Response to “About acceptance and rejection zones”

Desimoni and Brunetti raise some questions about the use of Eurachem/CITAC guide, because the Eurachem/CITAC guide does not discuss an ISO recommendation before performing a test, it should be decided whether it is to be a test for conformity or a test for non-conformity. In response, it is pointed out that although this recommendation is not discussed explicitly, it is of necessity covered by the decision rule that describes how the measurement uncertainty will be taken into consideration with regard to accepting or rejecting a product according to its specification and the result of a measurement. In addition, they propose the introduction of an ‘inconclusive’ zone. We do not think that this is necessary, since the Eurachem/CITAC guide takes the view that action on rejection should be covered by the ‘decision rule’ and this can make equivalent provision for confirmation or interpretation.     

The role of the sample standard deviation in the analysis of measurement data

This paper builds on recent letters to the editor to consider different ways in which the ‘sample standard deviation’ of a set of repeated measurements might be used in the expression of accuracy or uncertainty. A distinction is made between using the sample standard deviation, s, to calculate a figure of merit for the measurement procedure and using s to express uncertainty in the estimate of a measurand. In particular, we consider whether s should be adjusted for bias. It is shown that most procedures involving s are valid without the application of any such adjustment. The paper emphasizes the importance of clear definitions and an unambiguous statement of purpose, and also emphasizes the need for a distinction in notation between a random variable and its observed value.     

Measurement of small quantities: further observations on Bayesian methodology

This article discusses the measurement of the sum of small positive quantities each estimated in separate analyses. It extends criticism recently given of ‘objective Bayesian’ methodology (Accred Qual Assur 15:181–188, 2010) and identifies two troublesome effects: the inherent bias in an analysis for a single quantity is compounded when the measurand is the sum of such quantities, and the precaution of overestimating measurement variability can actually make the resulting interval of measurement uncertainty less reliable! Unacceptable results are obtained. A cause of this behavior is identified, and a distinction between ‘objective’ and ‘subjective’ Bayesian statistics is discussed.     

Comments on “Quality assurance of nuclear analytical techniques based on Bayesian characteristic limits”

A paper by R. Michel in this journal (J. Radioanal. Nucl. Chem., 245 (2000) 137) describes, among other things, a numerical example: the calculation of characteristic limits in an analysis of ¹²⁹I via radiochemical NAA. A key problem in Bayesian characteristic limits is a proper formulation of the expression for the uncertainty associated with the measurand if its true value is equal to zero, ũ(0). We show that MICHEL’s expression for ũ ²(0) is not correct and propose a new one. Some numerical errors found in the paper are also indicated.     

A detailed study of the viscoelastic nature of vapor sorption and transport in a cellulosic polymer. I. Origin and physical implications of deviations from Fickian sorption kinetics

Various aspects of the kinetics of sorption of acetone vapor by cellulose acetate films at 30°C have been studied in detail, the principal aim being to understand more thoroughly the physical nature and causes of non-Fickian behavior in this and other similar polymer-micromolecular penetrant systems. Particular attention was given to the changes in sorption (including absorption, desorption, and resorption) kinetics caused by (a) systematic variation of the vapor pressure of acetone in different ways and (b) changes in membrane thickness. It has been shown that both viscous volume swelling relaxation and longitudinal differential swelling stress effects must be invoked, in order to explain fully the observed behavior. Detailed analysis of two-stage sorption kinetics indicated (1) reasonable agreement between estimates of the diffusion coefficient reported by different authors, as long as a consistent analysis of the first stage is used, although the significance of the values given is open to some doubt, because the said first stage is found not to be free of non-Fickian features; and (2) reasonable conformity of the second stage to a first-order volume relaxation process (except a long times), with a relaxation frequency strongly dependent on the width of the concentration interval covered by the sorption experiment (and hence on the applied “osmotic stress”). The close similarity of second-stage sorption to nonlinear viscoelastic creep behavior, previously found in the cellulose-water system was confirmed and is taken further here, by demonstrating semiquantitative agreement between the corresponding “elastic swelling” and mechanical bulk moduli. ©1995 John Wiley & Sons, Inc.     

