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SMART METROLOGY
Management of reference
measurement standards as part of
Smart Metrology: Gauge BlocksParis – CIM 2017 – 19 September
Jean-Michel POU1, Laurent LEBLOND2, Christophe DUBOIS1
1 Deltamu, 48 Rue de Sarliève, 63800 Cournon d’Auvergne
2 PSA Group, C.T. de Vélizy A, 2, route de Gisy, 78943 Vélizy-Villacoublay Cedex
Contents
• Calibration chain
• Calibration method
• Measurement model analysis
• Discussion / Application of
measurements
• Experiment results
• Conclusion
Calibration chain
General Conference on Weights and
Measures (CGPM)
Definitions
International Bureau of Metrology
(IBWM)
Comparison key
National Metrology Laboratories
'Member and Associate Member States'
Traceability and Research
Accredited laboratories
Calibration and Verification
Users
Research, Industry & Consumers
Gauge blocks: Method
In accredited laboratories,
calibration of gauge blocks is
carried out by means of direct
comparison.
Difference in length between
the gauge being calibrated
and the reference gauge is
measured at a specific
calibration test bench.
Gauge blocks: Method
The laboratory reference
gauge is calibrated by
'direct interferometry',
which gives a very low
uncertainty level.
Figure 6 is taken from article R 1 245V2 – Techniques of the Engineer – José Antonio Salgado / LNE (With thanks for author's permission)
Table taken from COFRAC convention No. 2-35 Rev 3 (LNE / January 2016)
Gauge blocks: Method
The measurement model for an accredited laboratory
may be written as:
Where
𝐿𝑔𝑡ℎ 𝑃𝑜𝑖𝑛𝑡 = 𝐿𝑔𝑡ℎ 𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐺𝑎𝑢𝑔𝑒 + 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 =
𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒂𝒄𝑡𝑢𝒂𝒍 + 𝑒𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡0 + 𝑒𝑙𝑜𝑐𝑎𝑙 𝑏𝑖𝑎𝑠 + 𝑒∆𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 + 𝑒 𝑟𝑒𝑝𝑒𝑎𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦
+ 𝑒 𝑏𝑒𝑛𝑐h 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦 + 𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑑𝑟𝑖𝑓𝑡
Gauge blocks: Analysis
𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒂𝒄𝒕𝒖𝒂𝒍 :
actual deviation of length between reference gauge
and gauge being calibrated. The 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙 will
never be known perfectly, if only because the reference
gauge itself cannot be perfectly known. It is this
deviation that gives rise to the calibration uncertainty
that needs to be assessed for any given gauge.
Gauge blocks: Analysis
𝑫𝒊𝒔𝒄𝒖𝒔𝒔𝒊𝒐𝒏 𝒐𝒇 𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒂𝒄𝒕𝒖𝒂𝒍 :
• Manufacturers undoubtedly do their best to achieve
the given nominal value.
• Each gauge produced has its own error (nothing is
perfect) but, on average, 10 mm gauges should
measure 10 mm.
• If the average gauge does not exist, the average of
the deviations measured during calibration is
nevertheless calculable!
Gauge blocks: Analysis
𝒆 𝒔𝒆𝒕𝒑𝒐𝒊𝒏𝒕𝟎 :
error due to repeatability when setting test bench to
zero relative to reference gauge
𝒆𝒍𝒐𝒄𝒂𝒍 𝒃𝒊𝒂𝒔 :
bias of measurement system comprising two opposing
probes. It should be remembered that this local error is
of the order of a few nanometres as the gauges are of
equal nominal length (in general).
Gauge blocks: Analysis
𝒆∆𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆:
error due to actual temperature at time of
measurement (not automatically equal to 20°C).
The gauges are usually made of the same material,
which allows natural correction of a large part of the
deviation between the temperature at time of
measurement and the 20°C reference temperature,
since both gauges experience the same dilatation.
Gauge blocks: Analysis
𝒆 𝒓𝒆𝒑𝒆𝒂𝒕𝒂𝒃𝒊𝒍𝒊𝒕𝒚 :
error due to repeatability at time of measurement of
gauge being calibrated.
𝒆 𝒓𝒆𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒅𝒓𝒊𝒇𝒕 :
actual deviation between the reference gauge value at
time of calibration and the value at time of use.
