IMEP-24 analysis of eight trace elements in toys

The International Measurement Evaluation Program (IMEP) organised the IMEP-24 interlaboratory comparison after reports in the media about high levels of lead in toys. The aim of this comparison was to verify the laboratories’ capacity to evaluate trace-element levels in a possible toy-like material according to the European Standard EN 71-3:1994. As test material, it used a former certified reference material containing levels of antimony, arsenic, barium, cadmium, chromium, mercury, lead and selenium around the limits set in the standard.Four expert laboratories confirmed the reference values (Xref) for all elements but Hg, and established a reference value for Hg. The scatter of the results reported by the participants was large, as expected, but showed a close to normal distribution around the reference values for five of the eight trace elements. The spread of results was mainly attributed to sampling and sample preparation.One major issue observed in this exercise was the lack of legislative rules about how to report the result, or, more specifically, the use of the analytical correction, which was introduced in EN 71-3:1994 to achieve consistent interpretation of results and which is to be applied when values are equal to or above the maximum limits set in the standard. Its application by the participants was very inconsistent and led to problems in their evaluation. There is clearly a need for clarification and for more formal regulations with regard to result reporting in order to minimise the risk of confusion.Participants were also asked to give their opinion with regard to the acceptability of the test material for the market. The majority correctly considered the material as non-compliant. However, almost one-third incorrectly assessed the material as compliant.     

IMEP-24 analysis of eight trace elements in toys

The International Measurement Evaluation Program (IMEP) organized the IMEP-24 interlaboratory comparison after reports in the media about high levels of lead in toys. The aim of this comparison was to verify the laboratories’ capacity to evaluate trace-element levels in a possible toy-like material according to the European Standard EN 71-3:1994. As test material, it used a former certified reference material containing levels of antimony, arsenic, barium, cadmium, chromium, mercury, lead and selenium around the limits set in the standard.Four expert laboratories confirmed the reference values (Xref) for all elements but Hg, and established a reference value for Hg. The scatter of the results reported by the participants was large, as expected, but showed a close to normal distribution around the reference values for five of the eight trace elements. The spread of results was mainly attributed to sampling and sample preparation.One major issue observed in this exercise was the lack of legislative rules about how to report the result, or, more specifically, the use of the analytical correction, which was introduced in EN 71-3:1994 to achieve consistent interpretation of results and which is to be applied when values are equal to or above the maximum limits set in the standard. Its application by the participants was very inconsistent and led to problems in their evaluation. There is clearly a need for clarification and for more formal regulations with regard to result reporting in order to minimize the risk of confusion.Participants were also asked to give their opinion with regard to the acceptability of the test material for the market. The majority correctly considered the material as non-compliant. However, almost one-third incorrectly assessed the material as compliant.     

Comparison of a special-purpose algorithm with general-purpose algorithms for solving geometric programming problems

We study the performance of four general-purpose nonlinear programming algorithms and one special-purpose geometric programming algorithm when used to solve geometric programming problems. Experiments are reported which show that the special-purpose algorithm GGP often finds approximate solutions more quickly than the general-purpose algorithm GRG2, but is usually not significantly more efficient than GRG2 when greater accuracy is required. However, for some of the most difficult test problems attempted, GGP was dramatically superior to all of the other algorithms. The other algorithms are usually not as efficient as GGP or GRG2. The ellipsoid algorithm is most robust.This work was supported in part by the National Science Foundation, Grant No. MCS-81-02141.     

枪弹头痕迹自动比对数学模型的研究及统计分析

对于题目中的几个问题,首先给出了一个计算并消除两组划痕数据之间平移误差和转动误差的精确算法,然后利用中值滤波+低通滤波+高斯滤波的方案来消除噪声和误差,最后对过滤后的数据进行分析,提取了一维特征向量并提出了比对特征相关系数作为检验弹头相似程度的标准.     

Using Complex Integration to Compute Multivariate Normal Probabilities

Abstract

The execution of most multiple comparison methods involves, at least in part, the computation of the probability that a multivariate normal or multivarite t random vector is in a hyper-rectangle. In multiple comparison with a control as well as multiple comparison with the best (of normal populations or multinomial cell probabilities), the correlation matrix R of the random vector is nonsingular and of the form , where D is a diagonal matrix and is a known vector. It is well known that, in this case, the multivariate normal rectangular probability can be expressed as a one-dimensional integral and successfully computed using Gaussian quadrature techniques. However, in multiple comparison with the mean (sometimes called analysis of means) of normal distributions, all-pairwise comparisons of three normal distributions, as well as simultaneous inference on multinomial cell probabilities themselves, the correlation matrix is singular and of the form . It is not well known that, in this latter case, the multivariate normal rectangular probability can still be expressed as a single integral, albeit one with complex variables in its integrand. Previously published proofs of the validity of this expression either contained a gap or relied on a numerical demonstration, and this article will provide an analytic proof. Furthermore, we explain how this complex integral can be computed accurately, using Romberg integration of complex variables when the dimension is low, and using ?idák's inequality as an approximation when the dimension is at least moderate.     

