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Centro Nacional de Metrología
SIM Regional Key Comparison SIM.L-K1.2007 Calibration of Gauge Blocks by Optical Interferometry
FINAL REPORT
JULY 2012
Colín C. Viliesid M. Chaudhary K. P. Decker J. Dvořáček F. Franca R. Ilieff S. Rodríguez J. Stoup J.
CENAM, Centro Nacional de Metrología CENAM, Centro Nacional de Metrología NPLI, National Physical Laboratory INDIA NRC-CNRC, National Research Council Canada CMI, Czech Metrology Institute INMETRO, Instituto Nacional de Metrología INTI, Instituto Nacional de Tecnología Industrial CEM, Centro Español de Metrología NIST, National Institute of Standards and Technology
Centro Nacional de Metrología (CENAM) km 4.5 Carretera a Los Cués, El Marqués, Querétaro 76246, MEXICO
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Contents
SIM Regional Key Comparison SIM.L-K1.2007.................................................................. 1 Calibration of Gauge Blocks by Optical Interferometry....................................................... 1 1. Introduction.................................................................................................................. 3 2. Participants..................................................................................................................4 3. Circulation Schedule....................................................................................................5 4. Comparison Artifacts ...................................................................................................5 5. Measurement Protocol ................................................................................................6 6. Measuring Instruments ................................................................................................ 6 7. State and Behavior of Artifacts .................................................................................... 6
7. 1 State of the Artifacts upon Reception................................................................... 6 7. 2 Stability of the Standards ..................................................................................... 8 8. Measurement Results of Participants........................................................................ 11 8.1 Measurement of the Central Length................................................................... 11 8.2 Measurement Difference of Length between the Two Measuring Faces ........... 15 8.3 Phase-change Correction................................................................................... 16 9. Analysis Method ........................................................................................................16 9.1 Key Comparison Reference Value (KCRV) Determination ................................ 16 9.2 Criteria to Determine the Largest Sub-set of “Consistent” Results to Compute the KCRV ......................................................................................................................16 9.3 KCRV Uncertainty ..............................................................................................17 10. Results of the Comparison..................................................................................... 19 10.1 KCRV Determination .......................................................................................... 19 10.2 Participants Results............................................................................................20 11. Discussion and Conclusions .................................................................................. 22 11.1 Discussion .......................................................................................................... 22 11.2 Conclusions........................................................................................................ 22 12. Acknowledgements................................................................................................ 23 13. References.............................................................................................................31 Annex A Elimination of Inconsistent Results ............................................................. 32 Annex B Calculation of Alternate Statistical Parameters. .......................................... 38 Annex C Correspondence with Participants. ............................................................. 40 C.1 Correspondence with NMISA. ............................................................................ 40 C.2 Correspondence with CMI.................................................................................. 40 Annex D Analysis of Results considering CMI correction. ......................................... 41 Annex E Phase Change Correction Determination by the Stack Method.................. 43
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1. Introduction
The Mutual Recognition Arrangement (MRA) of the Conférence Internationale des Poids et Mesures (CIPM) signed by the National Metrology Institutes (NMI) of different nations provides mutual recognition among the NMI of their national standards and their calibration services. A database has been set up by the Bureau Interantional des Poids et Mesures (BIPM) at its website where the Calibration and Measurement Capabilities (CMC) of each NMI are posted. To support the CMC claims of the NMI, the MRA requires, among other things, that they participate, on a regular basis, in Key Comparisons (KC) that test key measuring techniques. This would prove their technical competence, that they can provide this calibration service with the claimed uncertainty of the corresponding CMC and that they have metrological equivalence with the other signatory NMI that provide the same calibration service.
KC should take place at the highest level amongst the members of the corresponding Consultative Committee (CC), in this case the Consultative Committee for Length (CCL). Similar regional KC should also be organized in every region with at least a few NMI from the region participating in the regional comparison as well as in the CCL KC.
The CIPM has also instructed the different CC to identify key techniques in order to define KC. The calibration of Gauge Blocks (GB) by optical inteferometry has been identified as a key measuring technique by the Consultative Committee for Length (CCL). In one hand it requires good technical expertise and skills, the use of sophisticated equipment and stringent laboratory conditions; but in the other hand it is an unavoidable step in the dissemination of the length unit and therefore it is of paramount importance. These KC have been designated as K1 comparisons.
Both levels of comparisons should be organized regularly in time at a frequency established by each CC. The present comparison, SIM.L-K1.2007, is the second K1 comparison organized by SIM region since the signature of the MRA. It is intended to support and maintain the posted CMC of the NMI of the Americas that offer GB calibration by optical interferometry on the database, and, eventually, any other calibration services that stems out of this key technique.
The mesurand is the central length of the GB as defined in [1]. Additionally, for those laboratories willing to participate, a Pilot Study on the Optical Phase Change Correction on the Reflection of Light has been organized along with SIM.L-K1.2007 using the same GB and a set of platens that were circulated along with the GB. The results will be part of a separate Pilot Study report and are not part of this comparison.
The optical interferometry measurement of the GB is a first stage of the circulation of these GB. A second stage has been organized to measure them by mechanical comparison. The circulation of this second stage has just ended and, therefore, we can now disclose the results contained in this report.
The comparison had nine participants, five from the Americas, and four invited ones from other regions. The circulation took more than two years, from November 2007 until March 2010. The exercise was quite delayed as the allocated time periods could not be respected at several points.
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2. Participants
A total of nine NMI participated in this comparison that circulated 14 GB of different lengths and materials. The following table lists the information on the participating NMI.
Contact Joaquín Rodríguez González, Emilio Prieto Esteban Carlos Colín Castellanos, Miguel Viliesid Alonso Ing. Vladimir Stezka Ing. František Dvořáček Hakima Belaïdi Ricardo dos Santos França
Sergio Nicolás Ilieff, Carina Bastida
John Stoup
Sam Thema
K. P. Chaudhary
Jennifer Decker1, Pierre Dubé
NMI CEM, Centro Español de Metrología Alfar, 2. Tres Cantos 28760 Madrid, España
CENAM, Centro Nacional de Metrología km 4.5 Carretera a los Cués, El Marqués CP 76241, Querétaro, MEXICO
CMI, Czech Metrology Institute Slunecna 23 460 01 Liberec Czech Republic INMETRO, Instituto Nacional de Metrologia, Normalização e Qualidade Industrial. Av. N.Sra. das Graças, 50 – Villa Operária – Xerém – Duque de Caixas – RJ. CEP 25250-020 Brasil INTI, Instituto Nacional de Tecnología Industrial FISICA Y METROLOGÍA; Laboratorio de Óptica y Dimensional. Av. Gral. Paz 5445 – CC 157 – B1650WAB – San Martín, Bs.As.; Argentina. NIST, National Institute of Standards and Technology Room B113, Metrology Building Gaithersburg, MD 20899-0001 USA NMISA, National Metrology Institute of South Africa Private Bag X34 Lynnwood Ridge 0040 South Africa NPLI, National Physical Laboratory INDIA Dr. K,S. Krishnan Road, New Delhi 110012, India
National Research Council Canada Measurement Science and Standards Portfolio 1200 Montreal Road Campus Bldg M-36 Ottawa, Ontario, CANADA K1A 0R6
Information Tel. +34 91 8074 796 / 801 Fax +34 91 8074 807 e-mail: jrgonzalez@cem.minetur.es ; eprieto@cem.minetur.es Tel. +52 442 211 0500 Fax +52 442 211 0577 e-mail: ccolin@cenam.mx ; miguel.viliesid@cenam.mx. Tel. +42 485 107 532 Fax +42 485 104 466 e-mail: vstezka@cmi.cz
fdvoracek@cmi.cz Tel. +55 21 2679-9271 Fax +55 21 2679-9207 e-mail: hbelaidi@inmetro.go.br rsfranca@inmetro.gov.br
Tel. +54 11 47246200 Fax +54 11 47134140 e-mail: serlieff@inti.gov.ar ; bastida@inti.gob.ar
Tel. +1 301 975 3476 Fax + 1 301 869 0822 e-mail: John.Stoup@nist.gov
Tel. +27 12 841 4798 Fax +27 12 841 2131 e-mail: SThema@nmisa.org
Tel. +91 11 25732865 Fax +91 11 25726938 e-mail: kpc@mail.nplindia.ernet.in Tel. +1.613.991.1633 Fax +1.613.952.1394 e-mail: jennifer.decker@nrccnrc.gc.ca ; pierre.dubé@nrccnrc.gc.ca.
Table 1. List of participants in comparison SIM.L-K1.2007.
1 Formerly: Institute for National Measurement Standards (INMS); update contact: Pierre Dube pierre.dube@nrc-cnrc.gc.ca
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3. Circulation Schedule
The circulation of the artifacts was very delayed mainly due to customs clearance delays in several countries. A circulation time of 14 months was initially scheduled and it took 30 months, more than the double of the initial scheduled time. Table 2 shows the actual dates of reception and shipment of the artifacts by the participants as well as the date of reception of the participant’s results by the pilot laboratory.
