×

An enhanced two-quantile Wilks methodology for engineering uncertainty analysis. (English) Zbl 07889612

MSC:

62-XX Statistics
Full Text: DOI

References:

[1] JonesMN, FrutigerJ, InceNG, SinG. The Monte Carlo driven and machine learning enhanced process simulator. Comput Chem Eng. 2019;125:324‐338.
[2] DuongPLT, AliW, KwokE, LeeM. Uncertainty quantification and global sensitivity analysis of complex chemical process using a generalized polynomial chaos approach. Comput Chem Eng. 2016;90:23‐30.
[3] SoepyanFB, CremaschiS, SaricaC, SubramaniHJ, KoubaGE, GaoH. Estimation of percentiles using the Kriging method for uncertainty propagation. Comput Chem Eng. 2016;93:143‐159.
[4] RochmanD, SciollaC. Nuclear data uncertainty propagation for a typical PWR fuel assembly with burnup. Nuclear Eng Technol. 2014;46(3):353‐362.
[5] MartorellS, SánchezA, CarlosS. A tolerance interval based approach to address uncertainty for RAMS+ C optimization. Reliab Eng Syst Safety. 2007;92(4):408‐422.
[6] NuttWT, WallisGB. Evaluation of nuclear safety from the outputs of computer codes in the presence of uncertainties. Reliab Eng Syst Safety. 2004;83(1):57‐77.
[7] YuJ. A Bayesian inference based two‐stage support vector regression framework for soft sensor development in batch bioprocesses. Comput Chem Eng. 2012;41:134‐144.
[8] VasquezVR, WhitingWB, MeerschaertMM. Confidence interval estimation under the presence of non‐Gaussian random errors: applications to uncertainty analysis of chemical processes and simulation. Comput Chem Eng. 2010;34(3):298‐305.
[9] CalabriaR, PulciniG. Confidence limits for reliability and tolerance limits in the inverse Weibull distribution. Reliab Eng Syst Safety. 1989;24(1):77‐85.
[10] BlatmanG, DelageT, IoossB, PérotN. Probabilistic risk bounds for the characterization of radiological contamination. EPJ Nuclear Sci Technol. 2017;3. doi:10.1051/epjn/2017017
[11] FullwoodR. Probabilistic Safety Assessment in the Chemical and Nuclear Industries. Elsevier; 1999.
[12] HaleWT, WilhelmME, PalmerKA, StuberMD, BollasGM. Semi‐infinite programming for global guarantees of robust fault detection and isolation in safety‐critical systems. Comput Chem Eng. 2019;126:218‐230.
[13] D’AuriaFS, GlaeserH, LeeS, MiákJ, ModroM, SchultzR. Best Estimate Safety Analysis for Nuclear Power Plants: Uncertainty Evaluation. IAEA Safety Report Series. Vol 52. IAEA; 2008.
[14] WilksSS. Determination of sample sizes for setting tolerance limits. Ann Math Stat. 1941;12(1):91‐96. · JFM 67.0481.04
[15] SaezFS, SánchezA, VillanuevaJ, CarlosS, MartorellS. Comparison of some approaches for the estimation of tolerance limits in the context of LBLOCA uncertainty analysis. Nureth‐16. American Nuclear Society; 2015:5720‐5733.
[16] WilksSS. Statistical prediction with special reference to the problem of tolerance limits. Ann Math Stat. 1942;13(4):400‐409. · Zbl 0060.30602
[17] WaldA. An extension of Wilks’ method for setting tolerance limits. Ann Math Stat. 1943;14(1):45‐55. · Zbl 0060.30603
[18] SchefféH, TukeyJW. A formula for sample sizes for population tolerance limits. Ann Math Stat. 1944;15(2):217. · Zbl 0060.30606
[19] DionLG. An Approximate Solution of Wilks’ Tolerance Limit Equation, PhD thesis. Massachusetts Institute of Technology. Department of Economics and Engineering; 1951.
[20] BirnbaumZ, ZuckermanHS. A graphical determination of sample size for Wilks’ tolerance limits. Ann Math Stat. 1949;20(2):313‐316. · Zbl 0041.26101
[21] OwenDB. Handbook of Statistical Tables. Addison‐Wesley Longman Incorporated; 1962. · Zbl 0102.35203
[22] HarmanAJ. Wilks’ tolerance limit sample sizes. Sankhyā: Indian J Stat, Series A (1961‐2002). 1967;29(2):215‐218.
[23] D’AuriaF, PetruzziA. Background and qualification of uncertainty methods. Thicket. Pisa; 2008:283‐303.
[24] LeeSW, ChungBD, BangYS, BaeSW. Analysis of uncertainty quantification method by comparing Monte‐Carlo method and Wilks’ formula. Nuclear Eng Technol. 2014;46(4):481‐488.
[25] DengCC, LiuWL, YangJ, WuQ. Analysis and Validation of Wilks Nonparametric Uncertainty Method for Best‐Estimate Calculations in Nuclear Safety. Vol 57823. American Society of Mechanical Engineers; 2017:V004T06A015.
[26] HalleeBT, MetzrothKG. Evaluation of Wilks’ One‐Sided Non‐parametric Formula against Analytical Parametric Methods, Tech. Rep. Idaho National Lab.(INL); 2017.
