Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems

Reliability Engineering & System Safety - Tập 81 Số 1 - Trang 23-69 - 2003
J.C. Helton1, F.J. Davis2
1Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, USA
2Department 6849, MS 0779, Sandia National Laboratories, Albuquerque, NM 87185-0779, USA

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1996

1994

1993

1993

1989

Beck, 1987, Water-quality modeling: a review of the analysis of uncertainty, Water Resour Res, 23, 1393, 10.1029/WR023i008p01393

Helton, 1996, Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems, Reliab Engng Syst Saf, 54, 91, 10.1016/S0951-8320(96)00066-X

Helton, 1997, Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty, J Stat Comput Simul, 57, 3, 10.1080/00949659708811803

Cook, 1986, Controlling principles for prior probability assignments in nuclear risk assessment, Nuclear Sci Engng, 94, 107, 10.13182/NSE86-A27446

Mosleh, 1988, A critique of current practice for the use of expert opinions in probabilistic risk assessment, Reliab Engng Syst Saf, 20, 63, 10.1016/0951-8320(88)90006-3

Hora, 1989, Expert opinion in risk analysis: the NUREG-1150 methodology, Nuclear Sci Engng, 102, 323, 10.13182/NSE89-A23645

Svenson, 1989, On expert judgments in safety analyses in the process industries, Reliab Engng Syst Saf, 25, 219, 10.1016/0951-8320(89)90095-1

Keeney, 1991, Eliciting probabilities from experts in complex technical problems, IEEE Trans Engng Manage, 38, 191, 10.1109/17.83752

Bonano, 1990

Bonano, 1991, Theoretical foundations and practical issues for using expert judgments in uncertainty analysis of high-level radioactive waste disposal, Radioact Waste Manage Nuclear Fuel Cycle, 16, 137

Cooke, 1991

Meyer, 1991

Ortiz, 1991, Use of expert judgment in NUREG-1150, Nuclear Engng Des, 126, 313, 10.1016/0029-5493(91)90023-B

Chhibber, 1992, A taxonomy of issues related to the use of expert judgments in probabilistic safety studies, Reliab Engng Syst Saf, 38, 27, 10.1016/0951-8320(92)90103-R

Kaplan, 1992, Expert information versus expert opinions: another approach to the problem of eliciting combining using expert knowledge in PRA, Reliab Engng Syst Saf, 35, 61, 10.1016/0951-8320(92)90023-E

Otway, 1992, Expert judgement in risk analysis and management: process, context, and pitfalls, Risk Anal, 12, 83, 10.1111/j.1539-6924.1992.tb01310.x

Thorne, 1992, A review of expert judgement techniques with reference to nuclear safety, Prog Nuclear Saf, 27, 83, 10.1016/0149-1970(92)90001-J

Thorne, 1993, The use of expert opinion in formulating conceptual models of underground disposal systems and the treatment of associated bias, Reliab Engng Syst Saf, 42, 161, 10.1016/0951-8320(93)90087-F

Evans, 1994, Use of probabilistic expert judgement in uncertainty analysis of carcinogenic potency, part 1, Regul Toxicol Pharmacol, 20, 15, 10.1006/rtph.1994.1034

Budnitz, 1998, Use of technical expert panels: applications to probabilistic seismic hazard analysis, Risk Anal, 18, 463, 10.1111/j.1539-6924.1998.tb00361.x

Goossens, 1998, Joint EC/USNRC expert judgement driven radiological protection uncertainty analysis, J Radiol Prot, 18, 249, 10.1088/0952-4746/18/4/003

Siu, 1998, Bayesian parameter estimation in probabilistic risk assessment, Reliab Engng Syst Saf, 62, 89, 10.1016/S0951-8320(97)00159-2

Goossens, 2000, Expert judgement for a probabilistic accident consequence uncertainty analysis, Radiat Prot Dosimetry, 90, 295, 10.1093/oxfordjournals.rpd.a033151

McKay, 2000, Critique of and limitations on the use of expert judgements in accident consequence uncertainty analysis, Radiat Prot Dosimetry, 90, 325, 10.1093/oxfordjournals.rpd.a033155

Feller, 1971, vol. 2

McKay, 1979, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239, 10.2307/1268522

Iman, 1992, Uncertainty and sensitivity analysis for computer modeling applications, vol. 28, 153

MacDonald, 1986, Valuation of supplemental and enhanced oil recovery projects with risk analysis, J Petrol Technol, 38, 57, 10.2118/11303-PA

Breshears, 1992, Contaminant transport through agroecosystems: assessing relative importance of environmental, physiological, and management factors, Ecol Appl, 2, 285, 10.2307/1941862

Ma, 1993, Parameter sensitivity of a model of viral epidemics simulated with Monte Carlo techniques. II. Durations and peaks, Int J Biomed Comput, 32, 255, 10.1016/0020-7101(93)90018-2

Ma, 1993, Parameter sensitivity of a model of viral epidemics simulated with Monte Carlo techniques. I. Illness attack rates, Int J Biomed Comput, 32, 237, 10.1016/0020-7101(93)90017-Z

Whiting, 1993, Effect of uncertainties in thermodynamic data and model parameters on calculated process performance, Ind Engng Chem Res, 32, 1367, 10.1021/ie00019a011

Blower, 1994, Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example, Int Stat Rev, 62, 229, 10.2307/1403510

Gwo, 1996, Subsurface stormflow modeling with sensitivity analysis using a Latin-Hypercube sampling technique, Ground Water, 34, 811, 10.1111/j.1745-6584.1996.tb02075.x