NMI
CENAM (Pilot) CEM NPLI CMI NMISA
NRC-INMS NIST
INMETRO INTI
CENAM (Pilot)
Reception
2007-11-23 2008-03-02 2008-06-16 2008-09-10 2008-12-04 2009-04-20 2009-08-11 2009-11-13 2010-03-02
Dates
Shipment
2007-11-01 2008-01-14 2008-06-09 2008-08-05 2008-11-27 2009-04-17 2009-07-15 2009-09-08 2010-01-11
Reception of Results
2007-11-10 2008-09-01 2009-08-07 2008-10-17 Did not send-in results 2009-08-25 2010-03-02 2009-09-21 2010-01-11 2010-04-25
Table 2. SIM.L-K1.2007 dates of reception and shipment of artifacts and reception of results by the pilot lab.
4. Comparison Artifacts
A total of 14 grade K (according to [1]) rectangular GB were selected for the exercise. Seven steel GB and seven ceramics GB covering the range of short GB (from 0.5 mm to 100 mm). The specifications on the GB are shown in tables 3 and 4. The associated Coefficients of Thermal Expansion (CET) shown in the tables are those quoted by the manufacturers.
Nominal Length (mm) 1.000 5
5 7 10 50 75
100
Serial Number
010223 000482 010764 001329 012254 010630 010850
Coefficient of Thermal Expansion ( 10-6 K-1 )
10.9 1 10.9 ± 1 10.9 1 10.9 ± 1 10.9 1 10.9 1 10.9 1
Manufacturer
Mitutoyo Mitutoyo Mitutoyo Mitutoyo Mitutoyo Mitutoyo Mitutoyo
Table 3. Steel Gauge Blocks.
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Nominal Length (mm) 1.000 5 5 7 10 50 75 100
Serial Number
000288 051836 010323 052351 011002 010370 010773
Coefficient of Thermal Expansion ( 10-6 K-1 )
9.3 1 9.3 1 9.3 1 9.3 1 9.3 1 9.3 1 9.3 1
Manufacturer
Mitutoyo Mitutoyo Mitutoyo Mitutoyo Mitutoyo Mitutoyo Mitutoyo
Table 4. Ceramics Gauge Blocks.
5. Measurement Protocol
Detailed Measurement Instructions were included in the Comparison Protocol. The GB were supposed to be measured wrung to the platens or optical flats that the participant laboratories currently use to offer their gauge block calibration service.
Gauge block calibration by optical interferometry should be performed with the GB in vertical position wrung to a platen as indicated in [1]. The gauge block central length, lc, is the perpendicular distance between the central point of the free measurement surface of the gauge block and the surface where it is wrung.
The values asked to be reported in the protocol were the deviations from nominal length (ln) determined at the center for each measuring face “A” and “B”, ecX = lc – ln, (where X = “A” or “B”); the average of both values, eavg; the so called phase change correction, l; and the corrected average deviation after applying the phase change correction, ec.
The method most commonly used to determine the phase change correction, l is the stack method and it is described in Annex E.
6. Measuring Instruments
All participant laboratories measured the GB by optical absolute interferometry applying the method of exact fractions. The systems used, traceability, light sources and laboratory temperature variations of the participants are listed in table 5.
7. State and Behavior of Artifacts
7. 1 State of the Artifacts upon Reception
The participants were to inspect the state of the artifacts upon reception and inform the pilot according to the protocol. Although the selected GB were not new, they were in good conditions for measurement. A few of the steel GB suffered some damage after the circulation, but the results obtained in the comparison prove that the damages did not hamper or alter the measurements; and the pilot laboratory was able to wring them all to a platen at the end of the circulation. Figures 1 through 4 show the physical conditions of
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some of the damaged GB upon reception by the pilot laboratory at the end of the circulation.
NMI
Manufacturer and Type of Interferometer
Light sources and
wavelengths used
CEM
NPL-TESA, TwymanGreen
He-Ne 633 nm TESA laser,
He-Ne 543 nm TESA laser,
CENAM
NPL-TESA, TwymanGreen
He-Ne 633 nm TESA laser,
He-Ne 543 nm TESA laser,
CMI INMETRO
INTI NIST
NPL-TESA, TwymanGreen
Jena Zeiss Michelson/Twy man-Green
NPL-TESA, TwymanGreen
Hilger
He-Ne 633 nm TESA laser, He-Ne 543 nm TESA laser,
Double cathode 114Cd spectral lamp
He-Ne 633 nm TESA laser, He-Ne 543 nm TESA laser,
He-NE 633 nm Spectra Physics laser,
Traceability
To the Spanish realization of the metre: A 633 nm Iodinestabilized laser; and to a UK 543 nm Iodinestabilized laser. To the Mexican realization of the metre: A 633 nm Iodinestabilized laser (CNMPNM-2) To the Czech National Standard of Length (HeNe/I2 633nm, He-Ne/I2 543.5nm, fs comb)
To SI standards of INMETRO
Temperature variation range
during measurements
(°C)
19.891 – 20.156
19.95 – 20.15
19.640 – 20.198
19.92 – 20.36
To SI standards of INTI Not specified
NIST maintained IodineStabilized Laser
20.028 – 20.035
NMISA -----
------
-------
-----
NPLI
NPL-TESA, TwymanGreen
NRC-INMS
NRC-INMS own design, TwymanGreen
He-Ne 633 nm TESA laser,
He-Ne 543 nm TESA laser,
He-Ne 633 nm COHERENT laser,
He-Ne 612 nm TESA laser,
He-Ne 543 nm TESA laser,
He –Ne 1 152 nm laser,
Not specified
19.6 – 20.3
The 633 nm is traceable to an IodineStabilized laser. The other wavelengths are traceable to the primary time and frequency standard of Canada.
19.986 – 20.019 for steel 19.971 – 20.020 for ceramics
Table 5. GB interferometers, laser sources, traceability and temperature variation of the participant laboratories.
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Problems on some GB were reported by two participant NMI:
CEM from Spain. o The Ceramics 100 mm GB (serial no. 010773) presented wringing problems, but they were able to submit measurement results. o The case where the GB were packed was received with damages that were apparently suffered during transportation between Mexico and Spain.
INMETRO from Brazil. o Reports having had difficulties in wringing some GB due to damage on the measuring faces, but they were also able to provide measurement results.
Figures 1 and 2. Physical condition of the 1.000 5 mm GB and the 10 mm GB after circulation. Notice the scratches and spots on the measuring faces.
Figures 3 and 4. Physical condition of the 5 mm GB and the 100 mm GB after circulation. Notice the scratches and spots on the measuring face of the first one; and
indentations and scratches in second one.
7. 2 Stability of the Standards
The GB were measured several times by the pilot laboratory to verify their stability: when they were purchased (2002), two years before starting the comparison (Nov. 2005),
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before circulating them (Nov. 2007) and at the end of the circulation (April 2010). Table 6 shows the deviations from nominal length determined at these different occasions for the steel GB, including the stated values on the certificates of the manufacturer. Graphs 1 through 7 show these values for each GB along with the corresponding standard uncertainty bars.
Serial Number
010223 000482 010764 001329 012254 010630 010850
Nominal Length (mm)
1.000 5 5 7 10 50 75
100
Deviation from nominal value (nm)
Manufacturer
certificate
2002
2005
2007
2001
0
5
3
-4
40
14
11
35
30
19
13
-5
50
31
22
37
60
46
3
7
-50
-54
-104
-100
20
18
-50
-51
2010
-9 20 1 21 -3 -107 -64
Table 6. Pilot Laboratory measured values of the steel GB at different occasions.
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Table 7 shows the deviations from nominal length determined at these different occasions for the ceramics GB, including the stated values on the certificates of the manufacturer. Graphs 8 through 14 show these values for each GB with its standard uncertainty bars.
Serial Number
000288 051836 010323 052351 011002 010370 010773
Nominal Length (mm)
1.000 5 5 7 10 50 75
100
Manufacturer certificate 2001
0 ---50 ---90 100 -60
Deviation from nominal value (nm)
Manufacturer
2002
certificate
2007
2005
-6
----
-14
----
13
12
46
----
57
----
3
-13
95
----
139
110
----
118
-42
----
-34
2010
7 8 48 -19 117 124 -36
Table 7. Pilot Laboratory measured values of the ceramics GB in different occasions.
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8. Measurement Results of Participants
All laboratories sent their results by e-mail. NRC-INMS sent them by parcel service as well. All information was received on the specified formats from appendices A, B, C, D and E of the Technical Protocol.
8.1 Measurement of the Central Length
Tables 8 and 9 and graphs 16 through 22, show the deviations of the central length with respect to nominal values and the claimed standard measurement uncertainties of each participant for the seven steel GB; and graph 15 show the claimed standard uncertainties of the participants.
Nominal Value mm
1.000 5 5 7 10 50 75
100
Deviation from nominal length for Steel GB nm
CEM NPLI CMI NRC NIST INMETRO INTI
-10.5
-15
20.5
-18
-1
14
-13
16.5
18
60
25
41
48
13
-1.5
-12
37.5
-3
4
24
-14
28
56
62.5
26
44
37
23
-29.5
22
29.5
11
13
-10
-14
-156
25
-39
-95
-100
-114
-119
-103
-28
-8
-35
-41
-58
-49
Table 8. Measurement results of the participants for the Steel GB.