Simultaneous Model Selection via Rate-Distortion Theory,With Applications to Cluster and Significance Analysis of Gene Expression Data

High-dimensional data are prevalent across many application areas, and generate an ever-increasing demand for statistical methods of dimension reduction, such as cluster and significance analysis. One application area that has recently received much interest is the analysis of microarray gene expression data.

The results of cluster analysis are open to subjective interpretation. To facilitate the objective inference of such analyses, we use flexible parameterizations of the cluster means, paired with model selection, to generate sparse and easy-to-interpret representations of each cluster. Model selection in cluster analysis is combinatorial in the numbers of clusters and data dimensions, and thus presents a computationally challenging task.

In this article we introduce a model selection method based on rate-distortion theory, which allows us to turn the combinatorial model selection problem into a fast and simultaneous selection across clusters. The method is also applicable to model selection in significance analysis

We show that simultaneous model selection for cluster analysis generates objectively interpretable cluster models, and that the selection performance is competitive with a combinatorial search, at a fraction of the computational cost. Moreover, we show that the rate-distortion based significance analysis substantially increases the power compared with standard methods.

This article has supplementary material online.     

A comparison of location estimators for interlaboratory data contaminated with value and uncertainty outliers

While estimation of measurement uncertainty (MU) is increasingly acknowledged as an essential component of the chemical measurement process, there is little agreement on how best to use even nominally well-estimated MU. There are philosophical and practical issues involved in defining what is “best” for a given data set; however, there is remarkably little guidance on how well different MU-using estimators perform with imperfect data. This report characterizes the bias, efficiency, and robustness properties for several commonly used or recently proposed estimators of true location, μ, using “Monte Carlo” (MC) evaluation of “measurement” data sets drawn from well-defined distributions. These synthetic models address a number of issues pertinent to interlaboratory comparisons studies. While the MC results do not provide specific guidance on “which estimator is best” for any given set of real data, they do provide broad insight into the expected relative performance within broadly defined scenarios. Perhaps the broadest and most emphatic guidance from the present study is that (1) well-estimated measurement uncertainties can be used to improve the reliability of location determination and (2) some approaches to using measurement uncertainties are better than others. The traditional inverse squared uncertainty-weighted estimators perform well only in the absence of unrepresentative values (value outliers) or underestimated uncertainties (uncertainty outliers); even modest contamination by such outliers may result in relatively inaccurate estimates. In contrast, some inverse total variance-weighted-estimators and probability density function area-based estimators perform well for all scenarios evaluated, including underestimated uncertainties, extreme value outliers, and asymmetric contamination.     

A practical procedure for assigning a reference value and uncertainty in the frame of an interlaboratory comparison

A method is suggested for the calculation of a reference value and its uncertainty to be used in the frame of an interlaboratory comparison (ILC). It is assumed that the reference value of the measurand is determined independently from the ILC round. It is derived from a limited set of measurement results obtained from one or several expert laboratories. The procedure involves three stages: (1) check of the experimental data and possible corrections; (2) check of the consistency of data, and possibly increase of the uncertainties in order to attain internal consistency; (3) choice between fully, partially or un-weighted mean.     

ISO/IEC 17043: the new International Standard for proficiency testing

The revision of ISO/IEC Guide 43 is well underway by CASCO Working Group 28, with the author as Convener. The ballot on the committee draft was successfully completed in June 2008. The Working Group met in September to resolve the CD comments and to recommend that the document should advance as an ISO/IEC DIS. The document is in harmony with ISO/IEC 17025 (2005), ILAC G13 (2007), and the IUPAC Harmonized Protocol (2006) for proficiency testing. Major changes from Guide 43 include considerations for inspection bodies, requirements for metrological traceability of assigned values for calibration schemes, limitations on subcontracting, requirements for reporting the uncertainty of assigned values, and for including method information and technical commentary in scheme reports. Minor changes include requirements for equipment used in the manufacture and testing of proficiency test items, considerations for handling laboratories’ reported uncertainties, and the issuance of certificates of participation. These changes have not generated any substantial objections from the CASCO membership and liaisons.