Gauge blocks: Analysis
𝒆 𝒕𝑒𝒔𝑡 𝒃𝒆𝒏𝒄𝒉 𝒈𝒆𝒐𝒎𝒆𝒕𝒓𝒚 :
test bench geometry error, notably any parallelism
error between the position on the test bench of the
gauges relative to the measurement probes. If this
geometry problem does exist, of course, it only effects
the measured deviation, since both gauges are on the
same plate.
Gauge blocks: Discussion
The terms that constitute the deviation being
independent, the theoretical variance of the deviation
is equal to the sum of the theoretical variances, i.e.
measurement errors and manufacturing variance
(dispersal).
By averaging all the deviations, it becomes possible to
completely 'write off' the dispersal element
(measurement errors and manufacturing deviations)
Gauge blocks: Discussion
Therefore, under our
hypothesis, the deviation
average, estimated via the
arithmetic average of the
deviations obtained for the
gauges calibrated, should be
equal to the actual deviation
from the true value of the
reference gauge, the latter
being assumed to be stable.
Gauge blocks: Discussion
The test bench is set up via the reference gauge block.
If it is in reality lower than its nominal value, the
deviations measured will, on average, be positive.
Conversely, if it is higher than its nominal value, the
deviations measured will, on average, be negative.
Consequently, if we write 𝑥𝑖 as the value for the
deviation measured at ist calibration (ist gauge), we get:
𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙 = −
1
𝑛
𝑖=1
𝑛
𝑥𝑖
Gauge blocks: Discussion
Standard deviation of deviations measured, composed
of the variance of actual deviations and the sum of
variances of measurement errors, equals:
𝜎 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙
=
1
𝑛
𝑖=1
𝑛
(𝑥𝑖 − 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙)2
NB: 𝑛 is considered to be of sufficient magnitude in this
relation
Gauge blocks: Discussion
Since we have the deviation from nominal for each
reference gauge block and the associated uncertainties,
we can check our hypothesis. We shall consider, at the
risk 𝛼 = 5% of being wrong, that the averages are
statistically identical if
𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝐴𝑐𝑡𝑢𝑎𝑙 − 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑅𝑒𝑓 𝑔𝑎𝑢𝑔𝑒 𝑛𝑜𝑚𝑖𝑛𝑎𝑙
𝜎 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙
2
𝑛
+ 𝑢 𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛
2
≤ 2
Gauge blocks: Reliable
0
5
10
15
20
25
30
35
Pourcentage
-1 -,75 -,5 -,25 0 ,25 ,5 ,75 1 1,25 1,5
Ecart
0,125 0,368 80 -0,790 1,290
0,122 0,371 40 -0,790 1,260
0,128 0,370 40 -0,780 1,290
Moy. Dév. Std Nombre Minimum Maximum
Ecart, Total
Ecart, 1
Ecart, 6
Case study:
Number of
customer
gauges retained
Nominal
LNE
Deviation
uLNE*
Average
deviation
Standard
deviation
Deviation
(nm)
Ecart
(Nanomètre)
Comparison of
averages
Boite 1 Etalonnage 2 40 100 -0,083 0,018 -0,125 0,368 0,058 42 0,69
Gauge box
Gauge blocks: Reliable
Summary table of results obtained:
Number of
customer
gauges retained
Nominal
LNE
Deviation
uLNE*
Average
deviation
Standard
deviation
Deviation
(nm)
Ecart
(Nanomètre)
Comparison of
averages
Boite 1 Etalonnage 1 116 1 -0,047 0,010 -0,078 0,129 0,012 -59 3,77
Boite 1 Etalonnage 2 36 1 -0,039 0,010 -0,084 0,108 0,018 45 2,18
Boite 1 Etalonnage 1 112 5 -0,021 0,010 -0,011 0,116 0,011 -10 0,66
Boite 1 Etalonnage 2 37 5 -0,005 0,010 -0,009 0,131 0,022 4 0,17
Boite 1 Etalonnage 1 110 10 0,019 0,011 0,033 0,131 0,012 -14 0,85
Boite 1 Etalonnage 2 36 10 0,025 0,011 0,035 0,137 0,023 -10 0,40
Boite 1 Etalonnage 1 121 50 0,054 0,014 0,313 0,367 0,033 -259 7,18
Boite 1 Etalonnage 2 40 50 0,067 0,014 0,045 0,449 0,071 22 0,30
Boite 1 Etalonnage 1 120 100 -0,086 0,018 0,559 0,38 0,035 -645 16,60
Boite 1 Etalonnage 2 40 100 -0,083 0,018 -0,125 0,368 0,058 42 0,69
Boite 2 Etalonnage 1 111 1 0,044 0,010 0,020 0,126 0,012 24 1,53
Boite 2 Etalonnage 1 108 5 -0,013 0,010 -0,035 0,125 0,012 22 1,39
