FINAL REPORT SIM COMPARISON IN A MASS STANDARD
SIM.M.M-K4
Kornblit, F1; Leiblich, J.1 ; Becerra, L.O.2; Peña, L.M. 2; Luján, L.2; Díaz,J.C.2; Centeno, L.M.2; Ramos, O3; Rodríguez, S.3; Santo, C.4; Caceres, J.4; García, F.5;
Leyton, F.5; Claude J.6; Loayza, V.M.7; Cacais,F.A.7
Abstract: This report summarizes the results of a SIM comparison of a 1 kg mass standard carried out between 7 NMIS. The results reported by the participants are consistent with each other and they can be linked to the comparison CCM.M-K4 with satisfactory degrees of equivalence
1. General Information
The present comparison, named SIM.M.M.K4, was planned and carried out in order to evaluate the degree of equivalence in the calibration of high accuracy mass standards, and to provide evidence supporting CMCs claimed by the participants in high accuracy mass calibrations delivered by them. It is part of a more general project which includes three comparisons:
SIM.M.M-K4 for mass calibration of nominal value 1 kg SIM.M.M-K5 for mass calibration of nominal values 2 kg, 200 g, 50 g, 1 g and 200 mg SIM.M.D-K3 for volume determination of stainless steel weights of 2 kg, 1 kg, 200 g and 1 g
2. Data of the participant NMIs and Technical Contacts
The following SIM NMIs have participated in the comparison:
Institute
Country
Technical Contact(s)
LACOMET Costa Rica
Ramos, O; Rodríguez, S.
LATU
Uruguay
Santo, C.; Caceres, J.
INTI
Argentina
Kornblit, F; Leiblich, J.
CESMEC
Chile
García, F.; Leyton, F.
CENAM
México
Becerra, L.O.; Peña, L.M.; Luján, L.; Díaz,J.C.; Centeno, L.M.
NRC
Canada
Claude Jacques
INMETRO
Brazil
Loayza, V.M.; Cacais, F.A.
INTI (Argentina)1 has acted as the pilot laboratory
3. General Considerations and Procedure A stainless steel standard, made by Masstech and provided by CENAM was used for the comparison. Its volume referred to 20 ºC, V20 ºC,, was determined by CENAM in August 2012,
1INTI, Instituto Nacional de Tecnología Industrial (Argentina), contact e-mail: ferk@inti.gob.ar; 2CENAM, Centro Nacional de Metrología (México); 3LACOMET, Laboratorio Costarricense de Metrología; 4LATU, Laboratorio Tecnológico del Uruguay (Uruguay); 5CESMEC (Chile); 6NRC, National Research Council (Canada), 7INMETRO, Instituto Nacional de Metrologia, Qualidade e Tecnologia (Brazil)
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after the comparison. These result and the corresponding standard uncertainty uV are also shown in Table 1, as well as the identification of the standard.
Table 1. Data associated to the standard weight
Nominal value:
1 kg
Serial number:
1866
Identification: V20 ºC uV
540161557204 125,414 9 cm3 0,002 3 cm3
The traveling standard was placed in an individual wooden case for transportation purposes, which was placed in a carrying transportation case, jointly with the standards corresponding to the comparisons SIM.M.M-K5 and SIM.M.D-K3 In all the cases, the transportation among laboratories was made by hand, by technical staff of the NMIs.
A protocol was agreed previously to the comparison. In it, instructions to travel, initial inspection in each country, store, handling and acclimatization of the standards have been specified. Particularly, the following criteria were agreed:
• The standard was not washed during the comparison.
• Each NMI applied its own method to measure the mass of the standard, in order to achieve uncertainties as low as possible, according to its capabilities.
• The CIPM-2007 formula [1] was applied by all the participants in order determine the air density. The buoyancy corrections were applied by the participants retrospectively after the circulation of the transfer standard.
4. Schedule The measurements followed the schedule shown in Table 2.
Table 2. Measurement order and dates
N° Institute / Country
Date
-- CENAM / Mexico
July 2009
1 LACOMET / Costa Rica October 2009
2 LATU / Uruguay
January 2010
3 INTI / Argentina
April 2010
4 CESMEC / Chile
July 2010
5 CENAM / Mexico
June 2011
6 NRC /Canada 7 INMETRO/Brazil -- CENAM / Mexico
February 2011 January 2012 August 2012
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5. Stability of the standard The drift of the standard was evaluated from three measurements performed by CENAM, in July 2009, in June 2011, and in August 2012. The corresponding mass errors associated uncertainties are shown in Table 3. The corresponding normalized error En values are included too. Also, all these results are presented in Figure 1.
Table 3. Stability of the standard. Values obtained by CENAM
e / mg U (k=2)
En
July 2009
1,090
0,038
-0,1
June 2011
1,102
0,031
0,1
August 2012
1,096
0,031
0,0
It can be concluded that no significant effects associated to drifts of the standard are to be considered.
6. Summary of the reported results The results sent by the participants are expressed as the mass error e from the nominal value 1 kg. They are shown in Table 4, as well as the corresponding uncertainty U (for k = 2).
Table 4. Mass errors e as reported by the participants, their associated uncertainties U (for k = 2), and non-linked reference value (NLRV)
e / mg
U / mg
LACOMET
1,050
0,098
LATU
1,143
0,070
INTI
1,051
0,056
CESMEC
1,060
0,160
CENAM
1,102
0,031
NRC
1,064
0,042
INMETRO
1,050
0,100
NLRV
1,083
0,020
7. Data consistency and calculation of a (non-linked) reference value In order to check the consistency among the results, a 2 test as proposed in [2] was applied. The
conditions to apply the so-called procedure A were assumed. The observed sum of squares
corresponding to the whole set of results was
2 obs
7,2
while the corresponding critical value for
6 degrees of freedom and significance level = 0,1 is 10,6. So, the reported data can be
considered as consistent.
