1. High Resolution Models using Monte Carlo Measurement Uncertainty Research Group Marco Wolf, ETH Zürich Martin Müller, ETH Zürich Dr. Matthias Rösslein, Empa St. Gallen Prof. Walter Gander, ETH Zürich PTB-BIPM Workshop Impact of Information Technology in Metrology June 4 th 2007

2. Outline  Introduction  Describing models with MUSE  Selected examples  Summary

3. Outline  Introduction  Describing models with MUSE  Selected examples  Summary

4. MUSE – Measurement Uncertainty Simulation and Evaluation  Software package for evaluation of measurement uncertainty  Currently developed at ETH Zürich in cooperation with Empa St. Gallen  Based on first supplement of GUM  Available from project page http://www.mu.ethz.ch for http://www.mu.ethz.ch  Linux/Unix  Windows

5. Uncertainty Measurement Evaluation  Analytical Solution  Only applicable in simple cases  Even then it gets too complicated

6. Uncertainty Measurement Evaluation  Analytical Solution  Only applicable in simple cases  Even then it gets too complicated  GUM Uncertainty Framework  Applicable in many cases  Does not use all information  Needs linearized model  Ambiguous calculation of degrees of freedom

7. Uncertainty Measurement Evaluation  Analytical Solution  Only applicable in simple cases  Even then it gets too complicated  GUM Uncertainty Framework  Applicable in many cases  Does not use all information  Needs linearized model  Ambiguous calculation of degrees of freedom  Monte Carlo Method  Always applicable  Arbitrary accuracy  Uses all information provided for input quantities

8. Outline  Introduction  Describing models with MUSE  Selected examples  Summary

9. Modeling Measurement Equipment  Models of measurement equipment  Basic Models can be instantiated abritrary often  Using different sets of parameters  Database of Basic Models  Equivalent models allow global and direct comparison of results

10. Describing Measurement Procedure using Processes  Using instances of Basic Models together with other processes  Processes encapsulate their own settings for each instance or other processes  Splitting of description of devices and measurement scenario  Dependencies can be modeled by connecting processes

11. Definition of Calculation Parameters  Random number generator  Options for adaptive Monte Carlo  Settings for self-validation  Settings for analyzing data files  Global variables and variation settings  Equation(s) of the measurand(s) Adaptive MC Variation Variables Number of simulations Analyzing Validation Random number genenerator

12. Combination for Measurement Scenario Adaptive MC Variation Variables Number of simulations Analysation Validation Instances of Basic Models Instances of Basic Models Process definition Calculation Section

13. Outline  Introduction  Describing models with MUSE  Selected examples  Summary

14. Example: Gauge Block Calibration  From GUM Supplement 1, section 9.5  Shows difference of results of MC and GUM uncertainty framework  Model equation with following distributions:  Normal  Arc sine (U-shaped)  Curvelinear trapezoidal  Rectangular  Student-t

15. Example: Gauge Block Calibration

18. Method Number of simulations Mean * Standard deviation * Shortest 95% interval * Shortest 99% interval * Shortest 99.9% interval * GUF83832[746, 930] MCM (GS1)1.36*10 6 83836[745, 931] MCM (MUSE)10 4 83836[707, 959][744, 933][766, 908] MCM (MUSE)10 5 83836[718, 958][743, 931][768, 909] MCM (MUSE)10 6 83836[718, 959][745, 931][768, 908] MCM (MUSE)10 7 83836[718, 959][745, 931][768, 908] MCM (MUSE)10 8 83836[718, 958][745, 931][768, 908] * in 1/nm

19. Example: Chemical experiment  More complex scenario using processes  Splitting the model equation into three parts:  Creating stock solution sols  Creating first solution sol1  Creating second solution sol2 sol s sol 1 sol 2

20. Example: Chemical experiment What is the difference if we use the same pipette?

21. Example: Chemical experiment

25. Example: Measurement series  More than one formula for measurement uncertainty  More complex evaluation of the overall measurement uncertainty in a measurement series  Simulation of different measurement scenarious and strategies for analysing Reference n Sample n-1,2 Sample n-1,1 Reference n-1... Sample 2,2 Sample 2,1 Reference 2 Sample 1,2 Sample 1,1 Reference 1

26. Reference n Sample n-1,2 Sample n-1,1 Reference n-1... Sample 2,2 Sample 2,1 Reference 2 Sample 1,2 Sample 1,1 Reference 1 Example: Measurement series

30. Outline  Introduction  Describing models with MUSE  Selected examples  Summary

31. Summary  The examples show some features of the software and that the software is capable of handling high resoluted models  MUSE is under continuous development. It is thought for advanced users who want to analyze their uncertainty budget in detail  Current work:  Calibration  Module to analyze results  Simplification of definition of measurement series  Parallel computing

32. Thank you! Contact us directly or write to: muse@inf.ethz.ch Homepage: www.mu.ethz.ch Contact us directly or write to: muse@inf.ethz.ch Homepage: www.mu.ethz.ch