A Bayesian approach to the evaluation of comparisons of individually value-assigned reference materials

Several recent international comparison studies used a relatively novel experimental design to evaluate the measurement capabilities of participating organizations. These studies compared the values assigned by each participant to one or more qualitatively similar materials with measurements made on all of the materials by one laboratory under repeatability conditions. A statistical model was then established relating the values to the repeatability measurements; the extent of agreement between the assigned value(s) and the consensus model reflected the participants’ measurement capabilities. Since each participant used their own supplies, equipment, and methods to produce and value-assign their material(s), the agreement between the assigned value(s) and the model was a fairer reflection of their intrinsic capabilities than provided by studies that directly compared time- and material-constrained measurements on unknown samples prepared elsewhere. A new statistical procedure is presented for the analysis of such data. The procedure incorporates several novel concepts, most importantly a leave-one-out strategy for the estimation of the consensus value of the measurand, model fitting via Bayesian posterior probabilities, and posterior coverage probability calculation for the assigned 95% uncertainty intervals. The benefits of the new procedure are illustrated using data from the CCQM-K54 comparison of eight cylinders of n-hexane in methane.     

Visualisation of interlaboratory comparison results in PomPlots

In this work a novel graphical method is applied to the presentation of intercomparison results. This is demonstrated with the results of a recent intercomparison in measuring the ¹³⁷Cs, ⁴⁰K, and ⁹⁰Sr activity concentration in milk powder. The “PomPlot”, an intuitive graphical method, is used for producing a summary overview of the participants’ results of a common measurand. The “PomPlot” displays (relative) deviations of individual results from the reference value on the horizontal axis and (relative) uncertainties on the vertical axis.     

On the use of the ‘uncertainty budget’ to detect dominant terms in the evaluation of measurement uncertainty

In the evaluation of measurement uncertainty, the uncertainty budget is usually used to identify dominant terms that contribute to the uncertainty of the output estimate. Although a feature of the GUF method, it is also recommended as a qualitative tool in MCM by using ‘nonlinear’ equivalents of uncertainty contributions and sensitivity coefficients. In this paper, the use of ‘linear’ and ‘nonlinear’ parameters is discussed. It is shown that when and only when the standard uncertainty of the output estimate is nearly equal to the square root of the sum of the squares of the individual uncertainty contributions, will the latter be a reliable tool to detect the degree of contribution of each input quantity to the measurand uncertainty.     

What exactly is uncertainty?

Uncertainty is defined in VIM3 as a ‘parameter’ but that, in my view, is a mistake that detracts from the clarity of the concept. Trying to overcome the resulting difficulties while retaining ‘parameter’ has brought about progressive amendments to the definition, and an increasing list of footnotes that have failed to resolve the issue. Surely the uncertainty of a result is the density function (or mass function) that best describes the probability of possible values of the measurand.     

Evaluation of proficiency testing results taking into account their uncertainties

A new composite score for the evaluation of performance of proficiency testing participants is proposed. The score is based on a combination of the z-score, uncertainty of a participant’s measurement result and uncertainty of the proficiency testing scheme’s assigned value. The use of such a composite score will allow evaluation not only of the participant’s ability to determine an analyte in corresponding matrix, but also their understanding of the uncertainty in the obtained analytical result. The score may be helpful for the laboratory’s quality system and for laboratory accreditation according to ISO 17025.     

