Table 1.
Number of courses in which various technical aspects of measurement uncertainty are taught for audiences including employees of NMIs, calibration or testing laboratories, in legal metrology and at universities (from [36]). For reference, the equivalent question (Q) number for the questionnaire in Table 2 is given.
| Audience | |||||
|---|---|---|---|---|---|
| Technical content of uncertainty course | Equivalent topic in Table 2 | NMI | lab | legal | uni |
| Mathematical tools reviewed / as prerequisite | Q1 | 7/7 | 9/7 | 0/2 | 6/6 |
| (some) Probability concepts | Q2 | 15 | 22 | 6 | 12 |
| Basic metrological concepts | Q3 | 15 | 23 | 6 | 15 |
| Standard uncertainties for input quantities | Q4 | 15 | 24 | 6 | 16 |
| Law of propagation of uncertainty (LPU) | Q5 (maybe Q6) | 13 | 23 | 6 | 15 |
| Propagation of distributions via Monte Carlo | Q11 | 7 | 8 | 1 | 9 |
| Validate LPU against Monte Carlo results | Q13 | 7 | 8 | 1 | 6 |
| LPU & Monte Carlo for multivariate models | Q8, Q12 | 3 | 2 | 0 | 2 |
| Reporting of measurement results | Q18 | 14 | 22 | 6 | 16 |
| Number of courses | 15 | 24 | 6 | 16 | |
Table 2.
Topics of the questionnaire on which EA and Italian accredited calibration and testing laboratories and their assessors indicated their knowledge (‘know’) and interest (‘inter’). The values indicate the average score and the color highlights the level (dark gray = highest level, light gray = medium level, white = lower level) of knowledge and interest reported (see Appendix B and text for details). Emphasized topics largely correspond to topics included in the course survey [36].
| Questionnaire topic | Accredited calib. labs | Technical assessors | Accredited test labs | Technical assessors | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| EA | Italy | EA | Italy | EA | Italy | EA | Italy | |||||||||||
| know | inter | know | inter | know | inter | know | inter | know | inter | know | inter | know | inter | know | inter | |||
| Basic math. & metrolog. concepts | Mathem. elements forevaluating uncertainty | Q1 | 2.81 | 3.60 | 2.65 | 3.37 | 2.93 | 3.74 | 3.12 | 3.60 | 2.53 | 3.33 | 2.57 | 3.23 | 2.68 | 3.33 | 2.74 | 3.31 |
| Probability andstatistics elements | Q2 | 2.53 | 3.50 | 2.46 | 3.40 | 2.93 | 3.67 | 3.00 | 3.48 | 2.44 | 3.21 | 2.44 | 3.24 | 2.63 | 3.24 | 2.55 | 3.36 | |
| Fundamental concepts of metrology | Q3 | 3.21 | 3.67 | 3.17 | 3.31 | 3.42 | 3.72 | 3.64 | 3.48 | 2.80 | 3.47 | 2.85 | 3.50 | 2.94 | 3.51 | 3.06 | 3.57 | |
| Propagating uncertainties (GUM approach) | Evaluation of type A& B uncertainty components | Q4 | 2.79 | 3.66 | 2.54 | 3.47 | 3.00 | 3.79 | 3.20 | 3.64 | 2.22 | 3.13 | 2.28 | 3.20 | 2.41 | 3.14 | 2.70 | 3.44 |
| Combined stand. uncertainty for uncorr. inputs | Q5 | 2.60 | 3.47 | 2.36 | 3.29 | 2.95 | 3.67 | 3.20 | 3.60 | 2.18 | 3.05 | 2.07 | 3.12 | 2.32 | 3.13 | 2.35 | 3.32 | |
| Combined stand. uncertainty for correlated inputs | Q6 | 2.37 | 3.48 | 2.24 | 3.42 | 2.63 | 3.72 | 2.76 | 3.52 | 2.16 | 3.06 | 2.07 | 3.11 | 2.29 | 3.01 | 2.39 | 3.35 | |
| Expanded uncertainty (U) & coverage factors (k) | Q7 | 2.84 | 3.57 | 2.83 | 3.38 | 3.19 | 3.79 | 3.36 | 3.48 | 2.54 | 3.29 | 2.61 | 3.36 | 2.66 | 3.24 | 2.89 | 3.47 | |
| Applying multivariate measurement models | Q8 | 1.98 | 3.24 | 1.66 | 2.90 | 2.12 | 3.51 | 2.16 | 3.28 | 1.84 | 2.82 | 1.65 | 2.83 | 2.07 | 2.96 | 1.85 | 2.99 | |
| Theoretical or empirical measurement models | Q9 | 2.11 | 3.24 | 1.99 | 3.11 | 2.28 | 3.60 | 2.52 | 3.44 | 2.04 | 2.91 | 1.93 | 3.05 | 2.21 | 3.00 | 2.11 | 3.15 | |
