Ideas underlying the Quantification of Margins and Uncertainties

Key ideas underlying the application of Quantification of Margins and Uncertainties (QMU) to nuclear weapons stockpile lifecycle decisions are described. While QMU is a broad process and methodology for generating critical technical information to be used in U.S. nuclear weapon stockpile management, this paper emphasizes one component, which is information produced by computational modeling and simulation. In particular, the following topics are discussed: (i) the key principles of developing QMU information in the form of Best Estimate Plus Uncertainty, (ii) the need to separate aleatory and epistemic uncertainty in QMU, and (iii) the properties of risk-informed decision making (RIDM) that are best suited for effective application of QMU. The paper is written at a high level, but provides an extensive bibliography of useful papers for interested readers to deepen their understanding of the presented ideas.     

Probabilistic bounding analysis in the Quantification of Margins and Uncertainties

The current challenge of nuclear weapon stockpile certification is to assess the reliability of complex, high-consequent, and aging systems without the benefit of full-system test data. In the absence of full-system testing, disparate kinds of information are used to inform certification assessments such as archival data, experimental data on partial systems, data on related or similar systems, computer models and simulations, and expert knowledge. In some instances, data can be scarce and information incomplete. The challenge of Quantification of Margins and Uncertainties (QMU) is to develop a methodology to support decision-making in this informational context. Given the difficulty presented by mixed and incomplete information, we contend that the uncertainty representation for the QMU methodology should be expanded to include more general characterizations that reflect imperfect information. One type of generalized uncertainty representation, known as probability bounds analysis, constitutes the union of probability theory and interval analysis where a class of distributions is defined by two bounding distributions. This has the advantage of rigorously bounding the uncertainty when inputs are imperfectly known. We argue for the inclusion of probability bounds analysis as one of many tools that are relevant for QMU and demonstrate its usefulness as compared to other methods in a reliability example with imperfect input information.     

Uncertainties Quantification of Effective Thermal Conductivity for Ceramic Fiber Blanket

In the present paper, a probabilistic propagation model for assessing the uncertainty of the effective thermal conductivity was developed based on a combined conduction and radiation heat transfer model of a ceramic fiber blanket composite. The Monte Carlo technique was used to cope with the uncertainties in the material density, radiative properties, and boundary temperatures observed in experimental tests. The calculated effective thermal-conductivity distribution for the sample was compared with the experimental measurements performed on multiple samples, and the predicted mean values were in good agreement with the measured data. The result validates the thermal predictive model and demonstrates the suitability of the stochastic model containing statistical distributions in the input variables. Statistical information also indicates that the uncertainty effect can be enlarged at high temperatures. Response sensitivity analysis between the random inputs and the effective thermal conductivity demonstrates that the randomness in the hot-side temperature, the cold-side temperature, and extinction coefficient of the sample has a significant influence on the variability of thermal-conductivity properties. The extinction coefficient becomes more and more important with an increase of temperature due to the dominant radiative heat transfer contribution at high temperature. The analysis provides good insight into the scattering control in the experimental measurement and theoretical prediction of the effective thermal conductivity of a ceramic fiber composite.     

Uncertainties in Dosimetry

In common useage, the word uncertainty may be taken as beingequivalent to doubt, hesitation, or insecurity. All of thesenegative terms are synonyms for uncertainty. Most people preferto believe that their thought processes lead them to make clearand unambiguous decisions. In the legal courtroom, all thingsare considered to be, figuratively speaking, black or white.Indecision or vagueness on the part of witnesses is anathema,and jurors are instructed to be sure they are convinced beyonda reasonable doubt of the guilt or innocence of the accused.But, in the scientific world,     

Expressing and Estimating Uncertainties in Photometry

Recommendations are made on determining measurement uncertainties for certain photometric quantities. General equations are given for the standard uncertainties and combinations of them with overall uncertainties. The terms in the equations are used in simulating measurements that may be correlated with the inputs, and examples are given of determining the measurement results and the number of degrees of freedom used in calculating cover factors and extended uncertainties.     