CENAM
-4 35 -5 37 7 -100 -51
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Nominal Value mm
1.000 5 5 7 10 50 75
100
Claimed standard uncertainties for Steel GB nm
CEM NPLI CMI NRC NIST INMETRO INTI
9.4
11
9.4
15
9
8
11
9.5
12
9.4
15
9.4
9
11
9.5
12
9.4
15
9.5
9
11
9.6
13
9.5
15
9.8
9
11
11.9
16
10.9
25
13.5
16
16
14.4
23
12.5
16
15.7
22
21
17.3
26
14.5
16
18
28
27
Table 9. Claimed standard uncertainties of the participants for Steel GB.
CENAM
9.6 9.6 9.7 9.8 14.8 19.4 24.5
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Tables 10 and 11 and graphs 24 through 30, show the deviations of the central length with respect to nominal values and their claimed standard measurement uncertainties of each participant for the seven ceramics GB; and graph 23 show the claimed standard uncertainties of the participants.
Nominal Value mm
1.000 5 5 7 10 50 75
100
Deviation from nominal length for Ceramics GB nm
CEM
2 16 44 -19 94 98.5 -50
NPLI
4 11 60 -14 147 156 28
CMI
-1 9 53.5 -18.5 114.5 140.5 2
NRC
11 16 66 -1 130 151 2
NIST
-5 14 54 -11 109 138 -16
INMETRO
-6 6 43 -19 92 124 -45
INTI
-22 1 36 -19 96 126 -21
Table 10. Measurement results of the participants for Ceramics GB.
CENAM
-14 12 57 -13 139 118 -34
Nominal Value
Claimed standard uncertainties for Ceramics GB nm
mm
CEM NPLI CMI NRC NIST INMETRO INTI CENAM
1.000 5
9.4
11
9.4
15
9
11
11
11.1
5
9.5
12
9.4
15
9.4
11
11
11.1
7
9.5
12
9.4
15
9.5
11
11
11.1
10
9.5
13
9.5
15
9.8
12
11
11.2
50
11.6
16
10.9
15
13.5
16
15
15.3
75
13.8
23
12.5
16
15.7
21
19
19.3
100
16.5
26
14.5
16
18
26
26
23.8
Table 11. Claimed standard uncertainties of the participants for Ceramics GB.
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8.2 Measurement Difference of Length between the Two Measuring Faces
The protocol also asked to report the length measured on each of the measuring faces. Any difference is probably due to the quality of the wringing surfaces of the GB; the quality of the auxiliary wringing surface and the ability of the technician. Graphs 31 and 32 show the absolute values of these differences for the participants on every GB.
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8.3 Phase-change Correction.
All participating laboratories applied the stack method to determine the phase-change correction for both materials except NIST. The latter laboratory assigns a value to each material and manufacturer of the GB according to a study they conducted in the 1990’s using their reference platens [3]. Table 12 summarizes the kind of platens the participants used and the phase-change correction values they submitted.
Participant
CEM NPLI CMI2 NRC NIST
INMETRO
INTI CENAM
Steel Gauge Blocks
Platen material
Phase-change correction (nm)
Ceramics Gauge Blocks
Platen material
Phase-change correction (nm)
Steel B6(08/05A)
-38.1
Ceramics (TESA-111)
-4.9
Steel (Id. 2)
-29
Steel (Id. 2)
-19
Steel (Id. 4)
+12 (-12)
Steel (Id. 4)
-10
Fused Silica Id. Zygo
+50
Fused Silica Id. Zygo
+53
See [3]
+28.9
See [3]
+16.5
Quartz (17/19/18/14/15/18/11)
+51
Quartz (15/16/11/12/18)
+12
Steel (TESA-83)
-24
Steel (TESA-82)
-21
Steel (TESA-86)
-19
Steel (TESA-86)
-16
Table 12. Phase-change correction of participants.
9. Analysis Method
9.1 Key Comparison Reference Value (KCRV) Determination
All usual parameters of the central tendency were calculated: the median, the simple mean and the inverse-variance weighted mean. All of these values appear on Annex B. However, the simple mean seemed the appropriate parameter to define the KCRV as all participants use the same calibration technique and state uncertainties that do not vary over a wide range.
9.2 Criteria to Determine the Largest Sub-set of “Consistent” Results to Compute the KCRV
The KCRV is determined, for each GB j, as the simple mean of the largest subset of mj participants which had “consistent” results3:
(1)
2 CMI informed that they made a mistake on the phase change correction after they received DRAFT A. Their corrected value is indicated in parenthesis. 3 Consistency is quoted because it is not checked in a rigorous statistical way but rather by the parameters that are described herein.
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Where:
eij
is the deviation from nominal value of participant i, i=
1,2,…,m on GB j
mj is the number of consistent results of the participants, mj n, where n is the total number of participants that measured
GB j
The number of participants in this comparison is n = 84.
Two parameters are considered in the elimination process of inconsistent results on GB j:
dij The absolute deviation from the mean of participant i on GB j; and ENij The Normalized error of participant i on GB j defined as
(2)
Where
is the Expanded Uncertainty of deviation dij, computed as:
(3) If laboratory i is taken in account in the calculation of the reference value; or
(4)
If laboratory i has been eliminated from the calculation of the reference value.
If ENij > 1 it is considered that the result is not consistent.
To establish the largest subset of laboratories that had consistent results, an iterative elimination process of outliers was applied for each GB j. To start, all participants are considered into the calculation of the simple mean and the corresponding Normalized Errors are computed. Then the data are ordered according to their deviations dij from largest to smallest along with their corresponding ENij values. If the first participant on the list, with the largest deviation also has an EN > 1, it is eliminated, m = n – 1 and the process is reiterated. The mean is recalculated and the remaining results are ordered according to their dij and along with their respective ENij. The process is repeated until no EN values greater than 1 are found. It is important to note that the largest values of dij do not necessarily correspond to the largest values of EN because the latter also depend on the declared uncertainty of the participant; although in most of cases they do. Figure 5 shows the block diagram of the elimination process applied on each GB j.
9.3 KCRV Uncertainty
4 CENAM, the pilot laboratory, contributes to the computation of the reference value only once with its first measurement.
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The standard uncertainty corresponding to the reference value of GB j is given by the
combined standard uncertainty of the simple mean, or internal uncertainty, of the mj consistent results:
where mj n
(5)
Figure 5. Flow chart showing the elimination process of inconsistent results for each GB j.
This value is used to calculate .
in equation (4) in the previous section:
1.1 Consistency of the Results taken into the KCRV Calculation
The standard deviation of the simple mean, by:
, or external uncertainty, of GB j is given
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where mj n (6)
If the measurement results and their uncertainties are consistent, the external uncertainty should be smaller or equal to the internal uncertainty. This is tested by means of the Birge Ratio defined as:
where RB 1 for consistent results.
(7)
10. Results of the Comparison
10.1 KCRV Determination
The Reference Values, , their Expanded Uncertainties,
, as well as the number of
participants that contributed to the calculation, , for the different GB j of both materials are shown in Table 13.
Nominal
Length 1.005
5 7 10 50 75 100
Reference Values
Ref. Value,
Steel
Ref. Value,
Ceramics
-10.3
9.0 6
-3.9
7.8 8
24.8
9.2 6
10.6
7.9 8
-5.3
9.2 6
51.7
7.9 8
35.9
8.5 7
-14.3
8.1 8
4.8
14.1 6
105.9
11.3 6
-105.6
17.0 5
136.2
13.9 7
-43.7
19.3 6
-23.1
15.6 7
Table 13. Reference values (simple mean of largest sub-set of “consistent” results) deviations from Nominal Value with Expanded Uncertainty and number of values contributing to the calculation of the Reference Value Computation (mj) for both steel and ceramics GB.
The elimination process of outliers is shown for each GB j in Annex A.
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10.2 Participants Results.
Tables 14 and 15 show the differences of the results of the participants with respect to the Reference Values of each GB j, dij ; along with the Expanded Uncertainty of these differences, U(dij); and the corresponding Normalized Error, ENij.
NMI (i→) Nom L (j↓)
1.000 5
5 7 10
50 75
100
CEM
CENAM
CMI
INMETRO
dij
U(dij)
ENij
dij
U(dij)
ENij
dij
U(dij)
ENij
dij
U(dij)
-0.3 18.8
0.0
6.3 19.2
0.3 30.8 18.8
1.5 24.3 16.0
-8.3 19.0
0.5 10.3 19.2
0.6 35.3 18.8
1.7 23.3 18.0
3.8 19.0
0.2
0.3 19.4
0.0 42.8 18.8
2.0 29.3 18.0
-7.9 19.2
0.4
1.1 19.6
0.1 26.6 19.0
1.3
1.1 18.0
-34.3 23.8
1.2
2.2 29.6
0.1 24.7 21.8
0.9 -14.8 32.0
-50.4 28.8
1.6
5.6 38.8
0.2 66.6 25.0
2.3 -8.4 44.0
-59.3 34.6
1.5 -7.3 49.0
0.2 35.7 29.0
1.0 -14.3 56.0
Table 14 A. Deviation from reference value for each GB, dij; claimed expanded uncertainty (k=2),
Uij; and Normalized Error ENij of the Steel GB for the first four participants.
