. Kleijnen Statistical tools for simulation practitioners , 1986 .

[62]  Robert J. Gelinas,et al.  Sensitivity analysis of ordinary differential equation systems—A direct method , 1976 .

[63]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[64]  R. P. Canale,et al.  Comparison of first‐order error analysis and Monte Carlo Simulation in time‐dependent lake eutrophication models , 1981 .

[65]  James S. Hodges,et al.  Uncertainty, Policy Analysis and Statistics , 1987 .

[66]  K. Shuler,et al.  Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. II Applications , 1973 .

[67]  P. A. Davis,et al.  Demonstration of a performance assessment methodology for high-level radioactive waste disposal in basalt formations , 1989 .

[68]  Herschel Rabitz,et al.  The Green’s function method of sensitivity analysis in chemical kinetics , 1978 .

[69]  Jay D. Johnson,et al.  Uncertainty and sensitivity analysis of a dry containment test problem for the MAEROS aerosol model , 1989 .

[70]  Byung Ho Lee,et al.  Uncertainty and Sensitivity Analyses in Evaluating Risk of High Level Waste Repository , 1988 .

[71]  J. Tukey THE PROPAGATION OF ERRORS, FLUCTUATIONS, AND TOLERANCES BASIC GENERALIZED FORMULAS , 1957 .

[72]  R. G. Derwent,et al.  Treating uncertainty in models of the atmospheric chemistry of nitrogen compounds , 1967 .

[73]  W. V. Harper,et al.  Sensitivity/uncertainty analysis of a borehole scenario comparing Latin Hypercube Sampling and deterministic sensitivity approaches , 1983 .

[74]  J. Halton A Retrospective and Prospective Survey of the Monte Carlo Method , 1970 .

[75]  F. T. Harper,et al.  Evaluation of severe accident risks: Quantification of major input parameters. Experts` determination of structural response issues , 1992 .

[76]  Ronald L. Iman,et al.  The Repeatability of Uncertainty and Sensitivity Analyses for Complex Probabilistic Risk Assessments , 1991 .

[77]  George A. F. Seber,et al.  Linear regression analysis , 1977 .

[78]  Eugene P. Dougherty,et al.  A computational algorithm for the Green's function method of sensitivity analysis in chemical kinetics , 1979 .

[79]  Kenneth A. Rose,et al.  Latin hypercube analysis of parameter sensitivity in a large model of outdoor recreation demand , 1984 .

[80]  G. Anandalingam Process Modelling under Uncertainty: Simulation Analysis of Indian Steel , 1987 .

[81]  Jack P. C. Kleijnen,et al.  Statistical Techniques in Simulation , 1977, IEEE Transactions on Systems, Man and Cybernetics.

[82]  Stephen D. Unwin,et al.  Controlling principles for prior probability assignments in nuclear risk assessment , 1986 .

[83]  Gene H. Golub,et al.  Matrix computations , 1983 .

[84]  E. Cazzoli,et al.  A probabilistic approach to quantifying uncertainties in the progression of severe accidents , 1989 .

[85]  M. E Paté-Cornell,et al.  Probability and uncertainty in nuclear safety decisions , 1986 .

[86]  W. W. Muir,et al.  Regression Diagnostics: Identifying Influential Data and Sources of Collinearity , 1980 .

[87]  M. Kramer,et al.  Sensitivity Analysis in Chemical Kinetics , 1983 .

[88]  P. G. Doctor,et al.  Sensitivity and uncertainty analyses for performance assessment modeling , 1989 .

[89]  J. S. Sandha,et al.  Data used in preliminary performance assessment of the Waste Isolation Pilot Plant (1990) , 1990 .

[90]  S. Ahmed,et al.  Uncertainty propagation in probabilistic risk assessment: A comparative study , 1981 .

[91]  Jon C. Helton,et al.  Risk methodology for geologic disposal of radioactive waste: sensitivity analysis techniques , 1978 .

[92]  J C Helton,et al.  Uncertainty analysis associated with radioactive waste disposal: a discussion paper , 1980 .

[93]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[94]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

[95]  B. A. Worley,et al.  Waste package performance assessment code with automated sensitivity-calculation capability , 1986 .

[96]  D. Cacuci Sensitivity theory for nonlinear systems. II. Extensions to additional classes of responses , 1981 .

[97]  Eugene P. Dougherty,et al.  Further developments and applications of the Green’s function method of sensitivity analysis in chemical kinetics , 1979 .

[98]  Yih‐Tsuen Wu,et al.  New Algorithm for Structural Reliability Estimation , 1987 .

[99]  Ronald L. Iman,et al.  A FORTRAN-77 PROGRAM AND USER'S GUIDE FOR THE GENERATION OF LATIN HYPERCUBE AND RANDOM SAMPLES FOR USE WITH COMPUTER MODELS , 1984 .

[100]  S. C. Chay,et al.  Review of the methodology for statistical evaluation of reactor safety analyses , 1975 .

[101]  Carl M. Harris Oil and Gas Supply Modeling under Uncertainty: Putting DOE Midterm Forecasts in Perspective , 1983 .

[102]  D. M. Rasmuson,et al.  Uncertainties in Nuclear Probabilistic Risk Analyses , 1984 .

