Illustration of sampling-based approaches to the calculation of expected dose in performance assessments for the proposed high level radioactive waste repository at Yucca Mountain, Nevada.

A deep geologic repository for high level radioactive waste is under development by the U.S. Department of Energy at Yucca Mountain (YM), Nevada. As mandated in the Energy Policy Act of 1992, the U.S. Environmental Protection Agency (EPA) has promulgated public health and safety standards (i.e., 40 CFR Part 197) for the YM repository, and the U.S. Nuclear Regulatory Commission has promulgated licensing standards (i.e., 10 CFR Parts 2, 19, 20, etc.) consistent with 40 CFR Part 197 that the DOE must establish are met in order for the YM repository to be licensed for operation. Important requirements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. relate to the determination of expected (i.e., mean) dose to a reasonably maximally exposed individual (RMEI) and the incorporation of uncertainty into this determination. This presentation describes and illustrates how general and typically nonquantitive statements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. can be given a formal mathematical structure that facilitates both the calculation of expected dose to the RMEI and the appropriate separation in this calculation of aleatory uncertainty (i.e., randomness in the properties of future occurrences such as igneous and seismic events) and epistemic uncertainty (i.e., lack of knowledge about quantities that are poorly known but assumed to have constant values in the calculation of expected dose to the RMEI)

Probability of loss of assured safety in systems with multiple time-dependent failure modes.

Weak link (WL)/strong link (SL) systems are important parts of the overall operational design of high-consequence systems. In such designs, the SL system is very robust and is intended to permit operation of the entire system under, and only under, intended conditions. In contrast, the WL system is intended to fail in a predictable and irreversible manner under accident conditions and render the entire system inoperable before an accidental operation of the SL system. The likelihood that the WL system will fail to deactivate the entire system before the SL system fails (i.e., degrades into a configuration that could allow an accidental operation of the entire system) is referred to as probability of loss of assured safety (PLOAS). Representations for PLOAS for situations in which both link physical properties and link failure properties are time-dependent are derived and numerically evaluated for a variety of WL/SL configurations, including PLOAS defined by (i) failure of all SLs before failure of any WL, (ii) failure of any SL before failure of any WL, (iii) failure of all SLs before failure of all WLs, and (iv) failure of any SL before failure of all WLs. The effects of aleatory uncertainty and epistemic uncertainty in the definition and numerical evaluation of PLOAS are considered

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

Ideas underlying quantification of margins and uncertainties(QMU): a white paper.

This report describes key ideas underlying the application of Quantification of Margins and Uncertainties (QMU) to nuclear weapons stockpile lifecycle decisions at Sandia National Laboratories. While QMU is a broad process and methodology for generating critical technical information to be used in stockpile management, this paper emphasizes one component, which is information produced by computational modeling and simulation. In particular, we discuss the key principles of developing QMU information in the form of Best Estimate Plus Uncertainty, the need to separate aleatory and epistemic uncertainty in QMU, and the risk-informed decision making that is best suited for decisive application of QMU. The paper is written at a high level, but provides a systematic bibliography of useful papers for the interested reader to deepen their understanding of these ideas

Survey of sampling-based methods for uncertainty and sensitivity analysis.

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (1) Definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (2) Generation of samples from uncertain analysis inputs, (3) Propagation of sampled inputs through an analysis, (4) Presentation of uncertainty analysis results, and (5) Determination of sensitivity analysis results. Special attention is given to the determination of sensitivity analysis results, with brief descriptions and illustrations given for the following procedures/techniques: examination of scatterplots, correlation analysis, regression analysis, partial correlation analysis, rank transformations, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, squared rank differences/rank correlation coefficient test, two dimensional Kolmogorov-Smirnov test, tests for patterns based on distance measures, top down coefficient of concordance, and variance decomposition

A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory.

Evidence theory provides an alternative to probability theory for the representation of epistemic uncertainty in model predictions that derives from epistemic uncertainty in model inputs, where the descriptor epistemic is used to indicate uncertainty that derives from a lack of knowledge with respect to the appropriate values to use for various inputs to the model. The potential benefit, and hence appeal, of evidence theory is that it allows a less restrictive specification of uncertainty than is possible within the axiomatic structure on which probability theory is based. Unfortunately, the propagation of an evidence theory representation for uncertainty through a model is more computationally demanding than the propagation of a probabilistic representation for uncertainty, with this difficulty constituting a serious obstacle to the use of evidence theory in the representation of uncertainty in predictions obtained from computationally intensive models. This presentation describes and illustrates a sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Preliminary trials indicate that the presented strategy can be used to propagate uncertainty representations based on evidence theory in analysis situations where naive sampling-based (i.e., unsophisticated Monte Carlo) procedures are impracticable due to computational cost