Helton, 1996, Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment for the waste isolation pilot plant, Reliab Engng Syst Saf, 51, 53, 10.1016/0951-8320(95)00089-5

Chan, 1996, The consequences of uncertainty for the prediction of the effects of schistosomiasis control programmes, Epidemiol Infect, 11, 537, 10.1017/S0950268800059239

Sanchez, 1997, Uncertainty and sensitivity analysis of the basic reproductive rate: tuberculosis as an example, Am J Epidemiol, 145, 1127, 10.1093/oxfordjournals.aje.a009076

Blower, 2000, A tale of two futures: HIV and antiretroviral therapy in San Francisco, Science, 287, 650, 10.1126/science.287.5453.650

Cohen, 2000, A discrete-event computer model of feline Herpes virus within cat populations, Preventative Vet Med, 45, 163, 10.1016/S0167-5877(00)00132-X

Kolev, 1996, Uncertainty and sensitivity analysis of a postexperiment simulation of nonexplosive melt-water interaction, Exp Ther Fluid Sci, 13, 98, 10.1016/0894-1777(96)00034-9

Caswell, 1998, Harbor porpoise and fisheries: an uncertainty analysis of incidental mortality, Ecol Appl, 8, 1226, 10.1890/1051-0761(1998)008[1226:HPAFAU]2.0.CO;2

Hofer, 1999, Sensitivity analysis in the context of uncertainty analysis for computationally intensive models, Comput Phys Commun, 117, 21, 10.1016/S0010-4655(98)00153-2

Metropolis, 1949, The Monte Carlo method, J Am Stat Assoc, 44, 335, 10.2307/2280232

Hammersley, 1964

Teichroew, 1965, A history of distribution sampling prior to the era of the computer and its relevance to simulation, J Am Stat Assoc, 60, 27, 10.2307/2283135

Halton, 1970, A retrospective and prospective survey of the Monte Carlo method, SIAM Rev, 12, 1, 10.1137/1012001

James, 1980, Monte Carlo theory and practice, Rep Prog Phys, 43, 1145, 10.1088/0034-4885/43/9/002

Rubinstein, 1981

Turner, 1985, A Monte Carlo primer for health physicists, Health Phys, 48, 717, 10.1097/00004032-198506000-00001

Kalos, 1986

Rief, 1986, Review of Monte Carlo techniques for analyzing reactor perturbations, Nuclear Sci Engng, 92, 289, 10.13182/NSE86-A18178

Fishman, 1996

Albano, 1996, The Monte Carlo simulation method: a powerful tool for the study of reaction processes, Heterogeneous Chem Rev, 3, 389, 10.1002/(SICI)1234-985X(199612)3:4<389::AID-HCR68>3.0.CO;2-2

Binder, 1997, Applications of Monte Carlo methods to statistical physics, Rep Prog Phys, 60, 487, 10.1088/0034-4885/60/5/001

Hurtado, 1998, Monte Carlo techniques in computational stochastic mechanics, Arch Comput Meth Engng, 5, 3, 10.1007/BF02736747

Hahn, 1967

Tukey, 1957

Tukey, 1957

Tukey, 1957

Tomovic, 1972

Frank, 1978

1982, vol. 14

Rabitz, 1983, Sensitivity analysis in chemical kinetics, vol. 34, 419

Ronen, 1988

Turányi, 1990, Sensitivity analysis of complex kinetic systems. Tools and applications, J Math Chem, 5, 203, 10.1007/BF01166355

Cacuci, 1980, Sensitivity theory for general systems of nonlinear equations, Nuclear Sci Engng, 75, 88, 10.13182/NSE75-88

Cacuci, 1981, Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach, J Math Phys, 22, 2794, 10.1063/1.525186

Cacuci, 1981, Sensitivity theory for nonlinear systems. II. Extensions to additional classes of responses, J Math Phys, 22, 2803, 10.1063/1.524870

Cacuci, 1994, On the application of the adjoint method of sensitivity analysis to problems in the atmospheric sciences, Atmósfera, 7, 47

Dougherty, 1979, A computational algorithm for the Green's function method of sensitivity analysis in chemical kinetics, Int J Chem Kinet, 11, 1237, 10.1002/kin.550111203

Dougherty, 1979, Further developments and applications of the Green's function method of sensitivity analysis in chemical kinetics, J Chem Phys, 71, 1794, 10.1063/1.438530

Hwang, 1978, The Green's function method of sensitivity analysis in chemical kinetics, J Chem Phys, 69, 5180, 10.1063/1.436465

Vuilleumier, 1997, First- and second-order sensitivity analysis of a photochemically reactive system (a Green's function approach), Environ Sci Technol, 31, 1206, 10.1021/es960727g

1991

Berz, 1996

Bischof, 1996, Adifor 2.0: automatic differentiation of Fortran 77 programs, IEEE Comput Sci Engng, 3, 18, 10.1109/99.537089

Griewank, 1996, Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++, ACM Trans Math Software, 22, 131, 10.1145/229473.229474

Bischof, 1997, ADIC: an extensible automatic differentiation tool for ANSI-C, Software: Pract Experience, 27, 1427, 10.1002/(SICI)1097-024X(199712)27:12<1427::AID-SPE138>3.0.CO;2-Q

Carmichael, 1997, Sensitivity analysis for atmospheric chemistry models via automatic differentiations, Atmos Environ, 31, 475, 10.1016/S1352-2310(96)00168-9

