1. 1 Approaches in the Area of Measurement Uncertainties

2. 2 Introduction  Measurements  Uncertainties  Operations on measurands… …and corresponding uncertainties 72.15 Kg 76.40 Kg

3. 3 Introduction ( cont. )  Measurements : difference = 76.40 - 72.15 = + 4.25 Kg  ??? Can a jogging session have such an effect ?  Is that realistic (or even possible) ?  Effect of Uncertainties in every days’ life !  Digital readings are misleading  Sources of uncertainties to be identified  What is the real effect making “the same measurement twice“…and then making calculations on such values ?  … Radio measurements...

4. 4 History  In the days before the R&TTE Directive and the CEPT policies …  Equipment had to be type-approved in the various European Countries  Manufacturers would travel across Europe with equipment from Lab to Lab …  …and have their equipment measured  Panic … (very) different results where often found…  Can pass or fail be a random variable !

5. 5 An initial Methodology had been developed (before years 1990)  Definition of the methods of measurement…  Equipment measured in the same way in the various European Countries  Results to be presented in the same way  Including the characteristics of equipment to be used in the measurements …  Definition using the type of equipment (instrumentation)  Definition using the minimal performance (for instrumentation)

6. 6 Drawbacks of this old way handling of uncertainties  Lack of freedom for the industry  In terms of type of equipment to be used  Benefits from having better equipment in one subset of the test set up … lost …  Performance in terms of uncertainty could not be part of a commercial relationship…  How to relate the required performance in terms of equipment used for the measurement into parameters to be used for :  Systems deployment (operators …) ?  Sharing studies (ITU, CEPT) ?

7. 7 Targets for a New Approach (i.e. TR 100 028)  Allow for a continued enhancement of the performance in term of uncertainties  Allow for positive effects of improvements in terms of performance of instrumentation  New concept : “uncertainty budget”.  De-couple new editions of Standards from the evolution of Technology in the area of Instrumentation (avoids to update standards just to keep up with progress in the area of instrumentation!)  Enhanced transparency  Realistic uncertainty figures support, in particular : the optimization of system deployment avoiding discrepancies between results obtained by various partners (e.g. under the R&TTE regime)  Supports enhancement of the uncertainty figures.

8. 8 The New Approach (in accordance with TR 100 028 V 1.3.1)  Theoretical approach for the evaluation of uncertainties  Evaluation of the measurement uncertainty for each measurement  Agree on pass/fail criteria  Define maximum values for the uncertainty (e.g. in “Harmonized Standards under the R&TTE Directive”)  Prepare supporting documentation (e.g. TRs, forms…)

9. 9 The New Approach (in accordance with TR 100 028 V 1.3.1) (STEP 1)  Theoretical approach for the evaluation of uncertainties  Evaluation of the measurement uncertainty for each measurement  Agree on pass/fail criteria  Define maximum values for the uncertainty (e.g. in “Harmonized Standards under the R&TTE Directive”)  Prepare supporting documentation (e.g. TRs, forms…)

10. 10  Mapping of the measurement set up into :  random variables (sources of uncertainty) and  operations between these random variables  Evaluate (or define) the probabilistic properties of each of the above random variables (i.e. distributions)  Find how the mathematical properties of the measurement set up (i.e. of the signals), or steps correspond to the properties of the distributions mapped to the various uncertainty sources.

11. 11 Examples of sources of uncertainties  Related to instrumentation :  Levels of signal generators  Readings (e.g. value a frequency)  Related to the environment :  test conditions (e.g. effect of temperature)  Related to parts of the measurement set up :  cables and hardware (e.g. attenuators)  mismatch...

12. 12 Example of combinations The table found in TR 100 028, part 2 Annex D section D.3.12 provides for usual operations :  the resulting distributions  the values of the means and standard deviations...

13. 13 … and also support,in particular, for conversions between linear terms and dBs...

