Linking results of key and supplementary comparisons of AC/DC voltage transfer references

. A regional key comparison (KC) COOMET.EM-K6.a and a supplementary comparison (SC) COOMET.EM-S1 of AC/DC voltage transfer references were conducted between participating laboratories from the Eurasian region. Measurements were made over the period 2004 – 2014. The results showed good agreement between all but one of the participating laboratories. The proposed procedure of linking results of key and SCs of regional metrology organization of AC/DC voltage transfer references is presented. Linking results is realized for COOMET.EM-K6.a and CCEM-K6.a KCs, and for COOMET.EM-K6.a KC and COOMET.EM-S1 SC.


Introduction
Mutual recognition arrangement (MRA) of International Committee for Weights and Measures (CIPM) for national measurement standards and for calibration and measurement certificates issued by national metrology institutes (NMIs) is a response to a growing need for an open, transparent and comprehensive scheme to give users reliable quantitative information on the comparability of national metrology services and to provide the technical basis for wider agreements negotiated for international trade, commerce and regulatory affairs.
A regional metrology organization (RMO) key comparison (KC) is executed in the framework of a RMO. The link to the KC reference value (RV) for a KC carried out by a RMO is obtained by reference to the results from those NMIs which taken part in the CIPM KC also. The degree of equivalence relative to the KC RV of a measurement standard or a measurement result is the degree which the measured value is consistent with the KC RV [1,2].
To allow the participation in KC of all the NMIs of an RMO, the RMOs may organize their own KC. The RMO KC must be linked to the corresponding CIPM KC by means of joint NMIs (linking NMIs). This is mandatory to demonstrate global equivalence. Instead of the method to determine of RV, the RMO KC protocol must include the way which the results will be linked to the corresponding CIPM KCRV.
A supplementary comparison (SC) is a comparison, usually carried out by an RMO to meet specific needs not covered by KC (e.g. regional needs), for instance measurements of specific artefacts, or measurements of parameters not within the "normal" scope of the Consultative Committees (CC) of CIPM, and for supporting confidence in calibration and measurement certificates of NMIs [1,3].
SCs are normally organized by the RMOs to cover areas or techniques not covered by KCs. Rules for the participation in CIPM and RMO KCs apply to CIPM and RMO SCs also. The differences are next: approval is given by the corresponding RMO committee; degrees of equivalence relative to a SC RV may be computed, but this is not mandatory.
The proposed procedures linking of results of KCs CC of electric and magnetism (CCEM) and RMO of AC/DC voltage transfer references (COOMET.EM-K6.a [4] to CCEM-K6.a [5]), and key and SCs of RMOs of AC/DC voltage transfer references (COOMET.EM-S1 [6] to COOMET.EM-K6.a) was realized with using results of linking NMI (VNIIM, Russia).

Travelling standards for comparisons
The COOMET.EM-K6.a is the KC of national AC/DC voltage transfer references between the countries À participants of the RMO COOMET. In this comparison took part five NMIs: State Enterprise "Ukrmetrteststandard" (UMTS, Ukraine); VNIIM (Russia); SMS (Azerbaijan); BelGIM (Belarus); INM (Romania). UMTS (Ukraine) was the pilot laboratory in COOMET.EM-K6.a KC which would be responsible for providing the travelling standard, coordinating the schedule, collecting and analyzing the comparison data, and preparing of draft reports.
The coaxial connector for input voltage of the traveling standard П=ТЭ-6А is completed by detachable adapter in order to provide adaptation to usual connector N-type (female) [4].
The COOMET.EM-S1 SC is the comparison of national AC/DC voltage transfer references between the countries À participants of the RMO COOMET. In this comparison took part two NMIs: VNIIM (Russia) and UMTS (Ukraine). The VNIIM was pilot laboratory which is responsible for providing travelling standard, coordinating the schedule, collecting and analyzing the comparison data, and preparing of draft reports.
The AC/DC Thin-film Planar Multi-junction Thermal Converter (PMJTC) was used as the traveling standard. This PMJTC marked as 256 [6].
The input signals for COOMET.EM-K6.a and COO-MET.EM-S1 comparisons are shown in Table 1.

