Estimation of measurement uncertainty in chemical analysis

Self-test 10.3

Here you can test your understanding how the uncertainty component accounting for systematic effects can be estimated in practice.

Which are the possibilities of estimating the bias component of measurement uncertainty (component that accounts for the systematic effects) of an analytical procedure in your laboratory?

Analyse the certificated reference material (CRM), which corresponds to a matrix that is routinely analyzed in the laboratory.

Make spiking studies with samples that have the same or similar matrix with the routine samples.

Participate in an interlaboratory comparison (ILC) where the matrix is different from the laboratory’s routine analysis samples, but there is reference value that has a low uncertainty.

Make a large number of repeated measurements of a routine sample during a long time period.

Carefully calibrate the volumetric glassware used in the analysis.

Make the measurements at three different concentration levels.

Acquire the estimates of all the systematic effects from scientific literature.

The laboratory wants to estimate the bias component of uncertainty of protein determination in different products by the Kjeldahl method. There are two certified reference materials available: Ham with protein content (19.6 ± 0.6) g/100g (k=2, norm) and cheese with protein content (26.3 ± 0.7) g/100g (k=2, norm). The laboratory has carried out four bias determinations with the following results (each found value is found as a mean from a number of parallel measurements):

Please calculate the bias component of uncertainty (please give 2 or 3 decimals). Absolute uncertainties can be used in this case.

Clue 1:

The bias component is found as follows:

For finding the RMSbias and u(Cref) the bias values from the individual bias determinations (four altogether) and combined standard uncertainties of the reference materials used for the individual determinations (again, four altogether) have to be combined using the root mean square approach:

Clue 2:

The individual bias values are found as differences of the lab value and the reference value. The combined standard uncertainties of the reference values can be found by dividing the expanded uncertainties with the coverage factor.

Clue 3:

The individual bias values are (all in g/100g): 0.6, 0.9, 0.5, 0.8. The RMS_bias found from these data is 0.7176 g/100g (decimal places are deliberately given in excess).

Clue 4:

The individual u(Cref_i) values are (all in g/100g): 0.35, 0.35, 0.3, 0.3. The u(Cref) found from these data is 0.3260 g/100g (decimal places are deliberately given in excess).

Clue 5:

The u(bias) found from these data is 0.7882 g/100g (decimal places are deliberately given in excess). u(bias) is not yet the final uncertainty but rather an interim result for future calculations, so it should not be rounded to 1 or 2 significant digits.

Which of the following statements about the previous exercise are true? Please mark the true statements in the tick-boxes.

The results obatained with this procedure seem to be positively biased (i.e. systematically higher results are obtained).

This uncertainty calculation assumes that ham and cheese matrixes behave the same way in this analysis.

The found u(bias) value can be used as the combined standard uncertainty of this procedure.

Four bias determinations are sufficient and it is not necessary to do more bias determinations.

For determining within-lab long-term reproducibility and bias of determination of heavy metals in soil laboratory has a sewage sludge control sample. Sample preparation has been carried out with this sample (by microwave digestion) and the resulting solution is kept in refrigerator and analyzed on all days when determination of heavy metals is carried out. The solution is analyzed twice on the same day and standard deviation is calculated from the two results. These standard deviations are pooled over a time period of approximately one year. This pooled standard deviation is used as estimate of within-lab long-term reproducibility. The absolute differences between the two results are averaged over a time period of one year and the average absolute difference is used as bias estimate.

There are several flaws in the above described approach. Which statements are true?

Keeping solution in a refrigerator is a mistake.

If the lab does determination of heavy metals in soil then also the control sample should be a soil sample.

On every day the analysis should be carried out in full, with all steps, including also the sample preparation step, instead of just analyzing the solution.

The obtained pooled standard deviations are repeatability standard deviations, not within-lab long-term reproducibility standard deviations.

Bias cannot be determined this way.

Stable control sample is not needed for determining within-lab long-term reproducibility

Which of the following issues are important in determining bias?

Sufficient number of replicate measurements

Sufficiently long timeframe

Homogeneous sample

Matrix match

Concentration range match

Reliable reference value

Inclusion the sample preparation

Course introduction
1. The concept of measurement uncertainty (MU)
- Self-test 1
2. The origin of measurement uncertainty
- Self-test 2
3. The basic concepts and tools
4. The first uncertainty quantification
5. Principles of measurement uncertainty estimation
6. Random and systematic effects revisited
- Self-test 6
7. Precision, trueness, accuracy
- Self-test 7
8. Overview of measurement uncertainty estimation approaches
- Self-test 8
9. The ISO GUM Modeling approach
10. The single-lab validation approach
11. Comparison of the approaches
- Self-test 11
12. Comparing measurement results
13. Additional materials and case studies
14. Tests and Exercises
Frequently asked questions
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