14. 14  Possible simplifications  Differentiation  1st order approximations  Usage of sub-blocs (sub-systems)  Useful in the case where specific parts of a measurement system are often used together (e.g. automated test systems)  Useful when different units are used in different parts of the measurement set up (e.g. Volts and dBs).

15. 15 The basic trick about standard deviations  The table in D.3.12 shows, in particular, that :  a number of usual operations translate into simple operations on standard deviations …  As a result, one possible approach is the following :  list all contributions and characterize the corresponding standard deviations  combine all standard deviations in accordance with the rules given in the table (which provides a combined uncertainty, given by its standard deviation)  Invoque the “Central Limit Theorem” … which provides for a Gaussian having the standard deviation found above.

16. 16 Result : The distribution corresponding to the combined uncertainty (i.e. the probability of error “r”) Gaussian curves Standard deviation

17. 17 Changing Confidence Levels Expansion factor (k) : the factor allowing to change from one confidence level to another k=2 is an usual value ; provides approximately 95 % in the case of Gaussian (Normal) distributions

18. 18 The New Approach (in accordance with TR 100 028 V 1.3.1) (STEP 2)  Theoretical approach for the evaluation of uncertainties  Evaluation of the measurement uncertainty for each measurement  Agree on pass/fail criteria  Define maximum values for the uncertainty (e.g. in “Harmonized Standards under the R&TTE Directive”)  Prepare supporting documentation (e.g. TRs, forms…)

19. 19  List of the contributions (complete … not forgetting cables, mismatch, etc.)  Define units, shape and characteristics for each distribution  Find any natural assembly (i.e. definition of sub-sets)  Possible help : ETSI TRs (including spread sheets)  … find the right uncertainty value(s) (for the right confidence level or factor k )!

20. 20 The New Approach (in accordance with TR 100 028 V 1.3.1) (STEP 3)  Theoretical approach for the evaluation of uncertainties  Evaluation of the measurement uncertainty for each measurement  Agree on pass/fail criteria  Define maximum values for the uncertainty (e.g. in “Harmonized Standards under the R&TTE Directive”)  Prepare supporting documentation (e.g. TRs, forms…)

21. 21 Pass or fail ???  Found in the appropriate standard :  limit value for each parameter  maximum acceptable measurement uncertainty for each parameter  The measurement provides :  the measured value  the estimation of the uncertainty for a certain confidence level (i.e. 95%) or for a certain expansion factor k (i.e. k= 1.96 or 2.00)  The “shared risk approach”  measurement uncertainty stated together with measured value  direct compare value measured to limit (found in the standard)  measurement uncertainty has to be better than the “maximum acceptable uncertainty” (found in the standard)  Harmonized Standards under the R&TTE Directive clearly state the pass/fail criteria

22. 22 The New Approach (in accordance with TR 100 028 V 1.3.1) (STEP 4 and 5)  Theoretical approach for the evaluation of uncertainties  Evaluation of the measurement uncertainty for each measurement  Agree on pass/fail criteria  Include the maximum acceptable values for the uncertainty (and the limits e.g. in “Harmonized Standards under the R&TTE Directive”)  Prepare supporting documentation (e.g. TRs, forms…)

23. 23 Support documentation (e.g. TRs, forms…)  ETSI has developed a number of documents e.g. TR 100 028 (version 1.3.1 published early 2001) in support of the methodology, this TR includes spread sheets as well as.  ETSI has also developed forms (e.g. test report forms)  Bibliography …...Bureau International des Poids et Mesures (“BIPM method”)

24. 24 Conclusion  The usage of the probabilistic approach (as defined in TR 100 028), on a global basis is expected to :  Facilitate global roaming while simplifying the legal aspects (e.g. in “R&TTE geographical areas”)  Allow for an enhancement of the performance in terms of uncertainties, as the performance of instrumentation increases, without  Increase transparency and clarity and ease both : system deployment sharing studies