Boite 2 Etalonnage 1 104 10 0,043 0,011 0,084 0,138 0,014 -41 2,37
Boite 2 Etalonnage 1 116 50 -0,063 0,014 -0,005 0,292 0,027 -58 1,91
Boite 2 Etalonnage 1 119 100 0,347 0,018 0,536 0,417 0,038 -189 4,50
Gauge box
Gauge blocks: Reliable
Examination of an 'odd' case
-1,6
-1,4
-1,2
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
Analyse graphique
Ecart mesuré Moyenne LNE
Number of
customer
gauges retained
Nominal
LNE
Deviation
uLNE*
Average
deviation
Standard
deviation
Deviation
(nm)
Ecart
(Nanomètre)
Comparison of
averages
Boite 1 Etalonnage 1 120 100 -0,086 0,018 0,559 0,38 0,035 -645 16,60
Gauge box
Gauge blocks: Conclusion
In 80% of cases dealt with, our hypothesis seems to
be confirmed.
A few odd cases have not been able to be resolved
since we were dealing with old data. There is no
doubt that had the results been explored at the time,
the deviations would have been explained.
This approach gives calibration laboratories the power
to detect anomalies in their measurement standards.
In this way, they can be surer of their measurements
and, probably, lengthen periodicity
Centre d'affaires du Zénith,
48 Rue de Sarliève,
63800 Cournon d'Auvergne - France
+33 (0)473 151 300
jmpou@deltamu.com
www.smartmetrology.org

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Congrès International de Métrologie - Paris 2017

  • 1. SMART METROLOGY Management of reference measurement standards as part of Smart Metrology: Gauge BlocksParis – CIM 2017 – 19 September Jean-Michel POU1, Laurent LEBLOND2, Christophe DUBOIS1 1 Deltamu, 48 Rue de Sarliève, 63800 Cournon d’Auvergne 2 PSA Group, C.T. de Vélizy A, 2, route de Gisy, 78943 Vélizy-Villacoublay Cedex
  • 2. Contents • Calibration chain • Calibration method • Measurement model analysis • Discussion / Application of measurements • Experiment results • Conclusion
  • 3. Calibration chain General Conference on Weights and Measures (CGPM) Definitions International Bureau of Metrology (IBWM) Comparison key National Metrology Laboratories 'Member and Associate Member States' Traceability and Research Accredited laboratories Calibration and Verification Users Research, Industry & Consumers
  • 4. Gauge blocks: Method In accredited laboratories, calibration of gauge blocks is carried out by means of direct comparison. Difference in length between the gauge being calibrated and the reference gauge is measured at a specific calibration test bench.
  • 5. Gauge blocks: Method The laboratory reference gauge is calibrated by 'direct interferometry', which gives a very low uncertainty level. Figure 6 is taken from article R 1 245V2 – Techniques of the Engineer – José Antonio Salgado / LNE (With thanks for author's permission) Table taken from COFRAC convention No. 2-35 Rev 3 (LNE / January 2016)
  • 6. Gauge blocks: Method The measurement model for an accredited laboratory may be written as: Where 𝐿𝑔𝑡ℎ 𝑃𝑜𝑖𝑛𝑡 = 𝐿𝑔𝑡ℎ 𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐺𝑎𝑢𝑔𝑒 + 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 = 𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒂𝒄𝑡𝑢𝒂𝒍 + 𝑒𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡0 + 𝑒𝑙𝑜𝑐𝑎𝑙 𝑏𝑖𝑎𝑠 + 𝑒∆𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 + 𝑒 𝑟𝑒𝑝𝑒𝑎𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 + 𝑒 𝑏𝑒𝑛𝑐h 𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦 + 𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑑𝑟𝑖𝑓𝑡
  • 7. Gauge blocks: Analysis 𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒂𝒄𝒕𝒖𝒂𝒍 : actual deviation of length between reference gauge and gauge being calibrated. The 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙 will never be known perfectly, if only because the reference gauge itself cannot be perfectly known. It is this deviation that gives rise to the calibration uncertainty that needs to be assessed for any given gauge.