ENij 1.3 1.2 1.4 0.1 0.5 0.2
0.3
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NMI (i→) Nom L (j↓)
1.000 5
5 7 10
50 75
100
INTI
dij -2.8 -11.8 -8.8 -12.9 -18.8 -13.4 -5.3
U(dij) 22.0 22.0 22.0 22.0 32.0 42.0 54.0
ENij 0.1 0.6 0.4 0.6 0.6 0.4 0.1
NIST
dij 9.3
16.3 9.3 8.1 8.2 5.6 2.7
U(dij) 18.0 18.8 19.0 19.6 27.0 31.4 36.0
ENij 0.5 0.9 0.5 0.4 0.3 0.2 0.1
NPLI
dij -4.8 -6.8 -6.8 20.1 17.2 130.6 15.7
U(dij) 22.0 24.0 24.0 26.0 32.0 46.0 52.0
ENij 0.2 0.3 0.3 0.9 0.6 2.7 0.3
NRC
dij -7.8 0.3 2.3 -9.9 6.2 10.6 8.7
U(dij) 30.0 30.0 30.0 30.0 50.0 32.0 32.0
ENij 0.3 0.0 0.1 0.4 0.1 0.4 0.3
NMI (i→) Nom L (j↓)
1.000 5
5 7 10
50 75
100
Table 14 B. Deviation from reference value for each GB, dij; claimed standard uncertainty, Uij; and Normalized Error ENij of the Steel GB for the last four participants.
CEM
dij 5.9 5.4 -7.7 -4.7
-11.9 -37.7 -26.9
U(dij) 18.8 19.0 19.0 19.0 23.2 27.6 33
ENij 0.3 0.3 0.4 0.3 0.5 1.2 0.8
CENAM
dij -10.1
1.4 5.3 1.3 33.1 -18.2 -10.9
U(dij) 22.2 22.2 22.2 22.4 30.6 38.6 47.6
ENij 0.5 0.1 0.3 0.1 1.1 0.5 0.3
CMI
dij 2.9 -1.6 1.8 -4.2 8.6 4.3
25.1
U(dij) 18.8 18.8 18.8 19.0 21.8 25.0 29.0
ENij 0.2 0.1 0.1 0.2 0.4 0.2 0.9
INMETRO
dij -2.1 -4.6 -8.7 -4.7 -13.9 -12.2 -21.9
U(dij) 22.0 22.0 22.0 24.0 32.0 42.0 52.0
ENij 0.1 0.2 0.4 0.2 0.5 0.3 0.5
NMI (i→) Nom L (j↓)
1.000 5
5 7 10
50 75
100
Table 15 A. Deviation from reference value for each GB, dij; claimed standard uncertainty, Uij; and Normalized Error ENij of the Ceramics GB for the first four participants
INTI
NIST
NPLI
NRC
dij
U(dij)
ENij
dij
U(dij)
ENij
dij
U(dij)
ENij
dij
U(dij)
-18.1 22.0
0.9 -1.1 18.0
0.1
7.9 22.0
0.4 14.9 30.0
-9.6 22.0
0.5
3.4 18.8
0.2
0.4 24.0
0.0
5.4 30.0
-15.7 22.0
0.8
2.3 19.0
0.1
8.3 24.0
0.4 14.3 30.0
-4.7 22.0
0.2
3.3 19.6
0.2
0.3 26.0
0.0 13.3 30.0
-9.9 30.0
0.4
3.1 27.0
0.1 41.1 32.0
1.3 24.1 30.0
-10.2 38.0
0.3
1.8 31.4
0.1 19.8 46.0
0.5 14.8 32.0
2.1 52.0
0.0
7.1 36.0
0.2 51.1 52.0
0.9 25.1 32.0
Table 15 B. Deviation from reference value for each GB, dij; claimed standard uncertainty, Uij; and Normalized Error ENij of the Ceramics GB for the last four participants.
ENij 0.5 0.2 0.5 0.5 0.9 0.5 0.8
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The bilateral equivalences between every two laboratories were also calculated. For this purpose the following equations were applied:
where k = 1, 2,…,n ; l = 1, 2,…,n ; and k l (8)
(9)
(10)
Tables 16 through 22, show the bilateral equivalences between laboratories for the Steel GB; and tables 23 through 29 show the bilateral equivalences for the Ceramics GB.
11. Discussion and Conclusions
11.1 Discussion
The organization of the comparison started in January 2007 and the artifacts started circulation on November of the same year. There were quite a few delays on the original schedule mainly due to problems on customs clearance of the artifacts. Therefore, the circulation ended until mid-April, 2010; a time span of almost two and a half years for a total number of nine participants including the pilots measurements at the beginning and at the end.
The South African laboratory, NMISA, had problems and did not send-in measurement results. They requested a new opportunity to measure the GB again. However, as these GB were also going to be used at a subsequent exercise of Mechanical Comparison, it was not possible unfortunately. In Annex C 1 the correspondence with this laboratory is shown.
Draft A was sent-out for review of the participants on May 2010. Only František Dvořáček from CMI sent in a letter reckoning they made a mistake on the phase change correction sign and asked to correct it. The correspondence appears in Annex C 2. Annex D shows the comparison Analysis considering this correction. It is evident that there was a sign mistake and considering this correction CMI results are consistent six out of seven.
The Draft B version of the report could not be released until present, because the same artifacts were used for a second comparison of GB measured by mechanical comparison and the measured values could not be disclosed until all participants of the second comparison had sent-in their results. This second comparison had 15 participants and CENAM performed the final measurements on May 2011.
11.2 Conclusions
From Section 7 we observe that there were no appreciable changes on the measurements performed by the pilot laboratory of the ensemble of the GB of both materials over the last five years. Even though some drift may be appreciated on the steel GB during their first year of their history, the values
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shown prove they reached stability since 2005 approximately. Therefore, it can be assumed that the artifacts behaved adequately during the comparison exercise and that the exercise was valid.
Alternate statistical estimators and parameters were computed and are shown on Annex B. Although the analysis chosen used the simple mean to compute the KCRV. The results are shown for completeness and lead to the same conclusions.
The elimination process described in section 9 proved to be adequate as the Birge ratio becomes lower than 1 once the outliers are eliminated, therefore proving consistency of results. The detailed elimination process for each GB is shown in Annex A.
In general, the scatter of results was smaller for the Ceramics GB than for the Steel GB. This can partially be explained because of the Phase-Change Correction error of CMI, but even taking in account this correction (see Annex D) the results for the Steel GB are still more disperse. This may be due to the fact that Steel GB are more prone to scratches, rust or damage.
The results of most laboratories were satisfactory in most artifacts, but we would like to make a few comments on those results that had En > 1.
The case of CMI for the Steel GB has already been discussed.
For the longer GB of steel and one of Ceramic, CEM had En > 1 and their results are always under the mean which might suggest the investigation systematic effects that may grow with length.
INMETRO had En > 1 for some of the shorter steel GB (i.e. for nominal lengths of 1.0005, 5.0 and 7.0 mm). INMETRO believes that the positive deviations from the mean may have been caused by wringing problems associated with scratches on the surfaces.
NPLI had some problems with the 75 mm steel GB and the 50 mm ceramics. It is difficult to suggest a possible reason, but a frequent one is temperature. An investigation on the cause should also be carried out.
In general the results of all participants were satisfactory which prove their technical competency.
12. Acknowledgements
We would like to acknowledge:
SIM WG.4 Length and SIM Technical Committee for having funded the purchase of the fourteen GB to carry this comparison.
In an anonymous way, the technicians and colleagues from our different institutions that contributed directly or indirectly to the measurements of the artifacts in this comparison.
And specifically from CENAM, the pilot laboratory, Juan Carlos Zárraga who repeated the measurements made by Carlos Colín.
Our colleague from the Dimensional Metrology Division (DMD), Armando López Celis who gave us a hand with the spread sheet analysis of the results.
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NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NPLI
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl
CEM CENAM 6.5 26.9 0.2
CMI 31.0 26.6 1.2 24.5 26.9 0.9 INMETRO 24.5 24.7 1.0 18.0 25.0 0.7 -6.5 24.7 0.3
INTI -2.5 28.9 0.1 -9.0 29.2 0.3 -33.5 28.9 1.2 -27.0 27.2 1.0 NIST 9.5 26.0 0.4 3.0 26.3 0.1 -21.5 26.0 0.8 -15.0 24.1 0.6 12.0 28.4 0.4 NPLI -4.5 28.9 0.2 -11.0 29.2 0.4 -35.5 28.9 1.2 -29.0 27.2 1.1 -2.0 31.1 0.1 -14.0 28.4 0.5 NRC -7.5 35.4 0.2 -14.0 35.6 0.4 -38.5 35.4 1.1 -32.0 34.0 0.9 -5.0 37.2 0.1 -17.0 35.0 0.5 -3.0 37.2 0.1
Table 16. Bilateral equivalences for the 1.0005 mm Steel GB.
NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl
CEM
CENAM 18.5 27.0 0.7
CMI 43.5 26.7 1.6 25.0 26.9 0.9
INMETRO 31.5 26.2 1.2 13.0 26.3 0.5 -12.0 26.0 0.5 INTI -3.5 29.1 0.1 -22.0 29.2 0.8 -47.0 28.9 1.6 -35.0 28.4 1.2 NIST 24.5 26.7 0.9 6.0 26.9 0.2 -19.0 26.6 0.7 -7.0 26.0 0.3 28.0 28.9 1.0
NPLI 1.5 30.6 0.0 -17.0 30.7 0.6 -42.0 30.5 1.4 -30.0 30.0 1.0 5.0 32.6 0.2 -23.0 30.5 0.8
NRC
8.5 35.5 0.2 -10.0 35.6 0.3 -35.0 35.4 1.0 -23.0 35.0 0.7 12.0 37.2 0.3 -16.0 35.4 0.5 7.0
NPLI U(dkl) ENkl
38.4 0.2
Table 17 Bilateral equivalences for the 5 mm Steel GB.