The metrology of unstable measurands

 Type A statistical uncertainty in measurements is usually derived from the standard deviation of the measured data. This is correct as long as the measurand is stable over time and has a meaningful constant value. In such a case the average measurement and the standard deviations are meaningful. However, as measurement methods are refined and become more precise, we can observe that a given measurand may be unstable and change with time and the uncertainty in measurement must be redefined. This is specifically true in the metrology of time which can be measured today more precisly than any other measurand. We argue that in such a case the uncertainty in the prediction of the next measurement should be used instead of the uncertainty in measurement. Both uncertainties coincide for a stable measurand. The prediction of the next measurement is achieved by means of predictors. In this paper we describe the application of linear predictors and especially optimum linear predictors to predict in the presence of various types of instability. To illustrate the issues we use clock instabilities and clock metrology as this field is most developed. A measurand can be unstable but still predictable and thus useful. This is well known in the case of white noise about a linear drift for which the optimum predictor is a linear regression. Since the deviations from prediction of optimum prediction are of white noise, we can now use simple statistics to estimate the uncertainty of the optimum or close to optimum prediction. In this paper we present the various optimum or close to optimum linear predictors optimized for different types of instability and estimate the associated prediction uncertainties.     

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.     

Physico-chemical properties of aqueous extremely diluted solutions in relation to ageing

An extensive study has been carried out on aqueous ‘extremely diluted solutions’ (EDS). The employed experimental methodologies were well established physico-chemical techniques: flux calorimetry, conductometry, pH-metry, e.m.f. of suitable galvanic cell. The obtained results show that the preparation procedure significantly alters the physico-chemical behaviour of such solutions. Moreover, the analysis of the experimental data vs. the ‘arrow of time’ turned out to be astonishingly important. In fact some measured physico-chemical parameters evolve with time. Some experimentally measurable physico-chemical properties of the solvent water were largely affected by both time and the ‘life path’ of the samples. In particular, we evidenced two new experimental phenomena characterizing the EDS: the presence of a series of maximums in the measured electrical conductivity vs. the sample age; the dependence of said maximums on the volume of the EDS during its ageing. All of these new experimental results clearly suggest the presence of an extended and ‘ordered’ dynamics involving the whole of the water molecules in the liquid. A temporal evolution, featuring three maximums in the course of four years of ageing and the dependence on the ageing volumes do not fit the framework of classical thermodynamics. It therefore seems appropriate to interpret these phenomena on the basis of the thermodynamics of dissipative structures, which are far from equilibrium systems.     

Determination of parathion in biological fluids by means of direct solid-phase microextraction

A new and simple procedure for the determination of parathion in human whole blood and urine using direct immersion (DI) solid-phase microextraction (SPME) and gas chromatography/mass spectrometry (GC/MS) is presented. This technique was developed using only 100 μL of sample, and ethion was used as internal standard (IS). A 65-μm Carbowax/divinylbenzene (CW/DVB) SPME fibre was selected for sampling, and the main parameters affecting the SPME process such as extraction temperature, adsorption and desorption time, salt addition, agitation and pH effect were optimized to enhance the sensitivity of the method. This optimization was also performed to allow the qualitative determination of parathion’s main metabolite, paraoxon, in blood. The limits of detection and quantitation for parathion were 3 and 10 ng/mL for urine and 25 and 50 ng/mL for blood, respectively. For paraoxon, the limit of detection was 50 ng/mL in blood. The method showed linearity between the LOQ and 50 μg/mL for both matrices, with correlation coefficients ranging from 0.9954 to 0.9999. Precision and accuracy were in conformity with the criteria normally accepted in bioanalytical method validation. The mean absolute recoveries were 35.1% for urine and 6.7% for blood. Other parameters such as dilution of sample and stability were also validated. Its simplicity and the fact that only 100 μL of sample is required to accomplish the analysis make this method useful in forensic toxicology laboratories to determine this compound in intoxications, and it can be considered an alternative to other methods normally used for the determination of this compound in biological media.     

