The traceability to reference standards is a founding act in calibration laboratories. We show here that it is possible to know the value of the standards without calibrating them !!! And this example can be transposed to many other cases than gauge blocks. Even if it is difficult to accept the idea of no longer calibrating its references, it is easy to ensure their reliability, improve the management of their calibrations and, then, make better and cheaper!

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