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NMI (k→)
CEM
CENAM
CMI
INMETRO
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl
CEM
CENAM -3.5 27.2 0.1 CMI 39.0 26.7 1.5 42.5 27.0 1.6
INMETRO 25.5 26.2 1.0 29.0 26.5 1.1 -13.5 26.0 0.5
INTI NIST NPLI
-12.5 29.1 0.4 -9.0 29.3 0.3 -51.5 28.9 1.8 -38.0 28.4 1.3 5.5 26.9 0.2 9.0 27.2 0.3 -33.5 26.7 1.3 -20.0 26.2 0.8 18.0 -10.5 30.6 0.3 -7.0 30.9 0.2 -49.5 30.5 1.6 -36.0 30.0 1.2 2.0
NRC -1.5 35.5 0.0 2.0 35.7 0.1 -40.5 35.4 1.1 -27.0 35.0 0.8 11.0
INTI U(dkl) ENkl
NIST dkl U(dkl) ENkl dkl
29.1 0.6 32.6 0.1 -16.0 30.6 0.5 37.2 0.3 -7.0 35.5 0.2 9.0
NPLI U(dkl) ENkl
38.4 0.2
Table 18. Bilateral equivalences for the 7 mm Steel GB.
NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NPLI
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl
CEM
CENAM 9.0 27.4 0.3 CMI 34.5 27.0 1.3 25.5 27.3 0.9
INMETRO 9.0 26.3 0.3 0.0 26.6 0.0 -25.5 26.2 1.0
INTI -5.0 29.2 0.2 -14.0 29.5 0.5 -39.5 29.1 1.4 -14.0 28.4 0.5
NIST NPLI
16.0 27.4 0.6 7.0 27.7 0.3 -18.5 27.3 0.7 7.0 26.6 0.3 21.0 29.5 0.7 28.0 32.3 0.9 19.0 32.6 0.6 -6.5 32.2 0.2 19.0 31.6 0.6 33.0 34.1 1.0 12.0 32.6 0.4
NRC -2.0 35.6 0.1 -11.0 35.8 0.3 -36.5 35.5 1.0 -11.0 35.0 0.3 3.0 37.2 0.1 -18.0 35.8 0.5 -30.0 39.7 0.8
Table 19. Bilateral equivalences for the 10 mm Steel GB.
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NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NPLI
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl
CEM
CENAM 36.5 38.0 1.0 CMI 59.0 32.3 1.8 22.5 36.8 0.6
INMETRO 19.5 39.9 0.5 -17.0 43.6 0.4 -39.5 38.7 1.0
INTI NIST NPLI
15.5 39.9 0.4 -21.0 43.6 0.5 -43.5 38.7 1.1 -4.0 45.3 0.1 42.5 36.0 1.2 6.0 40.1 0.1 -16.5 34.7 0.5 23.0 41.9 0.5 27.0 41.9 0.6 51.5 39.9 1.3 15.0 43.6 0.3 -7.5 38.7 0.2 32.0 45.3 0.7 36.0 45.3 0.8 9.0 41.9 0.2
NRC 40.5 55.4 0.7 4.0 58.1 0.1 -18.5 54.5 0.3 21.0 59.4 0.4 25.0 59.4 0.4 -2.0 56.8 0.0 -11.0 59.4 0.2
Table 20. Bilateral equivalences for the 50 mm Steel GB.
NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NPLI
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl
CEM
CENAM 56.0 48.3 1.2 CMI 117.0 38.1 3.1 61.0 46.2 1.3
INMETRO 42.0 52.6 0.8 -14.0 58.7 0.2 -75.0 50.6 1.5
INTI 37.0 50.9 0.7 -19.0 57.2 0.3 -80.0 48.9 1.6 -5.0 60.8 0.1
NIST NPLI
56.0 42.6 1.3 0.0 49.9 0.0 -61.0 40.1 1.5 14.0 54.1 0.3 19.0 52.4 0.4 181.0 54.3 3.3 125.0 60.2 2.1 64.0 52.4 1.2 139.0 63.7 2.2 144.0 62.3 2.3 125.0 55.7 2.2
NRC 61.0 43.1 1.4 5.0 50.3 0.1 -56.0 40.6 1.4 19.0 54.4 0.3 24.0 52.8 0.5 5.0 44.8 0.1 -120.0 56.0 2.1
Table 21 Bilateral equivalences for the 75 mm steel GB.
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NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NPLI
NRC
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl
CEM
CENAM 52.0 60.0 0.9 CMI 95.0 45.1 2.1 43.0 56.9 0.8
INMETRO 45.0 65.8 0.7 -7.0 74.4 0.1 -50.0 63.1 0.8
INTI NIST NPLI
54.0 64.1 0.8 2.0 72.9 0.0 -41.0 61.3 0.7 9.0 77.8 0.1 62.0 49.9 1.2 10.0 60.8 0.2 -33.0 46.2 0.7 17.0 66.6 0.3 8.0 64.9 0.1 75.0 62.5 1.2 23.0 71.4 0.3 -20.0 59.5 0.3 30.0 76.4 0.4 21.0 75.0 0.3 13.0 63.2 0.2
NRC 68.0 47.1 1.4 16.0 58.5 0.3 -27.0 43.2 0.6 23.0 64.5 0.4 14.0 62.8 0.2 6.0 48.2 0.1 -7.0 61.1 0.1
Table 22. Bilateral equivalences for the 100 mm steel GB.
NMI (k→)
CEM
CENAM
CMI
INMETRO
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl
CEM
CENAM -16.0 29.1 0.6
CMI
-3.0 26.6 0.1 13.0 29.1 0.4
INMETRO -8.0 28.9 0.3 8.0 31.3 0.3 -5.0 28.9 0.2
INTI -24.0 28.9 0.8 -8.0 31.3 0.3 -21.0 28.9 0.7 -16.0 31.1 0.5
NIST NPLI
-7.0 26.0 0.3 9.0 28.6 0.3 -4.0 26.0 0.2 1.0 28.4 0.0 17.0 2.0 28.9 0.1 18.0 31.3 0.6 5.0 28.9 0.2 10.0 31.1 0.3 26.0
NRC
9.0 35.4 0.3 25.0 37.3 0.7 12.0 35.4 0.3 17.0 37.2 0.5 33.0
INTI
NIST
U(dkl) ENkl dkl U(dkl) ENkl dkl
28.4 0.6 31.1 0.8 9.0 28.4 0.3 37.2 0.9 16.0 35.0 0.5 7.0
NPLI U(dkl) ENkl
37.2 0.2
Table 23. Bilateral equivalences for the 1.0005 mm Ceramics GB.
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NMI (k→)
CEM
CENAM
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl
CEM
CENAM -4.0 29.2 0.1
CMI
-7.0 26.7 0.3 -3.0 29.1 0.1
INMETRO -10.0 29.1 0.3 -6.0 31.3 0.2 -3.0
INTI NIST NPLI
-15.0 29.1 0.5 -11.0 31.3 0.4 -8.0 -2.0 26.7 0.1 2.0 29.1 0.1 5.0 -5.0 30.6 0.2 -1.0 32.7 0.0 2.0
NRC
0.0 35.5 0.0 4.0 37.3 0.1 7.0
CMI
INMETRO
INTI
U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl
28.9 0.1 28.9 0.3 -5.0 31.1 0.2 26.6 0.2 8.0 28.9 0.3 13.0 28.9 0.4 30.5 0.1 5.0 32.6 0.2 10.0 32.6 0.3 -3.0 35.4 0.2 10.0 37.2 0.3 15.0 37.2 0.4 2.0
NIST U(dkl) ENkl dkl
30.5 0.1 35.4 0.1 5.0
NPLI U(dkl) ENkl
38.4 0.1
Table 24. Bilateral equivalences for the 5 mm Ceramics GB.
NMI (k→)
CEM
CENAM
CMI
INMETRO
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl
CEM
CENAM 13.0 29.2 0.4
CMI
9.5 26.7 0.4 -3.5 29.1 0.1
INMETRO -1.0 29.1 0.0 -14.0 31.3 0.4 -10.5 28.9 0.4
INTI -8.0 29.1 0.3 -21.0 31.3 0.7 -17.5 28.9 0.6 -7.0 31.1 0.2
NIST NPLI
10.0 26.9 0.4 -3.0 29.2 0.1 0.5 26.7 0.0 11.0 29.1 0.4 18.0 16.0 30.6 0.5 3.0 32.7 0.1 6.5 30.5 0.2 17.0 32.6 0.5 24.0
NRC 22.0 35.5 0.6 9.0 37.3 0.2 12.5 35.4 0.4 23.0 37.2 0.6 30.0
INTI
NIST
U(dkl) ENkl dkl U(dkl) ENkl dkl
29.1 0.6 32.6 0.7 6.0 30.6 0.2 37.2 0.8 12.0 35.5 0.3 6.0
NPLI U(dkl) ENkl
38.4 0.2
Table 25. Bilateral equivalences for the 7 mm Ceramics GB.