Conceptual structure of the 1996 performance assessment for the Waste Isolation Pilot Plant

The conceptual structure of the 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) is described. This structure involves three basic entities (EN1, EN2, EN3): (1) EN1, a probabilistic characterization of the likelihood of different futures occurring at the WIPP site over the next 10,000 yr, (2) EN2, a procedure for estimating the radionuclide releases to the accessible environment associated with each of the possible futures that could occur at the WIPP site over the next 10,000 yr, and (3) EN3, a probabilistic characterization of the uncertainty in the parameters used in the definition of EN1 and EN2. In the formal development of the 1996 WIPP PA, EN1 is characterized by a probability space (S{sub st}, P{sub st}, p{sub st}) for stochastic (i.e., aleatory) uncertainly; EN2 is characterized by a function {line_integral} that corresponds to the models and associated computer programs used to estimate radionuclide releases; and EN3 is characterized by a probability space (S{sub su}, P{sub su}, p{sub su}) for subjective (i.e., epistemic) uncertainty. A high-level overview of the 1996 WIPP PA and references to additional sources of information are given in the context of (S{sub st}, P{sub st}, p{sub st}), {line_integral} and (S{sub su}, P{sub su}, p{sub su})

Effect of delayed link failure on probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links.

Weak link (WL)/strong link (SL) systems constitute important parts of the overall operational design of high consequence systems, with the SL system designed to permit operation of the system only under intended conditions and the WL system designed to prevent the unintended operation of the system under accident conditions. Degradation of the system under accident conditions into a state in which the WLs have not deactivated the system and the SLs have failed in the sense that they are in a configuration that could permit operation of the system is referred to as loss of assured safety. The probability of such degradation conditional on a specific set of accident conditions is referred to as probability of loss of assured safety (PLOAS). Previous work has developed computational procedures for the calculation of PLOAS under fire conditions for a system involving multiple WLs and SLs and with the assumption that a link fails instantly when it reaches its failure temperature. Extensions of these procedures are obtained for systems in which there is a temperature-dependent delay between the time at which a link reaches its failure temperature and the time at which that link actually fails

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

The following topics related to radionuclide transport in the vicinity of the repository in the 1996 performance assessment for the Waste Isolation Pilot Plant are presented (1) mathematical description of models, (2) uncertainty and sensitivity analysis results arising from subjective (i.e., epistemic) uncertainty for individual releases, (3) construction of complementary cumulative distribution functions (CCDFs) arising from stochastic (i.e., aleatory) uncertainty, and (4) uncertainty and sensitivity analysis results for CCDFs. The presented results indicate that no releases to the accessible environment take place due to radionuclide movement through the anhydrite marker beds, through the Dewey Lake Red Beds or directly to the surface, and also that the releases to the Culebra Dolomite are small. Even when the effects of uncertain analysis inputs are taken into account, the CCDFs for release to the Culebra Dolomite fall to the left of the boundary line specified in the US Environmental Protection Agency's standard for the geologic disposal of radioactive waste (40 CFR 191, 40 CFR 194)

Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links.

Relationships to determine the probability that a weak link (WL)/strong link (SL) safety system will fail to function as intended in a fire environment are investigated. In the systems under study, failure of the WL system before failure of the SL system is intended to render the overall system inoperational and thus prevent the possible occurrence of accidents with potentially serious consequences. Formal developments of the probability that the WL system fails to deactivate the overall system before failure of the SL system (i.e., the probability of loss of assured safety, PLOAS) are presented for several WWSL configurations: (i) one WL, one SL, (ii) multiple WLs, multiple SLs with failure of any SL before any WL constituting failure of the safety system, (iii) multiple WLs, multiple SLs with failure of all SLs before any WL constituting failure of the safety system, and (iv) multiple WLs, multiple SLs and multiple sublinks in each SL with failure of any sublink constituting failure of the associated SL and failure of all SLs before failure of any WL constituting failure of the safety system. The indicated probabilities derive from time-dependent temperatures in the WL/SL system and variability (i.e., aleatory uncertainty) in the temperatures at which the individual components of this system fail and are formally defined as multidimensional integrals. Numerical procedures based on quadrature (i.e., trapezoidal rule, Simpson's rule) and also on Monte Carlo techniques (i.e., simple random sampling, importance sampling) are described and illustrated for the evaluation of these integrals. Example uncertainty and sensitivity analyses for PLOAS involving the representation of uncertainty (i.e., epistemic uncertainty) with probability theory and also with evidence theory are presented