1. 08/2-2009
COMMUTABILiTY

2. Commutability The hidden secrets
By Dietmar Stöckl
STT Consulting

3. Tin Can 3 - Commutability
Definition
Commutability of a reference material
property of a reference material, demonstrated by the closeness of agreement between the relation among the measurement results for a stated quantity in this material, obtained according to two given measurement procedures, and the relation obtained among the measurement results for other specified materials
NOTE 1 The reference material in question is usually a calibrator and the other specified materials are usually routine samples (can also be trueness controls, DS)
NOTE 2 The measurement procedures referred to in the definition are the one preceding and the one following the reference material (calibrator) in question in a calibration hierarchy (see ISO 17511) (in general, can be any two measurement procedures, DS).
JCGM 200:2008. International vocabulary of metrology – Basic and general concepts and associated terms (VIM). International Bureau of Weights and Measures (BIPM); Joint Committee for Guides in Metrology (JCGM): Paris, Freely available at:
Tin Can 3 - Commutability

4. Experiment and interpretation
Measure a minimum of 20 native samples and test samples (trueness controls, calibrators) in one run in replicate (EP 14, n = 3) with at least two measurement procedures
General interpretation
“Compare the behaviour of the test samples with the native samples”
EP 14 interpretation
Test samples should be within the prediction limits of the regression based on the native samples
Tin Can 3 - Commutability

5. Cholesterol example EP 14
+4%
The test sample is just at the prediction limit and is considered commutable. When this sample is used as trueness control in proficiency testing, the results are flawed by 4%!
Tin Can 3 - Commutability

6. Different point of view
+0.8%
Commutability should be judged versus the confidence interval of the regression line!
Tin Can 3 - Commutability

7. Commutability – A different view
Samples with confidence intervals versus CI of regression line.
Tin Can 3 - Commutability

8. Commutability of single, native samples
+3.8%
Single, native samples may have sample-related effects and may not represent the average sample! When this sample is used as trueness control in PT, the results are flawed by 3.8%!
Tin Can 3 - Commutability

9. Tin Can 3 - Commutability
Related samples
CAVE! The statistical treatment of related samples (dilutions of calibrators; PT materials with the same matrix) has not been addressed, yet.
Tin Can 3 - Commutability

10. Tin Can 3 - Commutability
Calibrator set
Tin Can 3 - Commutability

11. Commutability – Current concept
The statistical concept is wrong
It is about the confidence interval of the line and not about the prediction interval. We want to assess the trueness of the measurement procedure or we want to calibrate the procedure
Unsolved problem
Related samples
Remark
Not merely a statistical problem! Check the quality of the input data!
Tin Can 3 - Commutability