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NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NPLI
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl
CEM
CENAM 6.0 29.4 0.2
CMI
0.5 26.9 0.0 -5.5 29.4 0.2
INMETRO 0.0 30.6 0.0 -6.0 32.8 0.2 -0.5 30.6 0.0
INTI NIST NPLI
0.0 29.1 0.0 -6.0 31.4 0.2 -0.5 29.1 0.0 0.0 32.6 0.0 8.0 27.3 0.3 2.0 29.8 0.1 7.5 27.3 0.3 8.0 31.0 0.3 8.0 29.5 0.3 5.0 32.2 0.2 -1.0 34.3 0.0 4.5 32.2 0.1 5.0 35.4 0.1 5.0 34.1 0.1 -3.0 32.6 0.1
NRC 18.0 35.5 0.5 12.0 37.4 0.3 17.5 35.5 0.5 18.0 38.4 0.5 18.0 37.2 0.5 10.0 35.8 0.3 13.0 39.7 0.3
Table 26. Bilateral equivalences for the 10 mm Ceramics GB
NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NPLI
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl
CEM
CENAM 45.0 38.4 1.2 CMI 20.5 31.8 0.6 -24.5 37.6 0.7
INMETRO -2.0 39.5 0.1 -47.0 44.3 1.1 -22.5 38.7 0.6
INTI 2.0 37.9 0.1 -43.0 42.9 1.0 -18.5 37.1 0.5 4.0 43.9 0.1
NIST NPLI
15.0 35.6 0.4 -30.0 40.8 0.7 -5.5 34.7 0.2 17.0 41.9 0.4 13.0 40.4 0.3 53.0 39.5 1.3 8.0 44.3 0.2 32.5 38.7 0.8 55.0 45.3 1.2 51.0 43.9 1.2 38.0 41.9 0.9
NRC 36.0 37.9 0.9 -9.0 42.9 0.2 15.5 37.1 0.4 38.0 43.9 0.9 34.0 42.4 0.8 21.0 40.4 0.5 -17.0 43.9 0.4
Table 27. Bilateral equivalences for the 50 mm Ceramics GB.
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NMI (k→)
CEM
CENAM
CMI
INMETRO
INTI
NIST
NPLI
NMI (l↓) dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl dkl U(dkl) ENkl
CEM
CENAM 19.5 47.5 0.4 CMI 42.0 37.2 1.1 22.5 46.0 0.5
INMETRO 25.5 50.3 0.5 6.0 57.0 0.1 -16.5 48.9 0.3
INTI NIST NPLI
27.5 47.0 0.6 8.0 54.2 0.1 -14.5 45.5 0.3 2.0 56.6 0.0
39.5 41.8 0.9 20.0 49.8 0.4 -2.5 40.1 0.1 14.0 52.4 0.3 12.0 49.3 0.2 57.5 53.6 1.1 38.0 60.0 0.6 15.5 52.4 0.3 32.0 62.3 0.5 30.0 59.7 0.5 18.0 55.7 0.3
NRC 52.5 42.3 1.2 33.0 50.1 0.7 10.5 40.6 0.3 27.0 52.8 0.5 25.0 49.7 0.5 13.0 44.8 0.3 -5.0 56.0 0.1
Table 28. Bilateral equivalences for the 75 mm Ceramics GB.
NMI (k→)
NMI (l↓)
CEM CENAM
CMI INMETRO
INTI NIST NPLI NRC
CEM dkl U(dkl) ENkl
16.0 57.9 0.3 52.0 43.9 1.2
5.0 61.6 0.1 29.0 61.6 0.5 34.0 48.8 0.7 78.0 61.6 1.3 52.0 46.0 1.1
CENAM dkl U(dkl) ENkl
36.0 -11.0 13.0 18.0 62.0 36.0
55.7 0.6 70.5 0.2 70.5 0.2 59.7 0.3 70.5 0.9 57.4 0.6
CMI dkl U(dkl) ENkl
-47.0 -23.0 -18.0 26.0
0.0
59.5 0.8 59.5 0.4 46.2 0.4 59.5 0.4 43.2 0.0
INMETRO dkl U(dkl) ENkl
24.0 73.5 0.3 29.0 63.2 0.5 73.0 73.5 1.0 47.0 61.1 0.8
INTI dkl U(dkl) ENkl
5.0 63.2 0.1 49.0 73.5 0.7 23.0 61.1 0.4
NIST dkl U(dkl) ENkl
44.0 63.2 0.7 18.0 48.2 0.4
NPLI dkl U(dkl) ENkl
-26.0 61.1 0.4
Table 29. Bilateral equivalences for the 100 mm Ceramics GB.
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13. References
1. ISO 3650:1998(E), Geometrical Product Specification (GPS) – Length Standards – Gauge Blocks, International Organization for Standardization, Geneva, Switzerland.
2. Quinn, T.J, Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001), Metrologia, 2003, 40, pp103-133.
3. Stoup, John R., Faust Byron S., Doiron Ted D., Minimizing Errors in Phase Change Correction Measurements for Gauge Blocks Using a Spherical Contact Technique, Recent Developments in Optical Gauge Block Metrology, SPIE Proceedings Vol. 3477, pp 161-172, 1998.
4. Thalmann R., CCL-K1 Final report, Calibration of gauge blocks by interferometry, Wabern, Switzerland, November 2000. At BIPM website, http://www.bipm.fr.
5. Decker, J.E. and Pekelsky, J.R., 1997, Uncertainty Evaluation for Mesurement of Gauge Blocks by Optical Interferometry, Metrologia, 34, 479-493. [NRC Document No. 41374].
6.
Decker J.E., Altschuler J., Beladie H., Malinovsky I., Prieto E., Stoup J.,
Titov A., Viliesid M., Pekelsky J.R. Final Report on SIM.L-K1 (SIM.4.2) Regional
Comparison. Stage One: Calibration of gauge blocks by optical Interferometry,
Metrologia, 2007, 44, Tech. Suppl., 04001. At BIPM website, http://www.bipm.fr.
7. Viliesid M., Comparison CCL-K6 “Calibration of Coordinate Measuring Machine (CMM) Two-dimensional (2-D) Artifacts (Ball plates and Bore Plates)” Final Report, 2008- 10-27 At BIPM website, http://www.bipm.fr.
8. Cox, M.G., 2002, The evaluation of key comparison data, Metrologia, 2003, 39, pp 589-595.
9. Beissner, K., 2002, On a measure of consistency in comparison measurements, Metrologia, 2003, 39, pp 59-63.
10. Kacker, R., Datla, R., Parr, A., 2002, Combined result and associated uncertainty from interlaboratory evaluations based on the ISO Guide, Metrologia, 2003, 39, pp 279-293.
11. Koenders L., Supplementary Comparison According to the Rules of CCL Key Comparisons, EUROMET Project 707, Step Height Standards Final Report, Braunschweig, Germany, November 2005. At BIPM website, http://www.bipm.fr.
12. Decker J., Ulrich A., Lapointe A., Viliesid M., Pekelsky J. R., Two-part Study towards
Lowest Uncertainty Calibration O Ceramic Gauge Blocks: Interferometry And Mechanical Comparison Techniques, in Recent Developments in Traceable Dimensional Measurements, Proceedings of SPIE – The International Society for Optical Engineering, Vol. 4401 presented at Munich, Germany, June 2001.
13. Colín, C. Zárraga, J.C., Viliesid M., Estudio Experimental de la Corrección de Fase en
la Medición por Interferometría Absoluta de Bloques Patrón de Diferentes Materiales Adheridos sobre Platinas de Diferentes Materiales, II Congreso Chileno de Metrología METROCAL 2001, Concepción, Chile, April 2001.
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Annex A Elimination of Inconsistent Results
Nom. length
NMI CMI INMETRO NRC NPLI INTI CEM NIST CENAM
n=8 di 23.9 17.4 14.6 11.6 9.6 7.1 2.4 0.6
1.000 5 mm, Steel GB
Elim. CMI
Nom. length n = 7 Elim. INMETRO
Nom. length
EN
NMI
di
EN
NMI
1.3 INMETRO
20.8
1.3 NIST
1.1 NRC
11.2
0.4 NRC
0.5 NPLI
8.2
0.4 CENAM
0.6 INTI
6.2
0.3 NPLI
0.5 NIST
5.8
0.3 INTI
0.4 CEM
3.7
0.2 CEM
0.1 CENAM
2.8
0.2
CMI
0.0
INMETRO
n=6 di
9.3 7.8 6.3 4.8 2.8 0.3 30.8 24.3
STOP En
0.5 0.3 0.3 0.2 0.1 0.0 1.5 1.3
Table A1. Consecutive elimination of two inconsistent results to arrive to a set of 6 consistent ones for the 1.0005 mm Steel GB.
Nom. length
NMI CMI INTI INMETRO CEM NPLI NIST NRC CENAM
n=8 di 27.9 19.1 15.9 15.6 14.1 8.9 7.1 2.9
5 mm, Steel GB
Elim. CMI
Nom. length n = 7 Elim. INMETRO Nom. length
EN
NMI
di
EN
NMI
1.6 INMETRO
19.9
1.2 NIST
0.9 INTI
15.1
0.7 INTI
0.9 NIST
12.9
0.7 CENAM
0.9 CEM
11.6
0.6 CEM
0.6 NPLI
10.1
0.5 NPLI
0.5 CENAM
6.9
0.4 NRC
0.3 NRC
3.1
0.1
CMI
0.2
INMETRO
n=6 di
16.3 11.8 10.3
8.3 6.8 0.3 35.3 23.3
STOP EN
0.9 0.6 0.6 0.5 0.3 0.0 1.7 1.2
Table A2. Consecutive elimination of two inconsistent results to arrive to a set of 6 consistent ones for the 5 mm Steel GB.
