For measurement uncertainty for routine measurements we recommend the Nordtest TR537, www.nordtest.info together with the MUkit software from the Finnish Environmental Institute, SYKE or the Excel software from University of Stuttgart. A very good introduction from Tartu University you find here and an overview of different approaches to estimate uncertainty is given in Figure 1 of the Eurolab report, Measurement Uncertainty revisited. There is also a podcast on measurement uncertainty and the Nordtest approach - see below. An example of a summary report using MUkit software is shown below. The software also provides a full detailed report of your uncertainty calculations.
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PODCAST/VIDEO
This podcast is thanks to my Iranian colleague Hamidreza Dehnad who made this interview with me, Bertil Magnusson, in February 2021.
Hamidrezas background is industrial engineering and now working as consultant in the area of laboratory accreditation in Iran. ***********************************************************************************************************
Overview FAQ
GENERAL
* Reporting uncertainty
NORDTEST 537 (2017)
Here are some common questions and answers on this handbook
* Printing errors in Nordtest 537
* Questions about the Nordtest approach
* Bias
* Software MUkit
SAMPLING UNCERTAINTY
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- FAQ -
GENERAL
1. Reporting uncertainty
Use maximum two significant figures for the uncertainty and state the coverage factor. Try to use the same number of decimals as the result when reporting uncertainty in con contraption units.
Example of reporting from the Eurachem Guide
Total nitrogen: (3.52 ± 0.14) g/100 g *
*The reported uncertainty is an expanded uncertainty calculated using a coverage factor of 2 which gives a level of confidence of approximately 95 %.
NORDTEST 537 (2017)
Printing error?
Example A: BOD with Internal quality control+ a CRM in part 4 it shows a term sbias2/√n, should read (sbias/√n)2 ?
Reply: This is missing a parenthesis THANKS. The parenthesis is shown in next part of the formula.
Questions about the Nordtest approach
1 Is this approach ISO GUM compatible?
Reply: This handbook follows the GUM principles of uncertainty and is widely used by accredited laboratories in many different sectors.
2 ‹ Why the uncertainty from day to day variation from control
charts is calculated as u=stdev and is not calculated as u=
stdev/sqrt(n)?. Reply: The s should be calculated based on control values analysed the same way as test samples, i.e. if the test samples are analysed as duplicates (n = 2) the control values should also be based on duplicate analyses. Then you do not consider dividing - just use the s you obtained
3. In chapter 6.3 Recovery the u(vol) is calculated using square root of 3? Reply: If we assume that error of the flask can be up plus or minus 1 % then the standard uncertainty, u, can according to GUM for a so called rectangular distribution be calculated by dividing by square root of 3.
4. Software - MUkit - Repeatability - how to handle duplicates for samples with high concentrations that are diluted before measurement. The uncertainty may increase, especially if you have a lot of suspended matter in your test samples. Important is that you dilute each sample - not make one dilution and then analyse duplicates. So for duplicates either 1) always report results for the measured aliquot, i.e. the concentration for the diluted sample or 2) always report results based on the laboratory sample.
For PT samples however I strongly recommend that you report in to MUkit the concentration in the PT sample and not in any diluted sample.
Bias
1. Calculation of u(bias) from a bias limit
If a method has an acceptable bias limit of say ± 10%, and the data is within these limits this can lead to very high expanded uncertainties in some cases- can this be corrected or is it just the ‘natural’ consequence of high bias levels?
Reply: If instead of applying the measured bias you use the acceptable bias limit in the formula you can regard this as a rectangular distribution (i.e. the bias is anywhere within these limits for all samples within the scope of the method) and then divide by sqrt3 to get a standard uncertainty. If we take data from the EU drinking water directive where max bias is 10 % and max precision is 5 % (2 sRw max 10 %) at the relevant level for many parameters, the expanded uncertainty can then be calculated to be about 15 % relative.
See further details on page 158 in a chapter on measurement quality in a book
2. How to calculate bias using recovery data
In section 6.3 Recovery is an example of a validation of 6 different matrices. For each matrix we have a mean recovery and the overall mean recovery is 96,8 %. We use the same formula as for several CRM. The RMS of these values are 3,44 %. NOTE The guidance given in this section is applicable for test methods that do not include a recovery correction in the procedure for each analytical run. If however you have a fixed recovery in your method then you can validate the method with new experiments and use the same formula. The MUkit software handles recovery where at least 6 matrices are tested.
3 Use of a reference material without statement of uncertainty
If a control standard is prepared from reference materials that do not provide an uncertainty estimate on the certificate, can bias be evaluated based only using the targeted concentration? Reply: Not generally recommended but Yes but you need to guess an uncertainty and put in that value in the calculations
4 Dilution of a CRM
A control sample is prepared for NH3 analysis from a 300 ug/L CRM with an expanded uncertainty of +/- 0.5 % (95% Confidence Interval, k =2, norm). 70 controls are run over the course of the year. Average recovered value and standard deviation are calculated. Would the CRM standard uncertainty of 0.25% be used or does it need to be adjusted somehow based on the dilution down to the LCS concentration? Reply The uncertainty needs to be adjusted due to the dilution. Dilution by volume using a micropipette will usually have a standard uncertainty of around 0.5 % and dilution by weight a standard uncertainty 0.05 % (avoiding evaporation by e.g. delivering the liquid into a small testtube). For uncertainty of dilutions see further here
SAMPLING
1. Sampling uncertainty
In order to estimate measurement uncertainty for a sampling target also the sampling uncertainty should be estimated. Here you can use duplicate sampling according to Nordtest 604. The measurement uncertainty can then be calculated by combining the u(sampling) with the u(analysis) where the u(analysis) is estimated from Nordtest 537.