Giering, 1998, Recipes for adjoint code construction, ACM Trans Math Software, 24, 437, 10.1145/293686.293695

Tolsma, 1998, On computational differentiation, Comput Chem Engng, 22, 475, 10.1016/S0098-1354(97)00264-0

Eberhard, 1999, Automatic differentiation of numerical integration algorithms, Math Comput, 68, 717, 10.1090/S0025-5718-99-01027-3

Griewank, 2000

Andres, 1997, Sampling methods and sensitivity analysis for large parameter sets, J Stat Comput Simul, 57, 77, 10.1080/00949659708811804

Kleijnen, 1997, Sensitivity analysis and related analyses: a review of some statistical techniques, J Stat Comput Simul, 57, 111, 10.1080/00949659708811805

Bates, 1996, Experimental design and observation for large systems, J R Stat Soc Ser B—Methodol, 58, 77

Draper, 1996, An overview of design of experiments, Stat Pap, 37, 1, 10.1007/BF02926157

Draper, 1996, vol. 13, 10.1016/S0169-7161(96)13013-3

Koehler, 1996, vol. 13, 10.1016/S0169-7161(96)13011-X

Morris, 1995, Exploratory designs for computational experiments, J Stat Plann Inference, 43, 381, 10.1016/0378-3758(94)00035-T

Bowman, 1993, Design and analysis of numerical experiments, J Atmos Sci, 50, 1267, 10.1175/1520-0469(1993)050<1267:DAAONE>2.0.CO;2

Kleijnen, 1992, Sensitivity analysis of simulation experiments: regression-analysis and statistical design, Math Comput Simul, 34, 297, 10.1016/0378-4754(92)90007-4

Morris, 1991, Factorial sampling plans for preliminary computational experiments, Technometrics, 33, 161, 10.2307/1269043

Currin, 1991, Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments, J Am Stat Assoc, 86, 953, 10.2307/2290511

Sacks, 1989, Design and analysis of computer experiments, Stat Sci, 4, 409, 10.1214/ss/1177012413

Sacks, 1989, Designs for computer experiments, Technometrics, 31, 41, 10.2307/1270363

Cryer, 1999, Regional sensitivity analysis using a fractional factorial method for the USDA model GLEAMS, Environ Modell Software, 14, 613, 10.1016/S1364-8152(99)00003-1

Rao, 1997, Sensitivity studies of air scattered neutron dose from particle accelerators, J Stat Comput Simul, 57, 261

Kleijnen, 1992, Techniques for sensitivity analysis of simulation models: a case study of the CO2 Greenhouse effect, Simulation, 58, 410, 10.1177/003754979205800610

Engel, 1991, Response surface development using RETRAN, Nuclear Technol, 93, 65, 10.13182/NT91-A34519

Aceil, 1991, Sensitivity analysis of thermal-hydraulic parameters and probability estimation of boiling transition in a standard BWR/6, Nuclear Technol, 93, 123, 10.13182/NT91-A34498

Lee, 1987, A study on uncertainty and sensitivity of operational and modelling parameters for feedwater line break analysis, J Kor Nuclear Soc, 19, 10

Kim, 1986, A procedure for statistical thermal margin analysis using response surface method and Monte Carlo technique, J Kor Nuclear Soc, 18, 38

Myers, 1999, Response surface methodology—current status and future directions, J Qual Technol, 31, 30, 10.1080/00224065.1999.11979891

Myers, 1989, Response surface methodology: 1966–1988, Technometrics, 31, 137, 10.2307/1268813

Morton, 1983, Response surface methodology, Math Sci, 8, 31

Mead, 1975, A review of response surface methodology from a biometric viewpoint, Biometrics, 31, 803, 10.2307/2529809

Hill, 1966, A review of response surface methodology: a literature review, Technometrics, 8, 571, 10.2307/1266632

Myers, 1971

Box, 1987

Khuri, 1987

Kleijnen, 1987

Cukier, 1973, Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients, I. Theory, J Chem Phys, 59, 3873, 10.1063/1.1680571

Schaibly, 1973, Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients, II. Applications, J Chem Phys, 59, 3879, 10.1063/1.1680572

Cukier, 1978, Nonlinear sensitivity analysis of multiparameter model systems, J Comput Phys, 26, 1, 10.1016/0021-9991(78)90097-9

Sobol’, 1993, Sensitivity estimates for nonlinear mathematical models, Math Model Comput Exp, 1, 407

Chan, 2000, Winding stairs: a sampling tool to compute sensitivity indices, Stat Comput, 10, 187, 10.1023/A:1008950625967

Jansen, 1999, Analysis of variance designs for model output, Comput Phys Commun, 117, 35, 10.1016/S0010-4655(98)00154-4

Jansen, 1994, Monte Carlo estimation of uncertainty contributions from several independent multivariate sources, 334

Rabitz, 1999, Efficient input–output model representations, Comput Phys Commun, 117, 11, 10.1016/S0010-4655(98)00152-0

Saltelli, 1999, A quantitative model-independent method for global sensitivity analysis of model output, Technometrics, 41, 39, 10.2307/1270993

Homma, 1996, Importance measures in global sensitivity analysis of nonlinear models, Reliab Engng Syst Saf, 52, 1, 10.1016/0951-8320(96)00002-6

McRae, 1981, Global sensitivity analysis—a computational implementation of the Fourier amplitude sensitivity test (FAST), Comput Chem Engng, 6, 15, 10.1016/0098-1354(82)80003-3

