1. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations1 Uncertainty in Radiation Measurements  Uncertainty budgets for each type of instrument  Uncertainty in voltage readings according to DMM spec sheet  Uncertainty of the WRR representation by WSG instruments (=uncertainty of WRR reduction factors for WSG instruments) was set to 250 ppm, based on the statistics of WRR factors determined at IPC‘s 1980-2000

2. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations2 Uncertainty – Basics 1) Formulate a mathematical model of the measurement system  Formula 2) Identify all sources of uncertainty (basically all input parameters and measurands in that Formula)  Components 3) Estimate the Individual Uncertainty for each component according to its type (normal, rectangular, U-shape, cosine... distribution) 4) Calculate the Sensitivity of the measurand to each of the uncertainty components 5) Sum the squares of each component‘s individual uncertainty multiplied by its respective sensitivity factor  Combined Uncertainty 6) Multiply the combined uncertainty by the Coverage Factor (according to the effective degrees of freedom of the mathematical model)  Expanded Uncertainty

3. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations3 Example – PMO6 1) Mathematical Formula 2) Components of Uncertainty (C), P C (  U C1, I C1, U C2, I C2 ), P O (  U O, I O ), T 3) Individual Uncertainties u i (CUI+c t T)

4. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations4 Example – PMO6 (contd.) 3) Individual Uncertainties u i U and I are known to within the accuracy of the voltmeter  Rectangular Distribution For rectangular distributions the standard uncertainty is u=a/  3 ±a: accuracy of the voltmeter

5. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations5 Example – PMO6 (contd.) 4) Sensitivity Factors c i Partial Derivatives I  I I tctc

6. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations6 Example – PMO6 (contd.) u2=(uici)2u2=(uici)2 5) Combined Uncertainty 6) Expanded Uncertainty Effective degrees of freedom of the system:  Students t table: Coverage factor k=1.96 for a confidence level of 95% U=ku=1.96*u

7. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations7 Example – PMO6 Calibration Factor cos(p) A 0 poff-pointing A 0 „Atmospheric conditions“

8. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations8 Cosine Probability Distribution The off-pointing of the test pyrheliometer with respect to the reference instrument is always positive with an expectation value of zero. This is an example of an asymmetric probability distribution, where the standard procedure for calculating the sensitivity fails because ≠ cos( ). The following expansion is used to calculate c p

9. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations9 Uncertainty Budget

10. IPC-X 2005 October 6 th Uncertainty in Radiation Measurements and Calibrations10 Uncertainty Budget The contribution of each uncertainty component to the combined and expanded uncertainties