CCM Key Comparison CCM.D-K4 Hydrometer

Transcription

1 CCM.D-K4 Hydrometers Page of 45 Final report CCM Key Comparison CCM.D-K4 Hydrometer S. Lorefice, L. O. Becerra, E. Lenard 3, Y. J Lee 4, W.G. Lee 4, T. Madec 5, P. A. Mery 5, J. Cáceres 6, C. Santos 6, C. Vámossy 7, J. Man 8, K. Fen 8, K. Toda 9, J. Wright 0, H. Bettin, H. Toth Istitto Nazionale di Ricerca Metrologica (INRiM) Strada delle Cacce, 9; 035 Torino, ITALY Centro Nacional de Metrologia (CENAM) Km 4.5 Carretera a los Cés, Mpio El Marqés, Qerétaro MEXICO Główny Urząd Miar (GUM) l. Elektoralna ; Warszawa POLAND Korea Research Institte of Standards and Science (KRISS) 67 Gajeong-Ro Yseong-G, Daejeon REPUBLIC of KOREA Laboratoire National de Métrologie et d Essais (LNE), re Gaston Boissier ; 7574 Paris Cede 5, FRANCE Laboratorio Tecnológico del Urgay (LATU) Av. Italia 60, Montevideo - URUGUAY Magyar Kereskedelmi Engedélyezési Hivatal (MKEH)., Németvölgyi út 37-39; 4 Bdapest - HUNGARY National Measrement Institte (NMIA) Bradfield Rd, Lindfield, NSW AUSTRALIA National Metrology Institte of Japan (NMIJ) -8-3, Midirigaoka, Ikeda, Osaka, JAPAN National Institte of Standards and Technology (NIST) 00 Brea Dr., Mail Stop 836, Gaithersbrg, MD 0899 USA Physikalisch-Technische Bndesanstalt (PTB) Bndesallee 00; 386 Branschweig GERMANY S.Lorefice@inrim.it INRiM, Italy Janary 06

2 CCM.D-K4 Hydrometers Page of 45 CCM.D-K4 Hydrometer Abstract This report presents the comparison philosophy, methodology, analysis and the reslts of the designed CCM.D-K4 key comparison that covered the calibration of high resoltion hydrometers for liqid and alcoholometers in the density range 600 kg/m 3 to 000 kg/m 3 at the temperatre of 0 C. The main prpose of this comparison was not only to evalate the degree of eqivalence in the calibration of high accracy hydrometers between NMI participants, bt also to link, were it is possible, the reslts of previos Comparisons to Key Comparison Reference Vales (KCRVs) of CCM.D-K4. Eleven NMI laboratories took part in the CCM.D-K4 divided in two grops (petals). With the CCM.D-K4 prpose, two similar sets consisting of three hydrometers for liqid density determinations and an alcoholometer were circlated to the NMI participants as a travelling standard in the time interval from Janary 0 to April 0. Twelve Key Comparison Reference Vales (KCRVs) for each petal have been obtained at the density vales related to the tested density marks of the transfer standards by the reslts of participants. The KCRVs and corresponding ncertainties were calclated by the weighted mean in the case of consistent reslts, otherwise the median was sed. The degree of eqivalence (DoE) with respect to the corresponding KCRV was determined for each participant and, in this particlar comparison, the Weighted Least Sqares (WLS) method was sed to link the individal DoE of each participant by a continos fnction. Significant drift of the transfer standards was not detected. This report also gives instrctions on calclating pair-wise degrees of eqivalence, with the addition of any information on correlations that may be necessary to estimate more accrately as well as the procedre for linking international comparisons to the CCM.D-K4. Finally an eample of linkage to the CCM.D-K4 is given by dealing with the reslts of the bilateral comparison between INRiM and NMIA, which was added to this comparison so that all participants were engaged after the breakage of the artefact. A particlarly good agreement was fond among the reslts provided by most of the participants, even if some systematic differences and either nderestimated or overestimated ncertainties of the sbmitted reslts can be identified with respect to the KCRVs. In general the deviations of the laboratory reslts to the KCRVs are within of /3rd to /4th of a scale division and the ncertainty at 95 % is sally within half a division. Dring the analysis of the sbmitted reslts, a systematic difference between the first and last immersed mark was also noted, possibly de to a temperatre gradient along the stem and/or wetting of the stem arond the tested mark, and therefore a corrected claimed ncertainty from each laboratory is epected. However this comparison may help the laboratories to solve some residal or marginal problems as well as to better nderstand the ncertainty components. The comparison flly spports the calibration measrement capabilities table in the BIPM key comparison database (KCDB). The reslts can be sed to link regional comparisons to this CCM key comparison