Uncertainties of particle emission probabilities

This paper presents analytical methods for calculating uncertainties of particle emission probabilities, and shows how they are affected by decay-scheme normalization procedures. The equations have been derived with standard mathematical error-propagating techniques, using first-order approximations in Taylor series expansions of emission probabilities.     

Uncertainties in Interpolated Spectral Data

Interpolation is often used to improve the accuracy of integrals over spectral data convolved with various response functions or power distributions. Formulae are developed for propagation of uncertainties through the interpolation process, specifically for Lagrangian interpolation increasing a regular data set by factors of 5 and 2, and for cubic-spline interpolation. The interpolated data are correlated; these correlations must be considered when combining the interpolated values, as in integration. Examples are given using a common spectral integral in photometry. Correlation coefficients are developed for Lagrangian interpolation where the input data are uncorrelated. It is demonstrated that in practical cases, uncertainties for the integral formed using interpolated data can be reliably estimated using the original data.     

Analysis of Uncertainties in Dynamic Thermophysical Measurements

A technique of analyzing the dependence of the uncertainty of results as applied to a thermophysical experiment is presented. The dependence of the uncertainty of the result of investigation of a sample under a temperature change on the number, uncertainty, and place and moment of experimental sampling is investigated. A comparative analysis of several approaches to solution of this problem is given.     

Planning of Strength Margins Using Joint Modeling of Mean and Dispersion

Not only the strength of steel but also the variance of strength depends on composition and thermomechanical treatments. Information about the variance of strength is important when composition and thermomechanical treatments are planned to fulfill the strength requirements. In this work, heteroscedastic linear models were used for joint modeling of the mean and dispersion of strength. The models were used as tools in the optimization of the strength margins for steel plate products. The models were created by using industrial process data, and they were successfully used in a steel plate mill.     

临界流函数计算方法及其不确定度

简述了计算临界流函数的各种方法,对各种算法的使用范围、算法误差以及不确定度进行了比较,对在实际工作中如何正确地计算临界流函数和不确定度评定进行了讨论。     

Microform Calibration Uncertainties of Rockwell Diamond Indenters

National and international comparisons in Rockwell hardness tests show significant differences. Uncertainties in the geometry of the Rockwell diamond indenters are largely responsible for these differences. By using a stylus instrument, with a series of calibration and check standards, and calibration and uncertainty calculation procedures, we have calibrated the microform geometric parameters of Rockwell diamond indenters. These calibrations are traceable to fundamental standards. The expanded uncertainties (95 % level of confidence) are ±0.3 μm for the least-squares radius; ±0.01° for the cone angle; and ±0.025° for the holder axis alignment calibrations. Under ISO and NIST guidelines for expressing measurement uncertainties, the calibration and uncertainty calculation procedure, error sources, and uncertainty components are described, and the expanded uncertainties are calculated. The instrumentation and calibration procedure also allows the measurement of profile deviation from the least-squares radius and cone flank straightness. The surface roughness and the shape of the spherical tip of the diamond indenter can also be explored and quantified. Our calibration approach makes it possible to quantify the uncertainty, uniformity, and reproducibility of Rockwell diamond indenter microform geometry, as well as to unify the Rockwell hardness standards, through fundamental measurements rather than by performance comparisons.     

Uncertainties in quantization-noise estimates for analog-to-digitalconverters

Estimates of quantization noise, obtained by stimulating an ideal analog-to-digital converter with a sine wave contained in the input range, are affected by an appreciable uncertainty, which may affect SNR and ENB specifications, especially in the case of low resolution devices. The uncertainty can be eliminated, when possible, by the use of an input sine wave bringing the converter into saturation. The different effects of additive noise on the noise estimates obtained by the various test procedures are also discussed, showing, in particular, that quantization noise may be overestimated by histogram testing with a nonsaturating input sine wave. Therefore, any noise specification should clearly make reference to the test signal parameters and to the instrumentation characteristics     

