1.
Evaluate and quantify the drift of a
measuring instrument
Jean-Michel POU (Deltamu), Laurent LEBLOND (PSA Groupe - France)
Speaker: Peggy COURTOIS (Deltamu)

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.
• 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.
• 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.
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.
• 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.
• 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.
• 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.
• 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.
• 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.
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.
• 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.
• 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.
• 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.
• 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.
• 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