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 % |
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) |
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 |
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 | |
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? |