对专业工程服务公司的风险和不确定性的管理

专业工程服务公司为客户提供专家咨询及顾问服务,在经营管理过程中会不时并不可避免地遇到各种风险和不确定性因素。所遇到的风险既包括技术方面的也包括商业方面的。此外,专业公司还要面对一些能引起无法预见后果的不确定性因素。为提供卓越的服务并取得持续竞争优势,专业公司要建立起行之有效的方法和精工制作战略来应会这些风险和不确定性因素。     

Assessment of Uncertainties in Calibration of Langavant Calorimeters

The semi-adiabatic method, commonly referred to as the Langavant method, is widely applied for routine measurements of the hydration heat of cements. This standardized method is applicable to all cements and hydraulic binders, whatever their chemical composition, with the exception of quick-setting cements. The calorimeters used to perform these hydration heat measurements must be previously calibrated by electrical substitution, in order to determine their coefficient of total heat loss \(\alpha \) and their heat capacity \(\mu \) . LNE developed a facility enabling performance of the calibration of these Langavant calorimeters, in order to insure the traceability of the hydration heat measurements to basic quantities such as temperature, time, mass, and electrical quantities. Calibration results of a typical Langavant calorimeter are presented here. The measurement uncertainties of the parameters \(\alpha \) and \(\mu \) have been assessed according to the ISO/BIPM “Guide to the Expression of Uncertainty in Measurement.” The relative expanded uncertainties ( \(k = 2\) ) of the coefficient of total heat loss \(\alpha \) and the heat capacity \(\mu \) are estimated, respectively, to be about 0.7 % and 15 %.     

Fixed-Point Comparison Uncertainties for Two Cell Geometries

To realize the ITS-90 according to its definition, among others, the melting and freezing temperatures of ideally pure metals are needed. Therefore, many national metrology institutes (NMIs) utilize a group of cells instead of one single cell as the national reference for each temperature. With direct fixed-point cell comparisons on a regular basis, it is feasible to account for the small differences between the individual fixed-point temperatures and to detect possible temperature drifts of the cells. At PTB (the German NMI), in recent years, these groups of national standard cells and the so-called transfer cells for calibrations have been complemented by newly developed slim fixed points. These cells typically contain 75% to 80% less fixed-point material compared with standard cells. Slim cells are used for homogeneity investigations of large batches of fixed-point material, for doping experiments to determine the influence of very small amounts of impurities on the fixed-point temperature with very small uncertainties, and for the investigation of contamination or purification effects after the manufacture of a fixed-point cell. These investigations have shown that the main limitation of slim cells is the quality of the phase boundary. The small dimensions of the cell do not allow the formation of a closed phase boundary (or even two of them). However, this can be compensated using a quasi-adiabatic realization procedure, and in this way, uncertainties comparable to those of standard fixed-point cells can be achieved. In this article, the design of the cells as well as typical measurement results and uncertainties for the direct comparison of fixed-point cells of both types, the standard size and slim design, are presented.     

New Assignment of Mass Values and Uncertainties to NIST Working Standards

For some time it had been suspected that values assigned to NIST working standards of mass were some 0.17 mg/kg larger than mass values based on artifacts representing mass in the International System of Units (SI). This relatively small offset, now confirmed, has had minimal scientific or technological significance. The discrepancy was removed on January 1, 1990. We document the history of the discrepancy, the studies which allow its removal, and the methods in place to limit its effect and prevent its recurrence. For routine calibrations, we believe that our working standards now have a long-term stability of 0.033 mg/kg (3σ) with respect to the national prototype kilograms of the United States. We provisionally admit an additional uncertainty of 0.09 mg/kg (3σ), systematic to all NIST mass measurements, which represents the possible offset of our primary standards from standards maintained by the Bureau International des Poids et Mesures (BIPM). This systematic uncertainty may be significantly reduced after analysis of results from the 3rd verification of national prototype kilograms, which is now underway.