[27] HanS, KimT. Numerical experiments on order statistics method based on Wilks’ formula for best‐estimate plus uncertainty methodology. J Environ Manage. 2019;235:28‐33.
[28] PorterN. Wilks’ formula applied to computational tools: a practical discussion and verification. Ann Nucl Energy. 2019;133:129‐137.
[29] PerotN, Le CocguenA, CarréD, LamotteH, Duhart‐BaroneA, PointeauI. Sampling strategy and statistical analysis for radioactive waste characterization. Nucl Eng Des. 2020;364:110647.
[30] GibbonsJD, ChakrabortiS. Nonparametric Statistical Inference: Revised and Expanded. CRC Press; 2014.
[31] JohnsonNL, LeoneFC. Statistical and Experimental Design in Engineering and Physical Sciences. John Wiley; 1977. · Zbl 0397.62001
[32] KrishnamoorthyK, MathewT. Statistical Tolerance Regions: Theory, Applications, and Computation. Vol 744. John Wiley & Sons; 2009. · Zbl 1291.60001
[33] GillespieJA. Inner tolerance limits controlling tail proportions for the normal distribution. Commun Stat Simulat Comput. 1984;13(2):257‐267. · Zbl 0552.62018
[34] GarthwaitePH, KadaneJB, O’HaganA. Statistical methods for eliciting probability distributions. J Am Stat Assoc. 2005;100(470):680‐701. · Zbl 1117.62340
[35] MorrisDE, OakleyJE, CroweJA. A web‐based tool for eliciting probability distributions from experts. Environ Model Software. 2014;52:1‐4.
[36] Van DorpJR, MazzuchiTA. Solving for the parameters of a beta a distribution under two quantile constraints. J Stat Comput Simulat. 2000;67(2):189‐201. · Zbl 0980.62011
[37] ShihN. The model identification of beta distribution based on quantiles. J Stat Comput Simulat. 2015;85(10):2022‐2032. · Zbl 1457.62069
[38] FreyJ. Data‐driven nonparametric prediction intervals. J Stat Plan Inference. 2013;143(6):1039‐1048. · Zbl 1428.62183
[39] YoungDS, MathewT. Improved nonparametric tolerance intervals based on interpolated and extrapolated order statistics. J Nonparametric Stat. 2014;26(3):415‐432. · Zbl 1305.62188
[40] MeekerWQ, HahnGJ, EscobarLA. Statistical Intervals: a Guide for Practitioners and Researchers. Vol 541. John Wiley & Sons; 2017. · Zbl 1395.62002
[41] SongGS, KimMC. Mathematical formulation and analytic solutions for uncertainty analysis in probabilistic safety assessment of nuclear power plants. Energies. 2021;14(4):929.
[42] DavisRA. Practical Numerical Methods for Chemical Engineers: Using Excel with VBA. CreateSpace Independent Pub Platform; 2018.
[43] ArnoldBC, BalakrishnanN, NagarajaHN. A First Course in Order Statistics. SIAM; 2008. · Zbl 1172.62017
[44] NelsenRB. An Introduction to Copulas. 4th ed. Springer Science & Business Media; 2007.
[45] KurowickaD, CookeRM. Uncertainty Analysis with High Dimensional Dependence Modelling. John Wiley & Sons; 2006. · Zbl 1096.62073
[46] JungWD, LeeY, HwangM. Procedure for Conducting Probabilistic Safety Assessment: Level 1 Full Power Internal Event Analysis. Techreport. International Atomic Energy Agency; 2003.
[47] VeselyWE, GoldbergFF, RobertsNH, HaaslDF. Fault Tree Handbook. Tech. Rep. Nuclear Regulatory Commission Washington DC; 1981.
[48] FellerW. An Introduction to Probability Theory and its Applications. Vol 2. John Wiley & Sons; 2008.
[49] EideSA, WiermanTE, GentillonCD, RasmusonDM, AtwoodCL. Industry‐Average Performance for Components and Initiating Events at US Commercial Nuclear Power Plants. Tech. Rep. Nuclear Regulatory Commission; 2007.
[50] PedroniN, ZioE. Uncertainty analysis in fault tree models with dependent basic events. Risk Anal. 2013;33(6):1146‐1173.
[51] CookeRM, WaijR. Monte Carlo sampling for generalized knowledge dependence with application to human reliability. Risk Anal. 1986;6(3):335‐343.
[52] FiondellaL, XingL. Discrete and continuous reliability models for systems with identically distributed correlated components. Reliab Eng Syst Safety. 2015;133:1‐10.
[53] HallidayD, ResnickR, WalkerJ. Electric fields. In Fundamentals of Physics. John Wiley & Sons; 2005:580-604.
[54] CorlissWR. Nuclear Reactors for Space Power, Understanding the Atom Series. ERIC; 1971.
[55] KubiakTM, BenbowDW. The Certified Six Sigma Black Belt Handbook. Quality Press; 2016.
[56] TennantG. Six Sigma: SPC and TQM in Manufacturing and Services. Taylor & Francis; 2017.
[57] Van DorpJR, MazzuchiTA. Parameter specification of the beta distribution and its Dirichlet extensions utilizing quantiles. Stat Textbooks Monographs. 2004;174:283‐318.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.