Stephen C. Hora

Expert opinion in risk analysis; The NUREG-1150 methodology

The Reactor Risk Reference Document (US Nuclear Regulatory Commission, 1987) is the most comprehensive study and application of probabilistic risk analysis and uncertainty analysis methods for nuclear power generation safety since the Reactor Safety Study (US Nuclear Regulatory Commission, 1975). Many of the issues addressed in PRA work such as NUREG-1150 involve phenomena that have not been studied through experiment or observation to an extent that makes possible a definitive analysis. In many instances, the rarity or severity of the phenomena make resolution impossible at this time. In these instances, the best available information resides with experts who have studied the phenomena in question. This paper is about a reasoned approach to the acquisition of expert opinion for use in PRA work and other public policy areas.

Comparison of Asymptotically Distribution-Free Procedures for the Analysis of Complete Blocks

Abstract The Friedman test (or sign test when k = 2) depends entirely on within-block rankings. In a recent paper, Quade (1979) attempted to provide a test with more power than the Friedman test by considering a k-sample extension of the Wilcoxon signed ranks test. This is done by taking advantage of the between-block information. A third way to approach the problem and still retain both the within- and between-block information is first to transform all the observations to ranks from 1 to bk (b blocks and k treatments) and then to apply the parametric F test to the ranks. This approach is shown to be asymptotically distribution-free under suitable conditions. Computer simulation results indicate that this procedure is both robust and powerful for small sample sizes.

Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management

The quantification of a risk assessment model often requires the elicitation of expert judgments about quantities that cannot be precisely measured. The aims of the model being quantified provide important guidance as to the types of questions that should be asked of the experts. The uncertainties underlying a quantity may be classified as aleatory or epistemic according to the goals of the risk process. This paper discusses the nature of such a classification and how it affects the probability elicitation process and implementation of the resulting judgments. Examples from various areas of risk assessment are used to show the practical implications of how uncertainties are treated. An extended example from hazardous waste disposal is given.

The F Statistic in the Two-Way Layout With Rank–Score Transformed Data

Abstract The limiting null distribution of the usual F statistic for main effects in the two-way layout is shown to have the same limiting distribution when applied to ranks and scores based on ranks as when applied to normal data. The limit is taken as the cell size N increases without bound. The denominator of the F statistic times (J − 1)/J is shown to provide an unbiased and consistent estimator of the limit (as N → ∞) of N -1 times the variance of the treatment sum of scores when the null hypothesis is true. The test based on the scores statistic is demonstrated to be consistent for a wide class of fixed alternative hypotheses.

Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment for the waste isolation pilot plant

Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) are presented. The primary performance measure under study is the complementary cumulative distribution function (CCDF) used in assessing compliance with the U.S. Environmental Protection Agencys (EPAs) standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The analysis considers releases to the accessible environment initiated by exploratory drilling for natural resources and models cuttings removal to the surface due to drilling intrusions, brine and gas flow in the vicinity of the repository and through drilling intrusions away from the repository, radionuclide transport by the flow of brine through intruding boreholes, and brine flow and radionuclide transport in permeable formations overlying the repository (i.e., the Culebra Dolomite). The effects of 49 imprecisely known variables are assessed with techniques based on Latin hypercube sampling and regression analysis. In addition, the effects of several alternative conceptual models for radionuclide transport in the Culebra Dolomite are investigated. Important issues identified in the analysis include (1) the importance of characterizing retardations and solubilities for individual elements, (2) the impact of assumptions involving human activities, including the rate and properties of drilling intrusions, and (3) the need to resolve the question of whether a single-porosity or dual-porosity transport model is appropriate for use in the Culebra Dolomite.

Extension of Latin hypercube samples with correlated variables

A procedure for extending the size of a Latin hypercube sample (LHS) with rank correlated variables is described and illustrated. The extension procedure starts with an LHS of size m and associated rank correlation matrix C and constructs a new LHS of size 2m that contains the elements of the original LHS and has a rank correlation matrix that is close to the original rank correlation matrix C. The procedure is intended for use in conjunction with uncertainty and sensitivity analysis of computationally demanding models in which it is important to make efficient use of a necessarily limited number of model evaluations.

Asymptotic Relative Efficiencies of the Rank-Transformation Procedure in Randomized Complete Block Designs

Abstract This article provides insight into the powers of alternative tests for experimental effects in the presence of a blocking factor. Three rank tests and the usual F test are compared using asymptotic relative efficiencies (AREs). Rank tests provide a useful alternative method of analysis when the assumptions of the F test are not met. Further, rank tests are usually more powerful than the F test when outliers are present or when the distribution of the data possesses heavy tails. The rank tests studied are Friedmans test, the aligned-ranks test, and the rank-transformation procedure. The rank-transformation test consists of ranking all of the data as one sample and then applying the usual F test to the ranks. Two main themes form the body of the article. The first theme is the development of the limiting noncentrality parameter of the rank-transformation statistic. The development uses the methods popularized by Hajek and Sidak (1967). A lemma is given that establishes the joint limiting distribu...

A distribution-free test for the relationship between model input and output when using Latin hypercube sampling

Abstract A test for the detection of non-monotone relationships between the inputs and outputs of computer simulation models is described for use in sensitivity analyses employing Latin hypercube sampling. The test is based on the squared differences of the consecutive ranks of the output variable when the values of the output variable have been ordered by the corresponding values of an input variable. The test is distribution-free and does not require the values of the output variable to be independent of one another. Instead, the weaker assumption of exchangeability is used. The resulting test statistic is shown to be independent of Spearmans rank correlation coefficient, and a simple method for combining the two statistics is discussed. The test is illustrated with an example from a recent performance assessment for the Waste Isolation Pilot Plant.

Assessment of probability distributions for continuous random variables: A comparison of the bisection and fixed value methods

Abstract Comparisons between two methods of assessing an individuals probability distribution for a continuous variable are provided. These two methods are bisection assessment and direct assessment. The subjects in the study were scientists and engineers participating in a formal probability elicitation process directed toward assessing the risks from nuclear power generating stations. The subjects were trained in probability elicitation and then asked to give probability distributions for almanac values as part of the debiasing training. The results show little difference between the direct and the bisection methods. Slightly better performance, as measured through the calibration of the distributions, was obtained using the bisection method. This result is contrary to strong results obtained in previous studies. The difference in conclusions can be explained by differences in procedures for obtaining end points of the distributions. Also obtained was evidence showing the use of logarithmic scales in place of linear scales may improve the calibration of assessed distributions.

Nuclear waste and future societies: A look into the deep future

Abstract Inadvertent human intrusion is thought to be a significant, if not the most significant, threat to nuclear waste held in repositories. As part of the effort to access the safety of the first United States repository, the Waste Isolation Pilot Plant near Carlsbad, New Mexico, four interdisciplinary teams of experts were brought together to provide insights into the modes and likelihoods of such intrusions as far as 10,000 years in the future. A formal expert elicitation process was used in obtaining their judgments. The teams provided scenarios that, although formed using different approaches, reflected several central themes. These themes are the uncertainty about the need for resource exploration in the future, the rate at which technology develops or declines in future, the likely failure of government control of radioactive waste sites, and the preservation and potential loss of memory about nuclear waste. Identifying possible futures enhances the ability to construct a repository that will be robust against many different potential threats.