Saltelli, 1995, About the use of rank transformation in sensitivity analysis of model output, Reliab Engng Syst Saf, 50, 225, 10.1016/0951-8320(95)00099-2

Archer, 1997, Sensitivity measures, ANOVA-like techniques and the use of bootstrap, J Stat Comput Simul, 58, 99, 10.1080/00949659708811825

Saltelli, 1998, An alternative way to compute Fourier amplitude sensitivity test (FAST), Comput Stat Data Anal, 26, 267, 10.1016/S0167-9473(97)00043-1

Rabitz, 1999, General foundations of high-dimensional model representations, J Math Chem, 25, 197, 10.1023/A:1019188517934

Saltelli, 2000, Sensitivity analysis as an ingredient of modeling, Stat Sci, 15, 377, 10.1214/ss/1009213004

Cox, 1982, An analytic method for uncertainty analysis of nonlinear output functions, with applications to fault-tree analysis, IEEE Trans Reliab, 3, 465, 10.1109/TR.1982.5221435

McKay, 1995

McKay, 1997, Nonparametric variance-based methods of assessing uncertainty importance, Reliab Engng Syst Saf, 57, 267, 10.1016/S0951-8320(97)00039-2

McKay, 1999, Evaluating prediction uncertainty in simulation models, Comput Phys Commun, 117, 44, 10.1016/S0010-4655(98)00155-6

Haskin, 1996, Efficient uncertainty analyses using fast probability integration, Nuclear Engng Des, 166, 225, 10.1016/0029-5493(96)01267-8

Wu, 1987, Demonstration of a new, fast probability integration method for reliability analysis, J Engng Ind, Trans ASME, Ser B, 109, 24, 10.1115/1.3187088

Schanz, 1992, Evaluation of the Rackwitz-Fiessler uncertainty analysis method for environmental fate and transport method, Water Resour Res, 28, 1071, 10.1029/91WR02758

Wu, 1990, Advanced probabilistic structural method for implicit performance functions, AIAA J, 28, 1663, 10.2514/3.25266

Wu, 1987, New algorithm for structural reliability, J Engng Mech, 113, 1319, 10.1061/(ASCE)0733-9399(1987)113:9(1319)

Chen, 1983, Fast probability integration by three-parameter normal tail approximation, Struct Saf, 1, 169

Rackwitz, 1978, Structural reliability under combined random load sequences, Comput Struct, 9, 489, 10.1016/0045-7949(78)90046-9

Hasofer, 1974, Exact and invariant second-moment code format, J Engng Mech Div, Proc Am Soc Civil Eng, 100, 111

Castillo, 1997, Tail uncertainty analysis in complex systems, Artif Intell, 96, 395, 10.1016/S0004-3702(97)00052-0

Castillo, 1999, Uncertainty analyses in fault trees and Bayesian networks using FORM/SORM methods, Reliab Engng Syst Saf, 65, 29, 10.1016/S0951-8320(98)00083-0

Press, 1992

Barry, 1996, Recommendations on the testing and use of pseudo-random number generators used in Monte Carlo analysis for risk assessment, Risk Anal, 16, 93, 10.1111/j.1539-6924.1996.tb01439.x

L'Ecuyer, 1998, Random number generation, 93

Iman, 1982, A distribution-free approach to inducing rank correlation among input variables, Commun Stat: Simul Comput, B11, 311, 10.1080/03610918208812265

Steinberg, 1963, Generalized quota sampling, Nuclear Sci Engng, 15, 142, 10.13182/NSE63-A26413

Raj, 1968

Stein, 1987, Large sample properties of simulations using Latin hypercube sampling, Technometrics, 29, 143, 10.2307/1269769

Owen, 1992, A central limit theorem for Latin hypercube sampling, J R Stat Soc. Ser B, Methodol., 54, 541

Billingsley, 1968

Mathé, 2001, Hilbert space analysis of Latin hypercube sampling, Proc Am Math Soc, 129, 1477, 10.1090/S0002-9939-00-05850-0

Hoshino, 2000, On reduction of finite-sample variance by extended Latin hypercube sampling, Bernoulli, 6, 1035, 10.2307/3318470

1975

Lewis, 1978

Helton, 2002

McKay, 1976

Steck, 1976

Iman, 1980

Iman, 1984

Iman, 1978

Campbell, 1978

Cranwell, 1987

Sprung, 1983

Iman, 1985

Iman, 1988, An investigation of uncertainty and sensitivity analysis techniques for computer models, Risk Anal, 8, 71, 10.1111/j.1539-6924.1988.tb01155.x

1990, vols. 1–3

Breeding, 1992, Summary description of the methods used in the probabilistic risk assessments for NUREG-1150, Nuclear Engng Des, 135, 1, 10.1016/0029-5493(92)90300-K

Breeding, 1990, vol. 3

Payne, 1990, vol. 4

Gregory, 1990, vol. 5

Brown, 1990, vol. 6

Park, 1993, vol. 7

Breeding, 1992, The NUREG-1150 probabilistic risk assessment for the Surry Nuclear Power Station, Nuclear Engng Des, 135, 29, 10.1016/0029-5493(92)90301-B

Payne, 1992, The NUREG-1150 probabilistic risk assessment for the Peach Bottom Atomic Power Station, Nuclear Engng Des, 135, 61, 10.1016/0029-5493(92)90302-C