Proposed linking key comparisons procedure
Proposed to link the results from COOMET.EM-K6.a [4] to the CCEM-K6.a [5] which carried out between 1993 and 1999. VNIIM (Russia) is linking NMI as far as they participated in CCEM-K6.a. The procedure used for RMO KC data evaluation is intended to provide linking to CIPM KC data with low uncertainty [7,8].
The degrees of equivalence of ith NMI with respect to linking to CCEM-K6.a is estimated as with combine standard uncertainties where u c (x i ) is uncertainty of results from COOMET.EM-K6.a for NMI participant in COOMET.EM-K6.a. Measurements from the linking NMIs provide estimates where d iLINK is result from CCEM-K6.a for a linking NMI; D iLINK is result from COOMET.EM-K6.a for a linking NMI.
The linking NMI is VNIIM (Russia). No significant changes to the method of measurement used in CCEM-K6. a and COOMET.EM-K6.a were made by VNIIM. Table 2 lists the values of the quantities used in the calculation.
The best estimate of the result from NMI i had it participated in CCEM-K6.a is calculated using (1). The standard uncertainty is calculated as: where u(m ref ) = 0.018 is the uncertainty in u(m ref ), the CCEM-K6.a KCRV. The expanded uncertainty is The calculated degrees of equivalence with respect to CCEM-K6.a KCRV are tabulated in d i Table 3 (Azerbaijan is not significant of CIPM MRA in 2014).
The declared uncertainties are judged as confirmed if the following equation is satisfied    the measurement uncertainties claimed by the participants of comparisons are confirmed that, essentially, is the confirmation of corresponding measurement CMC [8,9]. Results of COOMET.EM-S1 SC(2) to be linked to COOMET.EM-K6.a KC(1) (SC to the KC). VNIIM (Russia) is linking NMI as far as they participated in CCEM-K6.a. RVs and its uncertainties are given in Table 4.
The degree of equivalence D i of AC/DC voltage transfer references and its expanded uncertainty U(D i ) that participated in COOMET.EM-K6.a [4] and COOMET. EM-S1 [6] comparisons are shown in Table 5 for frequencies 1 kHz; 20 kHz; 100 kHz; 1 MHz.
For each of the joint participants in both comparisons was calculated degree of equivalence and it uncertainty with used next formula [14]: where x i is measured value for participant; RV j is reference value of comparison (for frequencies for frequencies 1 kHz; 20 kHz; 100 kHz; 1 MHz); r i is correlation between the results from the participant and the RV j ; u(x i ) is combined   standard uncertainty of measured value for NMI; u(RV j ) is combined standard uncertainty of RV j . If correlations have been ignored (r i = 0) The results of the COOMET.EM-S1 comparison are to be expressed in relation to the COOMET.EM-K6.a RV À RV K6a . For this purpose the degrees of equivalence of COOMET.EM-S1 comparison (indicated D S1 ), will be corrected by a correction d, which is determined from the results of the participant linking NMI (VNIIM): where D K6aVNIIM is degree of equivalence of national standard VNIIM in COOMET.EM-K6.a KC; D S1VNIIM is degree of equivalence of national standard VNIIM in COOMET.EM-S1 comparison with the uncertainty: VNIIM correction d and its uncertainties are shown in Table 6.
The corrected degrees of equivalence for the participants in COOMET.EM-S1 in terms of RV K6a are then given by: with the uncertainty: The corrected degrees of equivalence for UMTS as participant of COOMET.EM-S1 in terms of RV K6a and it expanded uncertainty are shown on Table 7 and Figure 5 (COOMET.EM-K6.a; *COOMET.EM-S1, 1 kHz, 10 kHz, 100 kHz) and Figure 6 (COOMET.EM-K6.a; *COOMET. EM-S1, 1 MHz). Result of UMTS is linked to the COOMET.EM-K6.a comparison with using proposed procedure.  Table 7. Degrees of equivalence of UMTS and its uncertainties for COOMET.EM-S1 in terms RV COO-MET.EM-K6.a, 10 À6 . The results of a regional KC COOMET.EM-K6.a and SC COOMET.EM-S1 of AC/DC voltage transfer references showed good agreement between all but one of the participating laboratories. The results of RMO SCs for confirming CMCs NMIs are used. For each of the joint participants in key and SCs for equal nominal of electrical quantity can be calculated degrees of equivalence national standards and it uncertainty in term KC RV.
The procedure of practical linking the results of KCs CCEM and RMO of AC/DC voltage transfer references, and key and SCs of RMOs of AC/DC voltage transfer references are proposed.