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Nom. length
NMI CMI INMETRO INTI NPLI CENAM NRC CEM NIST
n=8 di 33.8 20.3 17.8 15.8 8.8 6.8 5.3 0.3
7 mm, Steel GB
Elim. CMI
Nom. length n = 7 Elim. INMETRO Nom. length
EN
NMI
di
EN
NMI
1.9 INMETRO
25.1
1.4 NIST
1.2 INTI
12.9
0.6 INTI
0.9 NPLI
10.9
0.5 NPLI
0.7 NIST
5.1
0.3 CEM
0.5 CENAM
3.9
0.2 NRC
0.2 NRC
1.9
0.1 CENAM
0.3 CEM
0.4
0.0
CMI
0.0
INMETRO
n=6 di
9.3 8.8 6.8 3.8 2.3 0.3 42.8 29.3
STOP EN
0.5 0.4 0.3 0.2 0.1 0.0 2.0 1.4
Table A3. Consecutive elimination of two inconsistent results to arrive to a set of 6 consistent ones for the 7 mm Steel GB.
Nom. length
NMI CMI NPLI INTI NRC CEM NIST CENAM
INMETRO
10 mm, Steel GB
n = 8 Elim. CMI
Nom. length
di
EN
NMI
23.3
1.3 NPLI
16.8
0.7 INTI
16.2
0.8 NRC
13.2
0.5 NIST
11.2
0.6 CEM
4.8
0.3 CENAM
2.2
0.1 INMETRO
2.2
0.1
CMI
n=7 di
20.1 12.9
9.9 8.1 7.9 1.1 1.1 26.6
STOP EN
0.9 0.6 0.4 0.4 0.4 0.1 0.1 1.3
Table A4. Consecutive elimination of one inconsistent result to arrive to a set of 7 consistent ones for the 10 mm Steel GB.
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Nom. length
NMI CEM CMI NPLI INTI INMETRO NIST NRC CENAM
n=8 di 33.1 25.9 18.4 17.6 13.6 9.4 7.4 3.4
50 mm, Steel GB
Elim. CEM
Nom. length
EN
NMI
1.4 CMI
1.2 INTI
0.6 INMETRO
0.6 NPLI
0.5 NIST
0.4 NRC
n=7 di
21.1 22.4 18.4 13.6
4.6 2.6
0.2 CENAM
1.4
0.1
Elim. CMI EN 0.9 0.8 0.6 0.5 0.2 0.1 0.0
Nom. length
NMI INTI NPLI INMETRO NIST NRC CENAM
CEM CMI
n=6 di
18.8 17.2 14.8
8.2 6.2 2.2 34.3 24.7
STOP EN
0.6 0.6 0.5 0.3 0.1 0.1 1.2 0.9
Table A5. Consecutive elimination of two inconsistent results to arrive to a set of 6 consistent ones for the 50 mm Steel GB. In this case CMI was also eliminated even though their EN Valueis smaller than 1, because they acknowledged they committed a mistake in the phase change correction.
Nom. length
NMI NPLI CEM CMI INTI INMETRO CENAM NIST NRC
n = 8 Elim. NPLI
Nom. length
di 112.3 68.8 48.3 31.8 26.8
EN
NMI
2.7 CMI
2.4 CEM
1.9 INTI
0.8 INMETRO
0.7 NRC
12.8
0.4 CENAM
12.8
0.4 NIST
7.8
0.3
n=7 di 64.3 52.7 15.7 10.7 8.3 3.3 3.3
75 mm, Steel GB
Elim. CMI
Nom. length
EN 2.6 1.9 0.4 0.3
0.3
NMI CEM NRC
CENAM NIST INTI
0.1
INMETRO
0.1
n=6 di 42.0 19.0 14.0 14.0 5.0 0.0
Elim. CEM EN 1.5 0.6 0.4 0.5 0.1
0.0
Nom. length
NMI INTI NRC INMETRO CENAM NIST
NPLI CMI CEM
n=5 di
13.4 10.6
8.4 5.6 5.6 130.6 66.6 50.4
STOP EN
0.4 0.4 0.2 0.2 0.2 2.7 2.3 1.6
Table A6. Consecutive elimination of three inconsistent results to arrive to a set of 5 consistent ones for the 75 mm Steel GB.
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Nom. length
NMI CEM CMI NPLI NRC INMETRO NIST CENAM INTI
n=8 di 56.4 38.6 18.6 11.6 11.4 5.6 4.4 2.4
100 mm, Steel GB
Elim. CEM
Nom. length n = 7 Elim. CMI
EN
NMI
1.7 CMI
1.3 INMETRO
0.4 CENAM
0.4 NPLI
0.2 INTI
0.2 NRC
di
En
30.6
1.0
19.4
0.4
12.4
0.3
10.6
0.2
10.4
0.2
3.6
0.1
0.1 NIST
2.4
0.1
0.0
Nom. length
NMI NPLI INMETRO NRC CENAM INTI NIST
CEM CMI
n=6 di
15.7 14.3
8.7 7.3 5.3 2.7 59.3 35.7
STOP EN
0.3 0.3 0.3 0.2 0.1 0.1 1.5 1.0
Table A7. Consecutive elimination of two inconsistent results to arrive to a set of 6 consistent ones for the 100 mm Steel GB.
1.000 5 mm, Ceramics GB
Nom. length
n = 8 STOP
NMI
di
EN
INTI
18.1
0.9
NRC
14.9
0.5
CENAM
10.1
0.5
NPLI
7.9
0.4
CEM
5.9
0.3
CMI
2.9
0.2
INMETRO
2.1
0.1
NIST
1.1
0.1
Table A8. All 8 results consistent for the 1.0005 mm Ceramics GB. No elimination needed.
5 mm, Ceramics GB
Nom. length
n=8
NMI
di
INTI
9.6
CEM
5.4
NRC
5.4
INMETRO
4.6
NIST
3.4
CMI
1.6
CENAM
1.4
NPLI
0.4
STOP EN
0.5 0.3 0.2 0.2 0.2 0.1 0.1 0.0
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SIM.L-K1:2007 Calibration of Gauge Blocks by Optical Interferometry
7 mm, Ceramics GB
Nom. length
n = 8 STOP
NMI
di
EN
INTI NRC
15.7
0.8
14.3
0.5
INMETRO
8.7
0.4
NPLI
8.3
0.4
CEM
7.7
0.4
CENAM
5.3
0.3
NIST
2.3
0.1
CMI
1.8
0.1
Table A10. All 8 results consistent for the 7 mm Ceramics GB. No
elimination needed.
36 / 43
Table A9. All 8 results consistent for the 5 mm Ceramics GB. No elimination needed.
10 mm, Ceramics GB
Nom. length
n = 8 STOP
NMI
di
EN
NRC CEM
13.3
0.5
4.7
0.3
INMETRO
4.7
0.2
INTI
4.7
0.2
CMI
4.2
0.2
NIST
3.3
0.2
CENAM
1.3
0.1
NPLI
0.3
0.0
Table A11. All 8 results consistent for the 10 mm Ceramics GB. No
elimination needed.
Nom. length
NMI NPLI CENAM INMETRO CEM INTI NRC NIST CMI
n=8 di 31.8 23.8 23.2 21.2 19.2 14.8 6.2 0.7
50 mm, Ceramics GB
Elim. NPLI
Nom. length n = 7 Elim. CENAM
Nom. length
EN
NMI
di
En
NMI
1.1 CENAM
28.4
0.8 CEM
16.6
1.0 NRC 0.7 INMETRO
0.8 CMI
3.9
0.2 CEM
0.9 NRC
19.4
0.7 INTI
0.7 NIST
1.6
0.1 CMI
0.5 INMETRO
18.6
0.6 NIST
0.2 INTI
14.6
0.5
NPLI
0.0
CENAM
n=6 di
24.1 13.9 11.9
9.9 8.6 3.1 41.1 33.1
STOP EN
0.9 0.5 0.5 0.4 0.4 0.1 1.3 1.1
Table A12. Consecutive elimination of two inconsistent results to arrive to a set of 6 consistent ones for the 50 mm Ceramics GB.
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Nom. length
NMI CEM NPLI CMI NRC CENAM NIST INMETRO
INTI
75 mm, Ceramics GB
n = 8 Elim. CEM
Nom. length
di
EN
NMI
68.8
1.2 NPLI
48.3
0.6 CENAM
31.8
0.4 NRC
26.8
0.6 INMETRO
13.5
0.4 INTI
12.8
0.2 CMI
12.8
0.2 NIST
7.8
0.2
CEM
n=7 di
19.8 18.2 14.8 12.2 10.2
4.3 1.8 37.7
STOP EN
0.5 0.5 0.5 0.3 0.3 0.2 0.1 1.2
Table A13. Consecutive elimination of one inconsistent result to arrive to a set of 7 consistent ones for the 75 mm Ceramics GB.
