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Evaluate and quantify the drift of a measuring

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L'évaluation de la dérive des instruments "mesureur" est une question majeure en métrologie, tant pour l'évaluation des incertitudes de mesure que pour celle des périodicités. Nous avons proposé dans le cadre du CIM 2019 une approche innovante permettant de traiter de cette question de façon statistique.

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Evaluate and quantify the drift of a measuring

  1. 1. Evaluate and quantify the drift of a measuring instrument Jean-Michel POU (Deltamu), Laurent LEBLOND (PSA Groupe - France) Speaker: Peggy COURTOIS (Deltamu)
  2. 2. Measuring instruments • Instruments measuring a range of measurements • Example: • Caliper • Ammeter • Temperature probe • pH-meter • … • Measuring instruments • How is the drift calculated? • New approach • Conclusion
  3. 3. • Measuring instruments • How is the drift calculated? • New approach • Conclusion x Time Measurement Calibration Results for a fixed point x x x Maximum Difference * See LAB GTA-10 x Standard Measurement Calibration Results x x x Drift contribution to the final uncertainty 𝑴𝒂𝒙 𝑴𝒂𝒙 𝑫𝒊𝒇𝒇 𝟑 How is the drift calculated? Usual approach
  4. 4. • Measuring instruments • How is the drift calculated? • New approach • Conclusion • Point to point analysis of the drift • Same points for future calibration • The maximum is not representative • Calibration points non independent (covariance) x Standard Measurement Calibration Results x x x How is the drift calculated? Disadvantages x Time Measurement Calibration Results for a fixed point x x x Maximum Difference
  5. 5. New approach VIM3-2008 International Vocabulary of Metrology (VIM3 – 2008) Calibration (§2.39) Operation that, under specified conditions: 1. Establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties 2. Uses this information to establish a relation for obtaining a measurement result from an indication 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙 + 𝒃 𝟐 𝒙 𝟐 + ⋯ + 𝒃 𝒏 𝒙 𝒏 • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis x Standard Measurement Calibration Results x x x 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙
  6. 6. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis New approach How to identify a drift? Standard Measurement Calibration Results x x x x 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙
  7. 7. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis New approach How to identify a drift? Standard Measurement Calibration Results x x x x b0 b1 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙 𝒚 = 𝒙 Perfect Instrument 𝒃 𝟎 = 𝟎 𝒃 𝟏 = 𝟏 𝒃 𝟎 = 𝟎 𝒃 𝟏 = 𝟏 1 0
  8. 8. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis New approach How to identify a drift? Standard Measurement Calibration Results 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙 Standard Measurement Calibration Results 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙 b0 b1 b0 b1
  9. 9. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis Etalonnage 1 Etalonnage 2 Etalonnage 3 Etalonnage 4 Etalonnage 5 Etalonnage 6 Etalonnage 7 Etalonnage 8 Etalonnage 9 Etalonnage 10 0,9985 0,999 0,9995 1 1,0005 1,001 1,0015 -0,15 -0,1 -0,05 0 0,05 0,1 0,15 Penteb1 Ordonnéeà l'origine b0 Evolution du point de coordonnées (b0;b1) au fil des étalonnages New approach How to identify a drift? Etalonnage 1 Etalonnage 2 Etalonnage 3 Etalonnage 4 Etalonnage 5 Etalonnage 6 Etalonnage 7 Etalonnage 8 Etalonnage 9 Etalonnage 10 1 1,00005 1,0001 1,00015 1,0002 1,00025 1,0003 1,00035 1,0004 1,00045 -0,02 0 0,02 0,04 0,06 0,08 0,1 0,12 Penteb1 Ordonnéeà l'origine b0 Evolution du point de coordonnées (b0;b1) au fil des étalonnages
  10. 10. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis New approach How to identify a drift? b0 b1 time b0 time b1 b0 b1
  11. 11. Etalonnage 1 Etalonnage 2 Etalonnage 3 Etalonnage 4 Etalonnage 5 Etalonnage 6 Etalonnage 7 Etalonnage 8 Etalonnage 9 Etalonnage 10 1 1,00005 1,0001 1,00015 1,0002 1,00025 1,0003 1,00035 1,0004 1,00045 -0,02 0 0,02 0,04 0,06 0,08 0,1 0,12 Penteb1 Ordonnéeà l'origine b0 Evolution du point de coordonnées (b0;b1) au fil des étalonnages • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis New approach How to identify a drift? -0,02 0 0,02 0,04 0,06 0,08 0,1 0,12 0 500 1000 1500 2000 2500 3000 3500 b0 Nombre de jours Evolution de l'ordonnée à l'origine b0 au fil des étalonnages 1 1,00005 1,0001 1,00015 1,0002 1,00025 1,0003 1,00035 1,0004 1,00045 0 500 1000 1500 2000 2500 3000 3500 b1 Nombre de jours Evolution de l'ordonnée à l'origine b1 au fil des étalonnages b0 b1
  12. 12. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis New approach How to identify a drift? Standard Measurement Calibration Results x x x x 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙 𝒚 = 𝒙 time b0 time b1 b0 b1
  13. 13. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis New approach How to quantify the drift? Standard Measurement Calibration Results 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙 time b0 time b1 T0 t b0 b1 Last Calibration Future Calibration (b0,b1) at T0 (b0(t),b1(t)) b0(t) b1(t) t T0
  14. 14. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis New approach How to quantify the drift? Standard Measurement Calibration Results (b0,b1) Contribution of the drift uncertainty to the measurement process: • Mean error: 𝒖 𝒔 𝒕 = 𝒆 𝒕 𝟑 • Random error: 𝒖 𝒓 𝒕 = 𝒔 𝒆 𝒕 𝑒 𝑡 : Deviation mean 𝑠 𝑒 𝑡 : Standard deviation Future Calibration (b0(t),b1(t)) Last Calibration
  15. 15. • New approach • VIM3 – 2008 • How to identify a drift? • How to quantify a drift? • Further analysis Further analysis • Drift model uncertainty: • Drift uncertainty based on the b0 and b1 coefficients • Monte Carlo simulation 𝑏0 𝑡 = 𝑎00 + 𝑎01 ∗ 𝑡 𝑏1 𝑡 = 𝑎10 + 𝑎11 ∗ 𝑡 • Drift from the residues in the calibration • Drift from the residues in the calibration is not taken into account • Fisher-Snédécor test x Standard Measurement Calibration Results x x x 𝒚 = 𝒃 𝟎 + 𝒃 𝟏 𝒙
  16. 16. • Uncertainty in the measurement process • How is the drift calculated? • New approach • Conclusion Conclusion Uncertainties for the instrument: • Calibration • Specifications • Drift • … New method • Behavior of the instrument in its full domain • Used for defining calibration periodicity • Mathematically more rigorous

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