  • 8. Gauge blocks: Analysis 𝑫𝒊𝒔𝒄𝒖𝒔𝒔𝒊𝒐𝒏 𝒐𝒇 𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒂𝒄𝒕𝒖𝒂𝒍 : • Manufacturers undoubtedly do their best to achieve the given nominal value. • Each gauge produced has its own error (nothing is perfect) but, on average, 10 mm gauges should measure 10 mm. • If the average gauge does not exist, the average of the deviations measured during calibration is nevertheless calculable!
  • 9. Gauge blocks: Analysis 𝒆 𝒔𝒆𝒕𝒑𝒐𝒊𝒏𝒕𝟎 : error due to repeatability when setting test bench to zero relative to reference gauge 𝒆𝒍𝒐𝒄𝒂𝒍 𝒃𝒊𝒂𝒔 : bias of measurement system comprising two opposing probes. It should be remembered that this local error is of the order of a few nanometres as the gauges are of equal nominal length (in general).
  • 10. Gauge blocks: Analysis 𝒆∆𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆: error due to actual temperature at time of measurement (not automatically equal to 20°C). The gauges are usually made of the same material, which allows natural correction of a large part of the deviation between the temperature at time of measurement and the 20°C reference temperature, since both gauges experience the same dilatation.
  • 11. Gauge blocks: Analysis 𝒆 𝒓𝒆𝒑𝒆𝒂𝒕𝒂𝒃𝒊𝒍𝒊𝒕𝒚 : error due to repeatability at time of measurement of gauge being calibrated. 𝒆 𝒓𝒆𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒅𝒓𝒊𝒇𝒕 : actual deviation between the reference gauge value at time of calibration and the value at time of use.
  • 12. Gauge blocks: Analysis 𝒆 𝒕𝑒𝒔𝑡 𝒃𝒆𝒏𝒄𝒉 𝒈𝒆𝒐𝒎𝒆𝒕𝒓𝒚 : test bench geometry error, notably any parallelism error between the position on the test bench of the gauges relative to the measurement probes. If this geometry problem does exist, of course, it only effects the measured deviation, since both gauges are on the same plate.
  • 13. Gauge blocks: Discussion The terms that constitute the deviation being independent, the theoretical variance of the deviation is equal to the sum of the theoretical variances, i.e. measurement errors and manufacturing variance (dispersal). By averaging all the deviations, it becomes possible to completely 'write off' the dispersal element (measurement errors and manufacturing deviations)
  • 14. Gauge blocks: Discussion Therefore, under our hypothesis, the deviation average, estimated via the arithmetic average of the deviations obtained for the gauges calibrated, should be equal to the actual deviation from the true value of the reference gauge, the latter being assumed to be stable.