Nom. length
NMI NPLI CEM INMETRO CMI NRC CENAM INTI
NIST
100 mm, Ceramics GB
n = 8 Elim. NPLI
Nom. length
di
EN
NMI
44.8
0.9 CEM
33.3
1.0 CMI
28.3
0.6 NRC
18.8
0.6 INMETRO
18.8
0.6 CENAM
17.3
0.4 NIST
4.3
0.1 INTI
0.8
0.0
NPLI
n=7 di
26.9 25.1 25.1 21.9 10.9
7.1 2.1 51.1
STOP EN 0.8 0.9 0.8 0.5 0.3 0.2 0.0 0.9
Table A14. Consecutive elimination of one inconsistent result to arrive to a set of 7 consistent ones for the 100 mm Ceramics GB.
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Annex B Calculation of Alternate Statistical Parameters.
Statistical estimator Simple arithmetic mean Standard uncertainty Birge Ratio Weighted mean Standard uncertainty Birge Ratio Median Observed chi-squared Degrees of freedom
Reduced chi-squared
Steel gauge blocks / Nominal length, mm
1.000 5
5
7
10
-10.3
24.8
-5.3
35.9
4.5
4.6
4.6
4.2
0.59
0.99
0.60
1.03
-8.8
25.9
-4.5
35.8
4.2
4.3
4.4
4.0
0.61
1.12
0.64
1.08
-11.8 21.5
-4.0
37.0
1.9
6.3
2.0
5.6
5
5
5
6
0.866 0.281 0.842 0.471
0.37
1.25
0.41
0.93
50 4.8 7.1 0.81 4.8 6.5 0.88 9.0 3.8 5 0.572 0.77
75 -105.6
8.5 0.54 -103.5 8.2 0.53 -100.0 1.1
4 0.888 0.28
100 -43.7 9.7 0.47 -41.5 8.8 0.45 -45.0 1.0
5 0.962 0.20
Statistical estimator
Ceramics gauge blocks / Nominal length, mm
1.000 5
5
7
10
50
Simple arithmetic mean -3.9
10.6
51.7
-14.3 105.9
Standard uncertainty
3.9
4.0
4.0
4.1
5.6
Birge Ratio
0.95
0.46
0.89
0.54 1.07
Weighted mean Standard uncertainty Birge Ratio
-4.3
10.6
50.6
-15.3 106.2
3.7
3.8
3.8
3.9
5.4
0.89
0.47
0.84
0.48 1.05
Median Observed chi-squared Degrees of freedom
-3.0
11.5
53.8
-18.8 102.5
5.6
1.6
4.9
1.6
5.5
7
7
7
7
5
0.591 0.980 0.667 0.978 0.358
Reduced chi-squared
0.79
0.22
0.71
0.23 1.10
75 136.2
6.9 0.78 137.3 6.5 0.73 138.0 3.2
6 0.781 0.54
100 -23.1 7.8 1.02 -18.5 7.0 1.21 -21.0 8.8
6 0.187 1.46
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Steel gauge blocks with CMI correction/ Nominal length, mm
Statistical estimator
1.000 5
5
7
10
50
75
Simple arithmetic mean
-9.3
26.4
-2.6
36.2
4.9 -105.6
Standard uncertainty
4.1
4.2
4.2
3.9
6.2
8.5
Birge Ratio
0.60
1.00
0.85
0.97
0.77 0.54
Weighted mean Standard uncertainty Birge Ratio
-7.9
27.7
-1.3
36.2
5.0 -103.5
3.9
3.9
4.0
3.7
5.6
8.2
0.60
1.10
0.92
0.90 0.80 0.53
Median Observed chi-squared Degrees of freedom
-10.5
25.0
-3.0
37.0
7.0 -100.0
2.1
7.2
5.1
5.7
3.8
1.1
6
6
6
7
6
4
0.907 0.301 0.534 0.580 0.697 0.888
Reduced chi-squared
0.36
1.20
0.85
0.81 0.64 0.28
100 -42.0 8.5 0.49
-38.9 7.6 0.47
-41.0 1.30
6 0.970 0.22
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Annex C Correspondence with Participants.
C.1 Correspondence with NMISA.
Dear Carlos The gauge blocks were calibrated using a Tungsten Carbide platen for both the steel and ceramic gauge blocks. No Phase correction were calculated as the wring not of a good quality.
After a long investigation the decision at NMISA was to change back to quartz platens.
Because of this NMISA would like if at all possible to re-measure the gauge blocks using quartz platens?
Please let me know if this is possible? Regards Oelof
C.2 Correspondence with CMI.
Dear Carlos,
I saw the results and check it in my papers and I found out that I made big mistake in calculation of phase correction of steel gauge blocks. In the calculation I confused the deviation of the pack and sum of deviations of the n individual GBs. Than I had wrong result (+12nm) and the correct result should be (-12nm) – all deviations in central points of steel GB I sent you 24 higher than I should. At the time I didn´t check it properly because the results was similar to the results of comparison method and we had delay and I hurried.
For many years we didn´t have any problems during the measuring but when we started this comparison all was agains us. First we had problems with air-conditioning during the comparison measuring and than during the interferometry measuring broke down the cammera and than also the computer so all I had to calculate manually. Last year we did reconstruction of our NPL TESA interferometer in co-operation with Swiss METAS and now we have new camera, computer and software.
Is possible to repair my mistake in results or is too late for this?
I am very apoligize for my confusions!
Best regards
Frantisek
Czech metrology institute
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Annex D
Analysis of Results considering CMI correction.
Following are the recalculated reference values considering the correct correction of the phase change correction by CMI.
Comparison Reference Values
Nominal length
1.000 5
Steel Ref Val URef val nRef Val
-9.3 8.2 7
5
26.4 8.3 7
7
-2.6 8.3 7
10
36.2 7.8 8
50
4.9 12.5 7
75
-105.6 17.0 5
100
-42.0 17.1 7
Table D1. Reference values (simple mean of largest sub-set of “consistent” results) deviations from Nominal Value with their Expanded Uncertainty and number of values contributing to the calculation
of the Reference Value Computation (n) for both steel and ceramics GB.
NMI (i→)
CEM
CENAM
CMI
INMETRO
Nom L
(j↓)
dij
U(dij) ENij
dij
U(dij)
ENij
dij
U(dij) ENij
dij
U(dij) ENij
1.005
-1.2 18.8 0.1 5.3
19.2 0.3
5.8
18.8 0.3 23.3
16.0 1.3
5
-9.9 19.0 0.5 8.6
19.2 0.5
9.6
18.8 0.5 21.6
18.0 1.1
7
1.1
-1.5 0.1 -2.4
-5.0 0.1 16.1
13.5 0.9 26.6
24.0 1.3
10
-8.2 19.2 0.4 0.8
19.6 0.0 2.3
19.0 0.1
0.8 18.0 0.0
50
-34.4
23.8 1.3 2.1
29.6 0.1
0.6
21.8 0.0 -14.9
32.0 0.5
75
-50.4
28.8 1.6 5.6
38.8 0.2 42.6
25.0 1.5
-8.4
44.0 0.2
100
-61.0
34.6 1.6 -9.0
49.0 0.2 10.0
29.0 0.3 -16.0
56.0 0.3
Table D2 A. Deviation from reference value for each GB, dij; claimed standard uncertainty, Uij; and
Normalized Error ENij of the the Steel GB for the first four participants.
2012-07-15
SIM.L-K1:2007 Calibration of Gauge Blocks by Optical Interferometry
42 / 43
NMI (i→)
INTI
NIST
NPLI
NRC
Nom L
(j↓)
dij
U(dij) ENij
dij
U(dij) ENij
dij
U(dij) ENij
dij
U(dij) ENij
1.005
-3.7 22.0 0.2 8.3
18.0 0.5
-5.7 22.0 0.3
-8.7
30.0 0.3
5
-13.4 22.0 0.7 14.6
18.8 0.8
-8.4 24.0 0.4
-1.4
30.0 0.1
7
-11.4 -14.0 0.6 6.6
4.0 0.4
-9.4 -12.0 0.4 -0.4
-3.0 0.0
10
-13.2 22.0 0.6 7.8
19.6 0.4
19.8 26.0 0.8 -10.2 30.0 0.4
50
-18.9 32.0 0.6 8.1
27.0 0.3
17.1 32.0 0.6
6.1 50.0 0.1
75
-13.4 42.0 0.4 5.6
31.4 0.2 130.6
46.0 2.7
10.6
32.0 0.4
100
-7.0 54.0 0.1 1.0
36.0 0.0
14.0 52.0 0.3
7.0 32.0 0.2
Table D2 B. Deviation from reference value for each GB, dij; claimed standard uncertainty, Uij; and
Normalized Error ENij of the the Steel GB for the last four participants.
2012-07-15
SIM.L-K1:2007 Calibration of Gauge Blocks by Optical Interferometry
43 / 43
Annex E
Phase Change Correction Determination by the Stack Method.
A method usually applied to determine l is the stack method where three or more GB are measured individually and then measured wrung together into a stack as shown in Figure 1.
From these measurements the global phase change correction for this set of GB may be
obtained as follows:
Figure 1. Stack method measurements to derive l. g represents the difference between the optical plane and the mechanical plane of the GB free surface, and p represents this
difference between planes for the platen.
N
lOS lOi
l
i 1
N 1
(E1)
Where:
lOs – Optical central length of the stack.
lOi – Optical central length of the ith individual GB, i = 1,2,…,N, of the stack.
N
– Number of gauge blocks in the stack.
2012-07-15
Ver+/-