The weighted average was calculated according to the same publication and has been established
as the non-linked reference value of the comparison (NLRV). It is shown in the last row of table 4,
as well as its associated uncertainty.
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Then, for each participant, degrees of equivalence D and normalized errors En were calculated according to (1)
D e NLRV ;
UD 2
u2 u2 ; NLRV
En D U D
(1)
where e, u are the results reported by the participant. These values are shown in Table 5. The values of D and UD are plotted in Figure 2.
Similarly, bilateral differences between pairs of participants and bilateral normalized errors were calculated according to (2). They are shown in Tables 6A and 6B.
Dij xi x j
Eij 2
Dij
ui2
u
2 j
(2)
Table 5. Degrees of equivalence and normalized errors,
respect to the non linked reference value
D / mg UD / mg
En
LACOMET
-0,03
0,10
-0,3
LATU
0,06
0,07
0,9
INTI
-0,03
0,05
-0,6
CESMEC
-0,02
0,16
-0,1
CENAM
0,02
0,02
0,7
NRC
-0,02
0,04
-0,5
INMETRO
-0,03
0,10
-0,3
Table 6A. Bilateral differences Di j= xi - xj, where xi refers to the result reported by the laboratory in the left column and xj refers to the result reported by the laboratory in the top row
Dij / mg LACOMET LATU
INTI
CESMEC CENAM
NRC
LATU
0,09
INTI
0,00
-0,09
CESMEC
0,01
-0,08
0,01
CENAM
0,05
-0,04
0,05
0,04
NRC
0,01
-0,08
0,01
0,00
-0,04
INMETRO
0,00
-0,09
-0,00
-0,01
-0,05
-0,01
Table 6B. Bilateral normalized errors Eij according to (2)
LACOMET LATU
INTI
LATU
0,8
INTI
0,0
-1,0
CESMEC
0,1
-0,5
0,1
CENAM
0,5
-0,6
0,8
NRC
0,1
-1,0
0,2
INMETRO
0,0
-0,8
0,0
CESMEC
0,2 0,0 -0,1
CENAM
-0,7 -0,5
NRC -0,1
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8. Link to CCM key comparisons In order to demonstrate equivalence, the present comparison was linked to CCM.M.M.K4 [3]. CENAM and NRC have participated in it and act as linking laboratories. Their degrees of equivalence (difference D0 from K4 reference value and the corresponding uncertainty U0 for k = 2) are shown in table 7:
Table 7. Degrees of equivalence of the linking
laboratories in CCM.M.M.K4
D0 / g
U0 / g
CENAM
-12
27
NRC
-14
34
The reference value linked to CCM.M.M.K4 (linked reference value) was calculated as:
LRV wC
eC D0,C wN wC wN
eN D0,N
(3)
where the subscripts C and N refer to CENAM and NRC data respectively, and the weights w are calculated as:
wC
u2
eC
1 DC,0
1 uC2 UC2,0
; 4
wN
u2
1 eN DN,0
1 uN2 UN2 ,0
4
(4)
The standard uncertainty associated to the linked reference value is
uLRV
1 wC wN
(5)
For the calculations in (4), the linking laboratories results in both comparisons were considered non-correlated.
So, (3) and (5) yield:
LRV 1.099 mg; uLRV 0.017 mg
Then, new degrees of equivalence were calculated, considering deviations DL = e - LRV, and
associated uncertainties UL 2
u
2 x
u2 LRV
. Then, linked normalized errors EnL were obtained as:
EnL DL U L
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These results are shown in table 8 and in Figure 2.
Table 8. Linked degrees of equivalence and normalized errors
DL/mg
UL/mg
EnL
LACOMET
-0,049
0,103
-0,5
LATU
0,044
0,077
0,6
INTI
-0,048
0,065
-0,8
CESMEC
-0,039
0,163
-0,2
CENAM
0,001
0,046
0,0
NRC
-0,035
0,053
-0,7
INMETRO
-0,049
0,105
-0,5
Figure 1. Plot showing the stability of the standard during the comparison (uncertainty bars correspond to k = 2)
1,2
m / kg
1,1
1,0 July 2009
June 2011
August 2012
Figure 2. Deviations D from NLRV and their associated expanded uncertainties (k = 2). The solid pink lines represent the expanded uncertainty (k = 2) associated to NLRV.
0,2
0,1
D / mg
0,0
-0,1
-0,2
LACOMET LATU
INTI CESMEC CENAM NRC INMETRO
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Figure 3. Deviations DL from LRV and their associated expanded uncertainties (k = 2). The solid pink lines represent the expanded uncertainty (k = 2) associated to LRV.
0,2
DL / mg
0,1
0,0
-0,1
-0,2
LACOMET LATU
INTI CESMEC CENAM NRC INMETRO
References
1. Picard A., Davis R.S., Gläser M., Fujii K., Revised formula for the density of moist air (CIPM2007), Metrologia 45 (2008), 149-155
2. Cox, M.G., The evaluation of key comparison data, Metrologia 39 (2002) 589-595
3. Luis Omar Becerra et al. Final Report of Key comparison of 1 kg stainless steel mass standards CCM.M-K4, Organized by the Working Group on Mass Standards of the Consultative Committee for Mass and Related Quantities (CCM) 2014, http://kcdb.bipm.org/appendixB/AppBResults/CCM.M-K4/CCM.M-K4.pdf
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