For measurement uncertainty for routine measurements we recommend the Nordtest TR537, www.nordtest.info together with the MUkit software. An example of a summary report using MU is shown below. The software also provides a full detailed report of your uncertainty calculations.

FAQ for measurement uncertainty and Nordtest 537 (2017)
Here are questions and answers on this handbook
Printing errors
GENERAL FAQ
BIAS
SAMPLING
Software MUkit

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.

GENERAL

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.

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.

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.

SOFTWARE - MUkit

Repeatability - how to handle duplicates for samples with high concentrations that are diluted before measurement.
In MUkit you can choose if the uncertainty is relative and the dilution does not increase the uncertainty. The uncertainty may increase 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.