  • 15. Gauge blocks: Discussion The test bench is set up via the reference gauge block. If it is in reality lower than its nominal value, the deviations measured will, on average, be positive. Conversely, if it is higher than its nominal value, the deviations measured will, on average, be negative. Consequently, if we write 𝑥𝑖 as the value for the deviation measured at ist calibration (ist gauge), we get: 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙 = − 1 𝑛 𝑖=1 𝑛 𝑥𝑖
  • 16. Gauge blocks: Discussion Standard deviation of deviations measured, composed of the variance of actual deviations and the sum of variances of measurement errors, equals: 𝜎 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙 = 1 𝑛 𝑖=1 𝑛 (𝑥𝑖 − 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙)2 NB: 𝑛 is considered to be of sufficient magnitude in this relation
  • 17. Gauge blocks: Discussion Since we have the deviation from nominal for each reference gauge block and the associated uncertainties, we can check our hypothesis. We shall consider, at the risk 𝛼 = 5% of being wrong, that the averages are statistically identical if 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝐴𝑐𝑡𝑢𝑎𝑙 − 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑅𝑒𝑓 𝑔𝑎𝑢𝑔𝑒 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝜎 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙 2 𝑛 + 𝑢 𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 2 ≤ 2
  • 18. Gauge blocks: Reliable 0 5 10 15 20 25 30 35 Pourcentage -1 -,75 -,5 -,25 0 ,25 ,5 ,75 1 1,25 1,5 Ecart 0,125 0,368 80 -0,790 1,290 0,122 0,371 40 -0,790 1,260 0,128 0,370 40 -0,780 1,290 Moy. Dév. Std Nombre Minimum Maximum Ecart, Total Ecart, 1 Ecart, 6 Case study: Number of customer gauges retained Nominal LNE Deviation uLNE* Average deviation Standard deviation Deviation (nm) Ecart (Nanomètre) Comparison of averages Boite 1 Etalonnage 2 40 100 -0,083 0,018 -0,125 0,368 0,058 42 0,69 Gauge box
  • 19. Gauge blocks: Reliable Summary table of results obtained: Number of customer gauges retained Nominal LNE Deviation uLNE* Average deviation Standard deviation Deviation (nm) Ecart (Nanomètre) Comparison of averages Boite 1 Etalonnage 1 116 1 -0,047 0,010 -0,078 0,129 0,012 -59 3,77 Boite 1 Etalonnage 2 36 1 -0,039 0,010 -0,084 0,108 0,018 45 2,18 Boite 1 Etalonnage 1 112 5 -0,021 0,010 -0,011 0,116 0,011 -10 0,66 Boite 1 Etalonnage 2 37 5 -0,005 0,010 -0,009 0,131 0,022 4 0,17 Boite 1 Etalonnage 1 110 10 0,019 0,011 0,033 0,131 0,012 -14 0,85 Boite 1 Etalonnage 2 36 10 0,025 0,011 0,035 0,137 0,023 -10 0,40 Boite 1 Etalonnage 1 121 50 0,054 0,014 0,313 0,367 0,033 -259 7,18 Boite 1 Etalonnage 2 40 50 0,067 0,014 0,045 0,449 0,071 22 0,30 Boite 1 Etalonnage 1 120 100 -0,086 0,018 0,559 0,38 0,035 -645 16,60 Boite 1 Etalonnage 2 40 100 -0,083 0,018 -0,125 0,368 0,058 42 0,69 Boite 2 Etalonnage 1 111 1 0,044 0,010 0,020 0,126 0,012 24 1,53 Boite 2 Etalonnage 1 108 5 -0,013 0,010 -0,035 0,125 0,012 22 1,39 Boite 2 Etalonnage 1 104 10 0,043 0,011 0,084 0,138 0,014 -41 2,37 Boite 2 Etalonnage 1 116 50 -0,063 0,014 -0,005 0,292 0,027 -58 1,91 Boite 2 Etalonnage 1 119 100 0,347 0,018 0,536 0,417 0,038 -189 4,50 Gauge box
  • 20. Gauge blocks: Reliable Examination of an 'odd' case -1,6 -1,4 -1,2 -1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 Analyse graphique Ecart mesuré Moyenne LNE Number of customer gauges retained Nominal LNE Deviation uLNE* Average deviation Standard deviation Deviation (nm) Ecart (Nanomètre) Comparison of averages Boite 1 Etalonnage 1 120 100 -0,086 0,018 0,559 0,38 0,035 -645 16,60 Gauge box
  • 21. Gauge blocks: Conclusion In 80% of cases dealt with, our hypothesis seems to be confirmed. A few odd cases have not been able to be resolved since we were dealing with old data. There is no doubt that had the results been explored at the time, the deviations would have been explained. This approach gives calibration laboratories the power to detect anomalies in their measurement standards. In this way, they can be surer of their measurements and, probably, lengthen periodicity
  • 22. Centre d'affaires du Zénith, 48 Rue de Sarliève, 63800 Cournon d'Auvergne - France +33 (0)473 151 300 jmpou@deltamu.com www.smartmetrology.org