[103]  Student,et al.  THE PROBABLE ERROR OF A MEAN , 1908 .

[104]  Michael H. Kutner Applied Linear Statistical Models , 1974 .

[105]  Jon C. Helton,et al.  An Approach to Sensitivity Analysis of Computer Models: Part II - Ranking of Input Variables, Response Surface Validation, Distribution Effect and Technique Synopsis , 1981 .

[106]  J. Berger Statistical Decision Theory and Bayesian Analysis , 1988 .

[107]  Kenneth H. Reckhow,et al.  Predicting Variability in a Lake Ontario Phosphorus Model , 1983 .

[108]  Robert V. O'Neill,et al.  A comparison of sensitivity analysis and error analysis based on a stream ecosystem model , 1981 .

[109]  D. Cacuci Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach , 1981 .

[110]  Jon C. Helton,et al.  Sensitivity analysis of the asymptotic behavior of a model for the environmental movement of radionuclides , 1985 .

[111]  J. F. Sykes,et al.  Parameter Identification and Uncertainty Analysis for Variably Saturated Flow , 1988 .

[112]  K. Shuler,et al.  Nonlinear sensitivity analysis of multiparameter model systems , 1977 .

[113]  N. D. Cox,et al.  Comparison of two uncertainty analysis methods , 1977 .

[114]  Soon Heung Chang,et al.  Comparative Study on Uncertainty and Sensitivity Analysis and Application to LOCA Model , 1988 .

[115]  H. Rief,et al.  Review of Monte Carlo Techniques for Analyzing Reactor Perturbations , 1986 .

[116]  J. C. Helton,et al.  Uncertainty analysis for geologic disposal of radioactive waste , 1981 .

[117]  P. G. Doctor,et al.  A comparison of uncertainty analysis methods using a groundwater flow model , 1988 .

[118]  Raymond A. Ferrara,et al.  Modeling sediment and water column interactions for hydrophobic pollutants. Parameter discrimination and model response to input uncertainty , 1984 .

[119]  R. Cheng,et al.  Confidence Bands for Cumulative Distribution Functions of Continuous Random Variables , 1983 .

[120]  Jon C. Helton,et al.  Sensitivity analysis techniques and results for performance assessment at the Waste Isolation Pilot Plant , 1991 .

[121]  F. O. Hoffman,et al.  An Examination of Response-Surface Methodologies for Uncertainty Analysis in Assessment Models , 1985 .

[122]  M. Stein Large sample properties of simulations using latin hypercube sampling , 1987 .

[123]  Robert G Hendrickson,et al.  A survey of sensitivity analysis methodology , 1984 .

[124]  James E. Campbell,et al.  Application of generic risk assessment software to radioactive waste disposal , 1990 .

[125]  R. H. Gardner,et al.  Parameter Uncertainty and Model Predictions: A Review of Monte Carlo Results , 1983 .

[126]  R M Cranwell,et al.  Performance assessment of radioactive waste repositories. , 1988, Science.

[127]  W. R. Rish Approach to uncertainty in risk analysis , 1988 .

[128]  D. Cochrane,et al.  A sampling study of the merits of autoregressive and reduced form transformation in regression analysis. , 1949, Journal of the American Statistical Association.

[129]  David F. Hendry,et al.  Monte carlo experimentation in econometrics , 1984 .

[130]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[131]  Robert L. Winkler,et al.  An Introduction to Bayesian Inference and Decision , 1972 .

[132]  C. Fortuin,et al.  Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory , 1973 .

[133]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[134]  Jon C. Helton,et al.  Uncertainty and Sensitivity Analysis of a Model for Multicomponent Aerosol Dynamics , 1986 .

[135]  E. A. Jacobson,et al.  INVESTIGATIONS OF SENSITIVITY AND UNCERTAINTY IN SOME HYOROLOGIC MODELS OF YUCCA MOUNTAIN AND VICINITY , 1985 .

[136]  Ronald L. Iman,et al.  Rejoinder to comments , 1980 .

[137]  John E. A. Marshall,et al.  Methodology development for statistical evaluation of reactor safety analyses , 1976 .

[138]  M. Uliasz Comparison of the sensitivity analysis methods for meteorological models , 1985 .

[139]  J. K. Vaurio,et al.  Probabilistic Analysis of Liquid-Metal Fast Breeder Reactor Accident Consequences with Response Surface Techniques , 1978 .

[140]  R. Iman,et al.  The Use of the Rank Transform in Regression , 1979 .

[141]  J. Turner,et al.  A Monte Carlo primer for health physicists. , 1985, Health physics.

[142]  J. C. Helton,et al.  An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models , 1988 .

[143]  Rechard Review and discussion of code linkage and data flow in nuclear waste compliance assessments , 1989 .

[144]  Ralph L. Keeney,et al.  Elicitation and use of expert judgment in performance assessment for high-level radioactive waste repositories , 1990 .

[145]  C. Voss,et al.  SUTRA (Saturated-Unsaturated Transport). A Finite-Element Simulation Model for Saturated-Unsaturated, Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically-Reactive Single-Species Solute Transport. , 1984 .

[146]  Jon C. Helton,et al.  Evaluation of severe accident risks, Peach Bottom, Unit 2: Main report , 1990 .