| Fitness for purpose and target uncertainty | Q17 | 2.04 | 3.23 | 2.12 | 3.29 | 2.47 | 3.56 | 2.72 | 3.48 | 2.05 | 3.08 | 2.23 | 3.43 | 2.31 | 3.19 | 2.52 | 3.57 | |
| Reporting measurement results | Q18 | 2.86 | 3.53 | 2.90 | 3.28 | 3.19 | 3.72 | 3.32 | 3.25 | 2.66 | 3.42 | 2.84 | 3.47 | 2.83 | 3.48 | 3.07 | 3.54 | |
| Conformity | Statements of conformity to specifications | Q21 | 2.27 | 3.34 | 2.45 | 3.49 | 2.65 | 3.74 | 2.84 | 3.44 | 2.26 | 3.20 | 2.39 | 3.43 | 2.45 | 3.29 | 2.80 | 3.65 |
| Uncertainty evaluation for specific data | Least squares method applied to metrology | Q10 | 2.18 | 3.29 | 2.07 | 3.24 | 2.49 | 3.65 | 2.68 | 3.52 | 1.91 | 2.76 | 2.07 | 2.98 | 2.19 | 2.92 | 2.24 | 3.15 |
| Uncertainty based on methods validation data | Q15 | 1.96 | 3.27 | 1.83 | 3.30 | 2.00 | 3.53 | 2.25 | 3.28 | 2.34 | 3.36 | 2.45 | 3.49 | 2.51 | 3.33 | 2.72 | 3.56 | |
| Uncertainty based on ILC/PT data & experience | Q16 | 2.04 | 3.30 | 2.28 | 3.61 | 2.16 | 3.58 | 3.00 | 3.52 | 2.15 | 3.21 | 2.33 | 3.47 | 2.30 | 3.18 | 2.61 | 3.55 | |
| Uncertainty for sampling | Q20 | 1.82 | 2.89 | 1.65 | 2.84 | 2.16 | 3.47 | 2.00 | 3.04 | 1.99 | 3.12 | 1.80 | 3.10 | 2.26 | 3.26 | 2.11 | 3.48 | |
| Propagating distributions (MonteCarlo) | Single measurand (Univariate model) | Q11 | 1.42 | 3.00 | 1.60 | 3.09 | 1.93 | 3.63 | 2.08 | 3.28 | 1.45 | 2.38 | 1.44 | 2.63 | 1.62 | 2.63 | 1.54 | 2.89 |
| More measurands (Multivariate model) | Q12 | 1.37 | 2.95 | 1.49 | 2.94 | 1.72 | 3.51 | 1.84 | 3.24 | 1.37 | 2.31 | 1.40 | 2.57 | 1.55 | 2.55 | 1.42 | 2.85 | |
| vs. GUM approach for uncertainty evaluation | Q13 | 1.44 | 2.93 | 1.50 | 3.11 | 1.84 | 3.60 | 1.92 | 3.36 | 1.42 | 2.50 | 1.36 | 2.70 | 1.67 | 2.72 | 1.43 | 3.06 | |
| Bayes appr. | Alternative methods for uncertainty | Q14 | 1.44 | 2.86 | 1.30 | 2.79 | 1.49 | 3.26 | 1.64 | 3.20 | 1.34 | 2.46 | 1.35 | 2.62 | 1.63 | 2.66 | 1.58 | 3.06 |
Table 3.
Proportion of courses aimed at different target audiences among the 43 courses included in the survey [36].
| Target audience for courses | Proportion |
|---|---|
| NMIs | 14 % |
| NMIs, calibration & testing labs | 21 % |
| Calibration & testing labs | 23 % |
| Academia, calibration & testing labs | 5 % |
| Academia | 23 % |
| Legal metrology | 12 % |
| Legal metrology, calibration & testing labs | 2 % |
Table 4.
Number of participants who answered a questionnaire on measurement uncertainty topics among different EA (and in parentheses Italian) accredited laboratories and their assessors.
| Calibration | Testing | |
|---|---|---|
| Accredited laboratories | 82 (133) | 258 (547) |
| Technical assessor | 59 (38) | 140 (155) |
Table 5.
List of questions provided to WELMEC WGs prior to a meeting between its representatives and partners of the MU Training activity.
| 1 | How is your involvement regarding measurement uncertainty best described? |
| 2 | Which literature/guides for uncertainty evaluation does your WG use most? |
| 3 | What are the biggest challenges you face when evaluating measurement uncertainty? |
| 4 | Are there applications for which guidance for appropriate uncertainty calculations is missing? |
| 5 | Would you be interested in measurement uncertainty training, please specify which ones? |
| 6 | What kind of research projects related to uncertainty evaluation would be useful for you? |
| 7 | Do you have any specific expectations from EMN MATHMET, or what could the EMN do to help you in your work with uncertainties? |