Gregory, 1992, The NUREG-1150 probabilistic risk assessment for the Sequoyah Nuclear Plant, Nuclear Engng Des, 135, 92, 10.1016/0029-5493(92)90303-D

Brown, 1992, The NUREG-1150 probabilistic risk assessment for the Grand Gulf Nuclear Station, Nuclear Engng Des, 135, 117, 10.1016/0029-5493(92)90304-E

Helton, 1993, Calculation of reactor accident safety goals, Reliab Engng Syst Saf, 39, 129, 10.1016/0951-8320(93)90038-Z

Payne, 1992, vol. 1

Payne, 1992, vol. 2

Payne, 1992, vol. 3

Payne, 1992, vol. 3

NAS/NRC (National Academy of Sciences/National Research Council). The Waste Isolation Pilot Plant, a potential solution for the disposal of transuranic waste. Washington DC: National Academy Press, Committee on the Waste Isolation Pilot Plant, Board on Radioactive Waste Management, Commission on Geosciences, Environment, and Resources, National Research Council. 1996.

Rechard, 2000, Historical background on performance assessment for the Waste Isolation Pilot Plant, Reliab Engng Syst Saf, 69, 5, 10.1016/S0951-8320(00)00023-5

US DOE (US Department of Energy). Title 40 CFR Part 191 compliance certification application for the Waste Isolation Pilot Plant, DOE/CAO-1996-(2184). Carlsbad, NM: US Department of Energy, Carlsbad Area Office. Waste Isolation Pilot Plant. 1996.

Helton, 2000, Special issue: the 1996 performance assessment for the Waste Isolation Pilot Plant, Reliab Engng Syst Saf, 69, 1, 10.1016/S0951-8320(00)00022-3

1985, 40 CFR Part 191: environmental standards for the management and disposal of spent nuclear fuel, high-level and transuranic radioactive wastes; final rule, Fed Register, 50, 38066

1996, 40 CFR Part 194: criteria for the certification and re-certification of the Waste Isolation Pilot Plant's compliance with the 40 CFR Part 191 disposal regulations; final rule, Fed Register, 61, 5224

Helton, 1993, Risk, uncertainty in risk, and the EPA release limits for radioactive waste disposal, Nuclear Technol, 101, 18, 10.13182/NT93-A34765

Helton, 1997, Performance assessment for the Waste Isolation Pilot Plant: from regulation to calculation for 40 CFR 191.13, Oper Res, 45, 157, 10.1287/opre.45.2.157

1998

2000

2000

Kincaid, 2000

1999

Gilbert, 1995, On the use of uncertainty analyses to test hypotheses regarding deterministic model predictions of environmental processes, J Environ Radioact, 27, 231, 10.1016/0265-931X(94)00040-4

Hyman, 1995, Parameter uncertainty and sensitivity in a liquid-effluent dose model, Environ Monitor Assess, 38, 51, 10.1007/BF00547126

Toran, 1995, Sensitivity analysis of solute transport in fractured porous media, Geophys Res Lett, 22, 1433, 10.1029/95GL01096

Anderson, 1996, Transmission dynamics and epidemiology of BSE in British cattle, Nature, 382, 779, 10.1038/382779a0

Fish, 1997, The effect of uncertainties in kinetic and photochemical data on model predictions of stratosphere ozone depletion, J Geophys Res, 102, 25537, 10.1029/97JD01971

Keramat, 1997, Latin hypercube sampling Monte Carlo estimation of average quality index for integrated circuits, Analog Integrated Circuits Signal Process, 14, 131, 10.1023/A:1008207113480

Ellerbroek, 1998, Modeling pesticide transport in an irrigated field with variable water application and hydraulic conductivity, J Environ Qual, 27, 495, 10.2134/jeq1998.00472425002700030004x

Chen, 1999, Comparison of empirical strategies to maximize GENEHUNTER Lod scores, Genet Epidemiol, 17, S103, 10.1002/gepi.1370170718

Considine, 1999, A Monte Carlo uncertainty analysis of ozone trend predictions in a two-dimensional model, J Geophys Res, 104, 1749, 10.1029/1998JD100028

Kros, 1999, Uncertainty assessment in modeling soil acidification at the European scale: a case study, J Environ Qual, 28, 366, 10.2134/jeq1999.00472425002800020002x

Mrawira, 1999, Sensitivity analysis of computer models: World Bank HDM-III model, J Transport Engng, 125, 421, 10.1061/(ASCE)0733-947X(1999)125:5(421)

Padmanabhan, 1999, Stochastic modeling of nonisothermal flow during resin transfer molding, Int J Heat Mass Transfer, 42, 3057, 10.1016/S0017-9310(98)00377-9

Soutter, 1999, Global sensitivity analyses of three pesticide leaching models using a Monte Carlo approach, J Environ Qual, 28, 1290, 10.2134/jeq1999.00472425002800040033x

Fischer, 2000, Techniques applied in the COSYMA accident consequence uncertainty analysis, Radiat Prot Dosimetry, 90, 317, 10.1093/oxfordjournals.rpd.a033154

Oh, 2000, Sensitivity analysis of time-dependent behavior in PSC box girder bridges, J Struct Engng, 126, 171, 10.1061/(ASCE)0733-9445(2000)126:2(171)

Morris, 2000, Three technometrics experimental design classics, Technometrics, 42, 26, 10.2307/1271429

Helton, 1993, Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal, Reliab Engng Syst Saf, 42, 327, 10.1016/0951-8320(93)90097-I