The impact of measurement uncertainty on the producer’s and user’s risks, on classification and conformity assessment: an example based on tests on some construction products

The reliability of test results and subsequent classification statements or product certification depend on the variability of the product’s properties and on the validity of the test procedures used. With an emphasis on measurement uncertainty, producer’s and user’s risks as well as probabilities of conformance, conformity and classification are calculated exemplarily for two requirements for mineral aggregates used in construction. An important methodological basis is an international draft document on measurement uncertainty in conformity assessment. The mathematical instruments given are applied and further developed to a risk scenario for product classification. The results from a classification point of view show that the reliability of test results for acid-soluble sulphates is mostly acceptable and both the producer’s and user’s risks are quite small. In contrast, the magnesium sulphate index test produces results which are hardly usable for classification and certification purposes or for risk management in production. Product certification bodies should generally have an appropriate approach when dealing with results where precision data are poor.     

Constructivism’s New Clothes: The Trivial, the Contingent, and a Progressive Research Programme into the Learning of Science

Constructivism has been a key referent for research into the learning of science for several decades. There is little doubt that the research into learners’ ideas in science stimulated by the constructivist movement has been voluminous, and a great deal is now known about the way various science topics may commonly be understood by learners of various ages. Despite this significant research effort, there have been serious criticisms of this area of work: in terms of its philosophical underpinning, the validity of its most popular constructs, the limited scope of its focus, and its practical value to science teaching. This paper frames this area of work as a Lakatosian Research Programme (RP), and explores the major criticisms of constructivism from that perspective. It is argued that much of the criticism may be considered as part of the legitimate academic debate expected within any active RP, i.e. arguments about the auxiliary theory making up the ‘protective belt’ of the programme. It is suggested that a shifting focus from constructivism to ‘contingency in learning’ will allow the RP to draw upon a more diverse range of perspectives, each consistent with the existing hard core of the programme, which will provide potentially fruitful directions for future work and ensure the continuity of a progressive RP into learning science.     

About acceptance and rejection zones as defined in the EURACHEM/CITAC Guide (2007) “Use of uncertainty information in compliance assessment”

Considering measurement uncertainty is mandatory in assessing conformance to legal or compositional limits, and specific guidelines are available issued by ASME, ISO and Eurachem/CITAC. However, differences between ISO and EURACHEM/CITAC wordings could induce some perplexities in the most careful readers. Possible problems arise from considering that, before performing a test, it should be decided whether it is to be a test for conformity or a test for non-conformity. This choice could perhaps require some renaming of acceptance/rejection zones as defined in the EURACHEM/CITAC Guide. A tentative solution is discussed in this contribution.     

Integration of metrological principles and performance evaluation in a proficiency testing scheme in support of the Council Directive 98/83/EC

Proficiency testing as a means of external quality assessment plays the role of independent evidence of laboratories’ performance. To enable laboratories to fulfil the requirements stated in legislation, methodology for evaluation of laboratories’ performance in proficiency testing schemes should incorporate principles of measurement results which are fit for intended use and incorporate evaluation of laboratories’ performances based on independent reference value. A proficiency testing scheme was designed to support Drinking Water Directive (98/83/EC) specifically. The methodology for performance evaluation, which takes into account a “fitness for purpose”-based standard deviation for proficiency assessment, is proposed and discussed in terms of requirements of the Drinking Water Directive. A ζ′-score, modified by application of target uncertainty was developed in a way that fulfils requirements defined in the legislation. As an illustration, results are reported for nitrate concentration in water. The approach presented can also be applied to other fields of measurements.     

Conventional true values compared

According to ISO/CD 18113-1:2005, the conventional true value of a control material can be an assigned value (obtained with a primary or reference measurement procedure), a consensus value or a procedure-defined value. The present study demonstrates that, for some biological quantities, the overall consensus value (“trimmed” mean value”) obtained in a proficiency testing program, which includes all results independently of the method of measurement, is not acceptable as a surrogate for a primary or reference method value. Therefore, for the biological quantities taken into account in this study, overall consensus value is not as good as primary or reference method value to estimate systematic error. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher. Apart from exceptional circumstances, they are not submitted to the usual referee procedure and go essentially unaltered.