1.5 Evaluation of regional key comparison data
1.5.1 Two approaches to interpreting and evaluating data of regional
The NMIs participate in the realization of the MRA through the regional metrological organizations. The basic problems of the RMO comparisons are
the extension of metrological equivalence to the NMIs which have not participated in CIPM key comparisons by way of conducting RMO key comparisons;
the confirmation of the calibration and measurement capabilities the NMIs have claimed by conducting supplementary comparisons.
In the MRA the procedure of linking RMO and CIPM key comparisons is treated as follows:“The results of the RMO key comparisons are linked to key comparison reference values established by CIPM key comparisons by the common participation of some institutes in both CIPM and RMO comparisons. The uncertainty with which comparison data are propagated depends on the number of institutes taking part in both comparisons and on the quality of the results reported by these institutes”.
The emphasis should be placed on the following aspects that are apparent from the quoted text:
linking of RMO and CIPM key comparisons is understood as a linking of regional comparison results with the KCRV, the value of which is established in CIPM key comparisons;
practically the linking is realized through the results of the participants of both com- parisons, the so-called “linking institutes (laboratories)”;
the procedure of linking inevitably introduces an additional component of uncer- tainty which depends on the number of linking institutes and the quality of their measurement results.
Let us consider the two schemes of realizing the linking procedures which are most oftenrealized in practice.
Example 1.Comparisons of microphones within the frequency range 125 Hz to 8 kHz.
First there were performed key comparisons CIPM – CCAUV.A-K12, in which twelve NMIs took part. The NPL (UK) was designated as pilot laboratory. The measurement procedure did not differ from routine calibration. All participants calibrated two trav- eling measurement standards in the points given. The KCRV was determined as a simple mean for a given frequency. Since the measurement results demonstrated the identical behavior for both microphones in the process of comparison, the results were averaged.
2 http://kcdb.bipm.org/AppendixB/KCDB_ApB_info.asp.
CCAUV.A-K1-K1
NPL (United Kingdom) pilot
DPLA (Denmark) NIST (United States)
NMIJ (Japan) PTB (Germany)
KRISS (Korea) CSIR-NML (South Africa)
CSIRO (Australia) NRC (Canada) CENAM (Mexico)
GUM (Poland) VNIIFTRI (Russia)
APMP.AUV.A-K1
NMIJ (Japan) KRISS (Korea) CMS/ITRI (Taiwan)
NIM (China) NIMT (Thailand) NMIA (Australia) NML/SIRIM (Malaysia)
NPLI (India) SCL (Hong Kong)
Figure 1.3.Participants of the CCAUV.A-K1-K1 – APMP.AUV.A-K1.comparisons.
Right after the CIPM comparisons, the regional comparisons APMP.AUV.A-K13, were carried out, in which nine NMIs took part. The comparison participants are pre- sented in Figure 1.3. The regional comparisons were performed according to a similar scheme. Laboratories in Japan, Korea, and Australia participated in both comparisons.
But only the laboratories in Japan and Korea were chosen as the linking ones, since the laboratory in Australia changed its equipment between the comparisons and, con- sequently, the systematic components also changed, and it was necessary to redefine its degrees of equivalence.
The linking between the comparisons was realized by adding a correction for the difference between the values of a measurand to the measurement results of the re- gional comparisons. This correction was calculated as a mean of the differences of the results which the linking institutes had obtained in the CIPM and RMO key com- parisons. The deviations of the thusly transformed results of the regional comparisons from the KCRV did not exceed the corresponding uncertainties, which is the confir- mation of their calibration capabilities according to the criterionEn.
The scheme of linking the regional and the CIPM comparisons is rather common in practice. Conditionally, it may be called the scheme of “transformation” of regional comparison results to the level of CIPM comparisons. This transformation can be achieved by adding a term or multiplying factor [96, 121, 135, and 157].Different principles of transformation will be considered below. It is important to note that a
3 http://kcdb.bipm.org/AppendixB/KCDB_ApB_info.asp.
Section 1.5 Evaluation of regional key comparison data 17
CENAM (Mexico) – pilot DPLA (Denmark) NPL (United Kingdom)
PTB (Germany) NMIJ (Japan) LNE (France) KRISS (Korea) GUM (Poland)
COOMET.AUV.A-K3.
DPLA (Denmark) GUM (Poland) VNIIFTRI (Russia)
INM (Romania)
CENAM (Mexico) – pilot DPLA (Denmark) NIST (United States)
NIM (China) CSIRO (Australia)
NRC (Canada) UME (Turkey) INMETRO (Brazil) VNIIFTRI (Russia) CCAUV.A-K3
Figure 1.4.Participants of the comparisons CCAUV.A-K3 and COOMET.AUV.A-K3.
procedure such as this is always accompanied by an increase in the measurement un- certainty of regional comparisons.
Example 2.Comparisons CCAUV.A-K3, COOMET.AUV.A-K34. The participants of comparisons are presented in Figure 1.4. These are also comparisons of micro- phones which a similar construction. But comparisons CCAUV.A-K3 were organized using a different scheme. Two complete sets of traveling measurement standards had been sent consisting of two microphones each to shorten the comparison time. Also, only two laboratories calibrated all four microphones during the comparison.
Thus the problem arose of providing a link of different circles of one and the same CIPM comparison. This problem was solved by applying the least-squares method [306]. The estimates of traveling standard values were obtained, and the degrees of equivalence were calculated. Then the criterion2was applied for checking the consis- tency of all data. This served as the confirmation of the calibration capabilities claimed by the participants of the whole group.
This approach was disseminated to the evaluation of data of the regional compar- isons COOMET.AUV.A-K3, which were considered as an additional circle of key comparisons. The data of the regional comparisons was combined with the data of the CIPM comparisons, and the pooled data was evaluated by the least-squares method.
An approach such as this naturally leads to a recalculation of the reference val- ues and degrees of equivalence established in the CIPM key comparisons. In order to reduce this effect to a minimum in processing the results of these particular compar-
4 http://kcdb.bipm.org /AppendixB/KCDB_ApB_info.asp
isons, only results of one linking laboratory, those of the Danish NMI, were taken into account.
After that, the pooled data consistency was checked, applying2criterion with the purpose of confirming the claimed calibration capabilities. It should be noted that the given approach for linking the regional comparisons does not lead to any increase of the initial uncertainty of regional comparison results, since the joint RMO-CIPM comparison is interpreted as a single key comparison including a number of circles with various (but similar) sets of traveling standards. It is important for these circles to be “crossed” through the results of linking institutes. This enables the tracing of the link of any two results through an uninterrupted chain.
These examples illustrate two existing approaches to understanding and interpret- ing the relationship between the RMO and CIPM key comparisons [96]. For the first approach this relationship is understood as a hierarchy scheme, on the upper level of which the CIPM key comparisons are located. In these comparisons the KCRV and degrees of equivalence of the participants are established, which remain fixed until the next CIPM key comparisons. The linking of the RMO KC with the KCRV is realized through the results of the linking institutes.
In the second approach all subsequent regional comparisons are perceive as loops of a single uninterrupted key comparison. With the appearance of new information all perviously obtained estimates have to be continuously recalculated.
Below only the first approach to ensuring the linking of comparisons will be treated as more appropriate for the MRA methodology, and the mathematical approaches that will be presented are intended just for its realization.