Conover, 1980

Golub, 1983

Anderson, 1984

Iman, 1980

Iman, 1982, Rank correlation plots for use with correlated input variables, Commun Stat: Simul Comput, B11, 335, 10.1080/03610918208812266

Ye, 2000, Algorithmic construction of optimal symmetric Latin hypercube designs, J Stat Plann Inference, 90, 145, 10.1016/S0378-3758(00)00105-1

Pebesma, 1999, Latin hypercube sampling of gaussian random fields, Technometrics, 41, 303, 10.2307/1271347

Avramidis, 1998, Correlation-induction techniques for estimating quantiles in simulation experiments, Oper Res, 46, 574, 10.1287/opre.46.4.574

Ye, 1998, Orthogonal column Latin hypercubes and their application in computer experiments, J Am Stat Assoc, 93, 1430, 10.2307/2670057

Tang, 1998, Selecting Latin hypercubes using correlation criteria, Stat Sin, 8, 965

Salagame, 1997, Factorial hypercube designs for spatial correlation regression, J Appl Stat, 24, 453, 10.1080/02664769723648

Owen, 1997, Monte Carlo variance of scrambled net quadrature, Siam J Numer Anal, 34, 1884, 10.1137/S0036142994277468

Loh, 1997, Estimating the integral of a squared regression function with Latin hypercube, Stat Probab Lett, 31, 339, 10.1016/S0167-7152(96)00048-X

Loh, 1996, On Latin hypercube sampling, Ann Stat, 24, 2058, 10.1214/aos/1069362310

Avramidis, 1996, Integrated variance reduction strategies for simulation, Oper Res, 44, 327, 10.1287/opre.44.2.327

Loh, 1996, A combinatorial central limit theorem for randomized orthogonal array sampling designs, Ann Stat, 24, 1209, 10.1214/aos/1032526964

Streltsov, 1996, Variance reduction algorithms for parallel replicated simulation of uniformized Markov chains, Discrete Event Dyn Syst: Theor Appl, 6, 159, 10.1007/BF01797237

Harris, 1995, Obtaining minimum-correlation Latin hypercube sampling plans using an IP-based heuristic, OR Spektrum, 17, 139, 10.1007/BF01719258

Owen, 1994, Controlling correlations in Latin hypercube samples, J Am Stat Assoc, 89, 1517, 10.2307/2291014

Owen, 1994, Lattice sampling revisited: Monte-Carlo variance of means over randomized orthogonal arrays, Ann Stat, 22, 930, 10.1214/aos/1176325504

Tang, 1994, A theorem for selecting OA-based Latin hypercubes using a distance criterion, Commun Stat—Theor Meth, 23, 2047, 10.1080/03610929408831370

Park, 1994, Optimal Latin-hypercube designs for computer experiments, J Stat Plann Inference, 39, 95, 10.1016/0378-3758(94)90115-5

Tang, 1993, Orthogonal array-based Latin hypercubes, J Am Stat Assoc, 88, 1392, 10.2307/2291282

Owen, 1992, Orhogonal arrays for computer experiments, integration and visualization, Stat Sin, 2, 439

Iman, 1980, Small sample sensitivity analysis techniques for computer models, with an application to risk assessment, Commun Stat: Theor Meth, A9, 1749, 10.1080/03610928008827996

Beckman, 1987, Monte-Carlo estimation under different distribution using the same simulation, Technometrics, 29, 153, 10.2307/1269770

Iman, 1981, Statistical methods for including uncertainties associated with the geologic isolation of radioactive waste which allow for a comparison with licensing criteria, 145

Helton, 1998

Vaughn, 2000, Representation of two-phase flow in the vicinity of the repository in the 1996 performance assessment for the Waste Isolation Pilot Plant, Reliab Engng Syst Saf, 69, 205, 10.1016/S0951-8320(00)00033-8

Helton, 2000, Uncertainty and sensitivity analysis for two-phase flow in the vicinity of the repository in the 1996 performance assessment for the Waste Isolation Pilot Plant: undisturbed conditions, Reliab Engng Syst Saf, 69, 227, 10.1016/S0951-8320(00)00034-X

Helton, 2000, Uncertainty and sensitivity analysis for two-phase flow in the vicinity of the repository in the 1996 performance assessment for the Waste Isolation Pilot Plant: disturbed conditions, Reliab Engng Syst Saf, 69, 263, 10.1016/S0951-8320(00)00035-1

Helton, 1999, Performance assessment in support of the 1996 compliance certification application for the Waste Isolation Pilot Plant, Risk Anal, 19, 959, 10.1111/j.1539-6924.1999.tb00453.x

Helton, 2000, Characterization of subjective uncertainty in the 1996 performance assessment for the Waste Isolation Pilot Plant, Reliab Engng Syst Saf, 69, 191, 10.1016/S0951-8320(00)00032-6

Ibrekk, 1987, Graphical communication of uncertain quantities to nontechnical people, Risk Anal, 7, 519, 10.1111/j.1539-6924.1987.tb00488.x

Iman, 1991, The repeatability of uncertainty and sensitivity analyses for complex probabilistic risk assessments, Risk Anal, 11, 591, 10.1111/j.1539-6924.1991.tb00649.x

Helton, 1995, Robustness of an uncertainty and sensitivity analysis of early exposure results with the MACCS reactor accident consequence model, Reliab Engng Syst Saf, 48, 129, 10.1016/0951-8320(95)00001-I

Iman, 1979, The use of the rank transform in regression, Technometrics, 21, 499, 10.2307/1268289

