EURACHEM/CITAC workshop on recent developments in

Authors: Alex Williams

Publish Date: 2012/03/13

Volume: 17, Issue: 2, Pages: 111-113

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Abstract

This was the topic of a workshop held in Lisbon in June 2011 which was organised by the Faculty of Sciences of the University of Lisbon EURACHEMPortugal and RELACRE the Portuguese Association of Accredited Laboratories on behalf of the EURACHEM/CITAC Measurement Uncertainty and Traceability Working Group This topical issue of ACQUAL contains a selection of the contributed papers at this workshop These papers and the posters presented at the workshop show how the evaluation of uncertainty is now being applied to a wide range of analyses Also it is interesting to see in how many cases the evaluation used method performance data and measurements on reference materials There were also a number of invited speakers who reported on recent developments and these together with some of the items arising from the discussion are summarised belowThe evaluation of measurement uncertainty for results close to zero is a problem that has been of concern for some time It was not considered in the ISO Guide to the Expression of Uncertainty in Measurement GUM 1 When the results are close to zero the uncertainty interval calculated according to the procedures given in GUM could include values below zero even when the measurand is for example a concentration which by definition cannot take a negative value Stephen L R Ellison in his presentation giving an overview of the revised EURACHEM/CITAC guide “Quantifying Uncertainty in Analytical Measurement” 2 pointed out that the guide now has a much larger section on how uncertainty can be evaluated and reported in this case Two procedures are described one utilising classical statistics 3 and the other utilising Bayes theorem 4The procedure for calculating the coverage interval using classical statistics is quite simple If the expanded uncertainty has been calculated to have for example a 95  coverage and would have extended below zero then it is just truncated at zero and this truncated classical confidence interval maintains exact 95  coverage This truncated interval becomes progressively more asymmetric as the result approaches zero However the observed mean is the best estimate of the value of the measurand until the observed mean falls below zero when the value of zero should be used Also as the observed mean value falls further below zero the simple truncated interval becomes unreasonably small but results in this region may indicate that something is wrong with the measurementThe Bayesian method allows the combination of information from the measurements with the information that the value of the concentration cannot be negative For measurement results that can be described in the form of a tdistribution then as shown in 4 the resulting probability distribution of the values attributable to the measurand is approximately a truncated tdistribution The observed mean or zero if the observed mean value is below zero should again be used as the reported value and the expanded uncertainty interval is calculated as the maximum density interval containing the required fraction of this truncated distribution How to calculate this interval is given in 2 This Bayesian interval provides the same minimal bias as the classical approach with the useful property that as the observed mean value falls further below zero the reported uncertainty increases Willink 5 pointed out that simulations showed that some Bayesian 95 intervals did not always contain the true value 95  of the time The Analytical Method Committee RSC 6 in responding to this showed that for the maximum density interval while the coverage is not exactly 95  for each individual value of the true mean the deviations from 95  are unlikely to be serious in practiceThe revised EURACHEM/CITAC guide 2 has a new section on The Monte Carlo Simulation MCS and this was covered in presentations by Stephen L R Ellison and Matthias Rösslein The MCS method described in GUM Supplement 1 7 is simple in principle and easy to use given appropriate software MCS requires the probability distributions called the PDFs or probability density functions for all the input quantities in the measurement equation used to calculate the result MCS calculates the result corresponding to one value of each input quantity drawn at random from its PDF and repeats this calculation a large number of times trials typically 105 to 106 This process produces a set of simulated results which under certain assumptions forms an approximation to the PDF for the value of the measurand From this set of simulated results the mean value and standard deviation are calculated In GUM Supplement 1 these are used respectively as the estimate of the measurand and the standard uncertainty associated with this estimateIn most cases using the firstorder Taylor series approximation given in GUM and the MCS method will give virtually the same value for the standard uncertainty associated with the estimate of the measurand Differences become apparent when distributions are far from Normal or where the measurement result depends nonlinearly on one or more input quantities and the uncertainty on these input quantities is large When the measurement model is nonlinear and the relative standard uncertainty is larger than 10 the MCS PDF is likely to be asymmetric In this case the mean value computed from the simulated results will be different from the value of the measurand calculated using the estimates of the input quantities as in GUM However in most cases the difference is likely to be less than the standard uncertainty For most practical purposes in chemical measurement the result calculated from the original input values should be reported the MCS estimate of standard uncertainty can however be usedMCS gives a good estimate of the standard uncertainty even for simulations with a few hundred trials and simulations of 500–5000 MCS samples are likely to be adequate for evaluating the standard uncertainty It is also possible to use the MCS result to determine confidence intervals without the use of effective degrees of freedom In this case to obtain sufficient information about the tails of the PDF for the output quantity can require calculating the result for at least 106 trials However it is important not to be misled by the apparent detail in the PDF obtained for the result The lack of detailed knowledge about the PDFs for the input quantities because the information on which these PDFs are based is not always reliable needs to be borne in mind The tails of the PDFs are particularly sensitive to such information Therefore as is pointed out in GUM section G 12 “it is normally unwise to try to distinguish between closely similar levels of confidence say a 94  and a 96  level of confidence” In addition the GUM indicates that obtaining intervals with levels of confidence of 99  or greater is especially difficult Further to obtain sufficient information about the tails of the PDF for the output quantity can require calculating the result for at least 106 trialsAn important application of measurement uncertainty is its use in the assessment of compliance When making an assessment of compliance the presence of unavoidable measurement uncertainty introduces the risk of making incorrect decisions ie of accepting a batch of material that is outside the specification or rejecting one that is within The probability of making a wrong decision depends both upon the size of the measurement uncertainty and on how the uncertainty is taken into account when assessing compliance

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