Kleijnen, 1999, Statistical analyses of scatterplots to identify important factors in large-scale simulations, 1: review and comparison of techniques, Reliab Engng Syst Saf, 65, 147, 10.1016/S0951-8320(98)00091-X

Kleijnen, 1999, Statistical analyses of scatterplots to identify important factors in large-scale simulations, 2: robustness of techniques, Reliab Engng Syst Saf, 65, 187, 10.1016/S0951-8320(98)00090-8

Iman, 1987, A measure of top-down correlation, Technometrics, 29, 351, 10.2307/1269344

Assunçao, 1994, Testing spatial randomness by means of angles, Biometrics, 50, 531, 10.2307/2533397

Ripley, 1987, Spatial point pattern analysis in ecology, vol. 14, 407

Zeng, 1985, A comparison of tests for randomness, Pattern Recog, 18, 191, 10.1016/0031-3203(85)90043-3

Diggle, 1983, Some distance-based tests of independence for sparsely-sampled multivariate spatial point patterns, Int Stat Rev, 51, 11, 10.2307/1402729

Byth, 1982, On robust distance-based intensity estimators, Biometrics, 38, 127, 10.2307/2530295

Byth, 1980, On sampling spatial patterns by distance methods, Biometrics, 36, 279, 10.2307/2529979

Diggle, 1979, On parameter estimation and goodness-of-fit testing for spatial point patterns, Biometrics, 35, 87, 10.2307/2529938

Diggle, 1979, Statistical methods for spatial point patterns in ecology, 95

Besag, 1977, Simple Monte Carlo tests for spatial pattern, Appl Stat, 26, 327, 10.2307/2346974

Diggle, 1976, Statistical analysis of spatial point patterns by means of distance methods, Biometrics, 32, 659, 10.2307/2529754

Ripley, 1979, Tests of randomness for spatial point patterns, J R Stat Soc, 41, 368

Cox, 1976, A conditioned distance ratio method for analyzing spatial patterns, Biometrika, 63, 483, 10.1093/biomet/63.3.483

Holgate, 1972, The use of distance methods for the analysis of spatial distribution of points, 122

Holgate, 1965, Tests of randomness based on distance methods, Biometrika, 52, 345, 10.1093/biomet/52.3-4.345

Garvey, 1998, From star charts to stoneflies: detecting relationships in continuous bivariate data, Ecology, 79, 442, 10.1890/0012-9658(1998)079[0442:FSCTSD]2.0.CO;2

Fasano, 1987, A multidimensional version of the Kolmogorov–Smirnov test, Mon Not R Astron Soc, 225, 155, 10.1093/mnras/225.1.155

Gosset, 1987, A 3-dimensional extended Kolmogorov–Smirnov test as a useful tool in astronomy, Astron Astrophys, 188, 258

Peacock, 1983, Two-dimensional goodness-of-fit testing in astronomy, Mon Not R Astron Soc, 202, 615, 10.1093/mnras/202.3.615

Helton, 2000

Hamby, 1995, A comparison of sensitivity analysis techniques, Health Phys, 68, 195, 10.1097/00004032-199502000-00005

Hamby, 1994, A review of techniques for parameter sensitivity analysis of environmental models, Environ Monitor Assess, 32, 135, 10.1007/BF00547132

Saltelli, 1993, Sensitivity analysis of model output. An investigation of new techniques, Comput Stat Data Anal, 15, 211, 10.1016/0167-9473(93)90193-W

Saltelli, 1990, Non-parametric statistics in sensitivity analysis for model output. A comparison of selected techniques, Reliab Engng Syst Saf, 28, 229, 10.1016/0951-8320(90)90065-U

Iman, 1981, An approach to sensitivity analysis of computer models, part 1. Introduction, input variable selection and preliminary variable assessment, J Qual Technol, 13, 174, 10.1080/00224065.1981.11978748

Iman, 1981, An approach to sensitivity analysis of computer models, part 2. Ranking of input variables, response surface validation, distribution effect and technique synopsis, J Qual Technol, 13, 232, 10.1080/00224065.1981.11978763

Kaplan, 1981, On the quantitative definition of risk, Risk Anal, 1, 11, 10.1111/j.1539-6924.1981.tb01350.x

Parry, 1981, Characterization and evaluation of uncertainty in probabilistic risk analysis, Nuclear Saf, 22, 28

Haan, 1989, Parametric uncertainty in hydrologic modeling, Trans ASAE, 32, 137, 10.13031/2013.30973

Apostolakis, 1990, The concept of probability in safety assessments of technological systems, Science, 250, 1359, 10.1126/science.2255906

Helton, 1994, Treatment of uncertainty in performance assessments for complex systems, Risk Anal, 14, 483, 10.1111/j.1539-6924.1994.tb00266.x

Hoffman, 1994, Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability, Risk Anal, 14, 707, 10.1111/j.1539-6924.1994.tb00281.x

Paté-Cornell, 1996, Uncertainties in risk analysis: six levels of treatment, Reliab Engng Syst Saf, 54, 95, 10.1016/S0951-8320(96)00067-1

Winkler, 1996, Uncertainty in probabilistic risk assessment, Reliab Engng Syst Saf, 54, 127, 10.1016/S0951-8320(96)00070-1

Barnett, 1997

Cullen, 1999, Addressing uncertainty-lessons from probabilistic exposure analysis, Inhal Toxicol, 11, 603, 10.1080/089583799197014

Francis, 1997, Risk in fisheries management: a review, Can J Fish Aquat Sci, 54, 1699, 10.1139/cjfas-54-8-1699

Cullen, 1999

Kelly, 2000, Separating variability and uncertainty in environmental risk assessment-making choices, Hum Ecol Risk Assess, 6, 1, 10.1080/10807030091124419

Hacking, 1975

Shafer, 1978, Non-additive probabilities in work of Bernoulli and Lambert, Arch Hist Exact Sci, 19, 309, 10.1007/BF00330065

Bernstein, 1996

Lohman, 2000, A probabilistic analysis of regional mercury impacts on wildlife, Hum Ecol Risk Assess, 6, 103, 10.1080/10807030091124464

Maxwell, 1999, Stochastic environmental risk analysis: an integrated methodology for predicting cancer risk from contaminated groundwater, Stochast Environ Res Risk Assess, 13, 27, 10.1007/s004770050030

Maxwell, 1999, A model for assessing and managing the risks of environmental lead emissions, Stochast Environ Res Risk Assess, 13, 231, 10.1007/s004770050041

Maxwell, 1999, A methodology to integrate site characterization information into groundwater-driven health risk assessment, Water Resour Res, 35, 2841, 10.1029/1999WR900103

McKone, 1994, Uncertainty and variability in human exposures to soil contaminants through home-grown food: a Monte Carlo assessment, Risk Anal, 14, 449, 10.1111/j.1539-6924.1994.tb00263.x

Allen, 1996, Investigation of the impact of pharmacokinetic variability and uncertainty on risks predicted with a pharmacokinetic model for chloroform, Toxicology, 111, 289, 10.1016/0300-483X(96)03383-5

Øvreberg, 1992, Putting error bars on reservoir engineering forecasts, J Petrol Technol, 44, 732, 10.2118/20512-PA

Price, 1996, Uncertainty and variation of indirect exposure assessments: an analysis of exposure to tetrachlorodibenzene-p-dioxin from a beef consumption pathway, Risk Anal, 16, 263, 10.1111/j.1539-6924.1995.tb00784.x

PLG (Pickard, Lowe and Garrick, Inc). Seabrook Station Preliminary Probabilistic Safety Assessment, PLG-0300, vols. 1–6, Summary. Prepared for Public Service Company of New Hampshire, Manchester and Yankee Atomic Electric Company, Framingham, MA. Irvine, CA: Pickard, Lowe and Garrick, Inc. 1983.

PLG (Pickard, Lowe and Garrick, Inc., Westinghouse Electric Corporation, and Fauske & Associates, Inc). Indian Point Probabilistic Safety Study, Prepared for the Power Authority of the State of New York and Consolidated Edison Company of New York, Inc. Irvine, CA: Pickard, Lowe and Garrick, Inc. 1982.

Howard, 2000, Regulatory basis for the Waste Isolation Pilot Plant performance assessment, Reliab Engng Syst Saf, 69, 109, 10.1016/S0951-8320(00)00028-4

Farmer, 1967, Reactor safety and siting: a proposed risk criterion, Nuclear Saf, 8, 539

Cox, 1982, Limit lines for risk, Nuclear Technol, 57, 320, 10.13182/NT82-A26301

Munera, 1986, On farmer's line, probability density functions, and overall risk, Nuclear Technol, 74, 229, 10.13182/NT86-A33808

Helton, 1998, Stochastic and subjective uncertainty in the assessment of radiation exposure at the Waste Isolation Pilot Plant, Hum Ecol Risk Assess, 4, 469, 10.1080/10807039891284433

Galson, 2000, Scenario development for the Waste Isolation Pilot Plant compliance certification application, Reliab Engng Syst Saf, 69, 129, 10.1016/S0951-8320(00)00029-6

Helton, 2000, Characterization of stochastic uncertainty in the 1996 performance assessment for the Waste Isolation Pilot Plant, Reliab Engng Syst Saf, 69, 167, 10.1016/S0951-8320(00)00031-4

Stoelzel, 2000, Direct releases to the surface and associated complementary cumulative distribution functions in the 1996 performance assessment for the Waste Isolation Pilot Plant: direct brine release, Reliab Engng Syst Saf, 69, 343, 10.1016/S0951-8320(00)00038-7

Berglund, 2000, Direct releases to the surface and associated complementary cumulative distribution functions in the 1996 performance assessment for the Waste Isolation Pilot Plant: cuttings, cavings and spallings, Reliab Engng Syst Saf, 69, 305, 10.1016/S0951-8320(00)00036-3

LaVenue, 1996

LaVenue, 1992

Stockman, 2000, Radionuclide transport in the vicinity of the repository and associated complementary cumulative distribution functions in the 1996 performance assessment for the Waste Isolation Pilot Plant, Reliab Engng Syst Saf, 69, 397

Stone, 1997

Stone, 1997

Ramsey, 2000, Radionuclide and colloid transport in the Culebra dolomite and associated complementary cumulative distribution functions in the 1996 performance assessment for the Waste Isolation Pilot Plant, Reliab Engng Syst Saf, 69, 397, 10.1016/S0951-8320(00)00040-5

Helton, 2000, Summary discussion of the 1996 performance assessment for the Waste Isolation Pilot Plant, Reliab Engng Syst Saf, 69, 437, 10.1016/S0951-8320(00)00019-3

Helton, 1999, Uncertainty and sensitivity analysis in performance assessment for the Waste Isolation Pilot Plant, Comput Phys Commun, 117, 156, 10.1016/S0010-4655(98)00171-4