3 CCM.D-K4 Hydrometers Page 3 of 45 Table of contents Abstract. PREFACE 4. ORGANIZATION 6. Participants and schedle 6. Transfer standards (hydrometer samples) 6.3 Conditions selected 7.4 Procedre and method of measrement 0.4. Uncertainty claims of NMIs 3. RESULTS 3. Data received from participants 3. Commnication from the participating laboratories Interpretation of the comparison: the degree of eqivalence DoE Key Comparison Reference Vales (KCRV) and degrees of eqivalence Continos fnctions of DoEs Degree of eqivalence between pairs of NMIs Linkage of international comparisons to the CCM.D-K The bilateral comparison INRiM NMIA and its linkage to CCM.D-K4 4. DISCUSSION and CONCLUSION 3 References 5 Acknowledgements 5 Appendi A 6 Hydrometer S/N Hydrometer S/N Hydrometer S/N Hydrometer S/N Hydrometer S/N Hydrometer S/N Hydrometer S/N Hydrometer S/N Appendi A 43

4 CCM.D-K4 Hydrometers Page 4 of 45. PREFACE A CIPM key comparison concerning the calibration of high resoltion hydrometers for liqid density determinations in the range 600 kg/m 3 to 000 kg/m 3 at the temperatre of 0 C was proposed dring the meeting of the Working Grop on Density (WG-Density) of the Consltative Committee for Mass and Related Qantities (CCM) held on April nd, 008 at the BIPM with the prpose to: Recognize and compare the different eperimental setps and calibration methods applied by the participants; Compare the participants methods for the ncertainty evalation and ascertain the consistency of their calibration reslts; Allow linkage of the regional comparisons previosly performed nder the aspices of the Regional Metrology Organizations APMP, EURAMET and SIM. This CIPM key comparison program, designated as CCM.D-K4 Hydrometer, was coordinated by the Istititto Nazionale di Ricerca Metrologica (INRiM, Italy). The Physikalisch-Technische Bndesanstalt (PTB, Germany) and the Centro Nacional de Metrologia (CENAM, Meico) spported the pilot to determine the technical protocol for this key comparison. A total of National Metrology Instittes, divided into two grops took part in this comparison. The Key comparison CCM.D-K4 Hydrometer, which covered the density range 600 kg/m 3 to 000 kg/m 3 at 0 C, comes after varios comparisons in Hydrometry performed everywhere since the 90s. For the prpose of this project two similar sets consisting of three high-accracy hydrometers for liqid density determinations and an alcoholometer (alcohol hydrometer) cl. were arranged and each set of them was circlated to each of the two grops as travelling standards in the time interval from Janary 0 to April 0. The corrections to be applied to the stated scale readings at 0 C is often the parameter compared in inter-comparisons. Each laboratory, belonging to an individal petal, determined the corrections to be applied to three stated scale readings at 0 C of different hydrometers in accordance with the technical protocol and the report form received in advance []. The present report, which is based on the niform treatment of the reslts of the participants, describes the organization of the actal project, the method for analysis of the calibration data and the comparison reslts. The reslts also allowed determination of the degrees of eqivalence of each participating NMI with the Key Comparison Reference Vales (KCRV) of the CCM.D-K4. The Final report is intended to be a pblication for the CIPM Key Comparison Data Base.

5 CCM.D-K4 Hydrometers Page 5 of 45 Table. List of the participating NMIs and technical contacts. Laboratory Istitto Nazionale di Ricerca Metrologica (INRiM) Strada delle Cacce, Torino - ITALY Centro Nacional de Metrologia (CENAM) Km 4.5 Carretera a los Cés, Mpio El Marqés, Qerétaro - MEXICO Korea Research Institte of Standards and Science (KRISS) Div. Physical Metrology Center for Mass and Related Qantities 67 Gajeong-Ro Yseong-G, Daejeon REPUBLIC of KOREA Physikalisch-Technische Bndesanstalt (PTB) Bndesallee Branschweig - GERMANY Magyar Kereskedelmi Engedélyezési Hivatal (MKEH) 4 Bdapest., Németvölgyi út Bdapest - HUNGARY National Institte of Standards and Technology (NIST) 00 Brea Dr., Mail Stop 836, Gaithersbrg, MD 0899 United States of America National Metrology Institte of Japan (NMIJ) -8-3, Midirigaoka, Ikeda, Osaka, JAPAN Central Office of Measres - Glówny Urzad Miar (GUM) Physical Chemistry Department, Density, Viscosity and Spectral Analysis Laboratory, l. Elektoralna Warszawa - POLAND Laboratoire National d'essais (LNE) re Gaston Boissier 7574 Paris Cede 5 - FRANCE National Measrement Institte (NMIA) Bradfield Rd, Lindfield, NSW AUSTRALIA Laboratorio Tecnológico del Urgay (LATU) Av. Italia 60 Montevideo - URUGUAY Contry code IT MX KR DE HU US JP PL FR AU UY Contact Person Salvatore Lorefice s.lorefice@inrim.it Tel: Fa: Lis Omar Becerra lbecerra@cenam.m Tel.: to 04 et. 360 Fa: Yong Jae Lee yjlee@kriss.re.kr Tel.: Fa: Hans Toth, Horst Bettin Hans.Toth@PTB.DE Horst.Bettin@PTB.DE Tel.: Fa: Csilla Vámossy vamossycs@mkeh.h Tel.: Fa: John Wright John.wright@nist.gov Tel Fa: Knihiko Toda k.toda@aist.go.jp Tel.: Fa: Elżbieta Lenard, e.lenard@gm.gov.pl Tel : Fa : Tangy Madec, Pal-Andre Mery tangy.madec@lne.fr Pal-Andre.Mery@lne.fr Tel: Fa: John Man, Kitty Fen John.man@measrement.gov.a Kitty.fen@measrement.gov.a Tel.: Fa: Joselaine Cáceres, Cladia Santo jcaceres@lat.org.y csanto@lat.org.y Tel.: Fa:

6 CCM.D-K4 Hydrometers Page 6 of 45. ORGANIZATION. Participants and schedle Ten NMIs, pls the pilot institte, agreed to participate in the comparison ab-initio. Table comprises the participating NMIs and the technical contacts. For the prpose of this project, the participating laboratories were divided into two grops (petal A and petal B) the three laboratories INRiM, CENAM and PTB performed measrements in both loops. The organization of the comparison was changed in the density range of 000 kg/m 3 de to the breakage of one alcoholometer, a bilateral comparison between INRiM and NMIA was added to the two schedled petals so that all participants were engaged. In addition to the nforeseen difficlty relating to the artefact breakage, transportation, cstoms and administrative constraints forced changes in the original schedle of the comparison. Table shows the cstom formalities reqired for movement of goods in international trade and Table 3 shows the final circlation scheme defined for each artefact.. Transfer standards (hydrometer samples) INRiM spplied two similar sets of for hydrometers to be assigned to each petal and sed as transfer standards (TSs) at 0 C, as shown in Table 4. Each set consisted of two hydrometers with a scale division of 0. kg/m 3 working close to 600 kg/m 3 and 500 kg/m 3, an alcoholometer (alcohol hydrometer) cl. and a hydrometer with a scale division of 0. kg/m 3 working close to 000 kg/m 3. The cbic epansion coefficient for all hydrometers was assmed to be C - with an ncertainty of 0-6 C -, rectanglar distribtion. Dring the transfer one of the two alcholometers was broken and it was replaced with another one having the same physical featres. Table. Cstom formalities reqired for the movement of the transfer standards throgh the Laboratory participants Formalities Petal A Petal B A.T.A Carnet Japan (NMIJ) Astralia (NMIA), Korea (KRISS), USA (NIST) Proforma invoice Meico (CENAM), Urgay (LATU) Meico (CENAM) Free circlation France (LNE), Germany (PTB), Poland (GUM), Italy (INRiM) Hngary (MKEH), Italy (INRiM)

7 CCM.D-K4 Hydrometers Page 7 of 45 The pilot laboratory did not detect any significant change in calibration on any of the artefacts after retrning from circlation. Althogh at present these conditions did not allow to determine the stability of each artifact for a long time, they confirm the stability of the transfer standards dring the comparison..3 Conditions selected The corrections to be applied to the stated scale readings at 0 C is sally the measrand in hydrometry. The participating laboratories were asked to calibrate the assigned hydrometers at three gradations i ( to 3) of the scale and the correction C i had to be calclated for each one of them at the reference temperatre of 0 C: C i = ρ i ρ ri. () The participants were free to perform all measrements sing their own procedre as well as determining the density ρ i of the boyant liqid in which the hydrometer wold freely float at the scale mark ρ ri. The test points and the srface-tension vales of the liqid, in which each hydrometer was intended to be sed, were stated in advance. It was, however, reqired that the hydrometers only stay at the laboratory for the time necessary for calibration and not longer than the allotted time. When the standards arrived at the participating laboratory, a visal inspection was made and each artefact was allowed to acclimate to the laboratory environment in agreement with the given instrction. INRiM collected all information concerning the stats of the transfer standards, the apparats sed dring the comparison and the measrement reslts of each participant n of the j petal (j=a or B), hereinafter referred to as jni instead of the symbol C i of eqation () at the tested density mark i.

8 CCM.D-K4 Hydrometers Page 8 of 45 Table 3. Final circlation scheme defined for each artefact. Institte (schedled period) Id. hydrometer Range in kg/m INRiM (9//0 0/0/) X X X X X X X X X NMIA (04/03 7/03/) X X X X CENAM (9/03 6/04/) (06/06 05/07/) X X X X X X X X LATU (03/08 3/08/) X X X X NMIJ (4/0 4/0/) X X X X KRISS (06/0 4/0/) X X X X NIST (8/07 03/08/) X X X X LNE (04/0 6//) X X X X GUM (0// 6/0/) X X X X MKEH (06/0 0/0/) X X X X PTB (/03 7/04/) X X X X X X X X

9 CCM.D-K4 Hydrometers Page 9 of 45 Table 4. Technical information and a pictre related to the reference hydrometers sed as transfer standards (TS) in this key comparison. Petal A Petal B Scale div. of body [mm] Length of body [mm] of stem [mm] Length of stem [mm] Weight [g] g/cm 3 g/cm 3 g/cm % Vol. 0 0 % Vol. 0. % Vol g/cm 3 g/cm 3 g/cm g/cm 3 g/cm 3 g/cm 3

10 CCM.D-K4 Hydrometers Page 0 of 45.4 Procedre and method of measrement Table 5 smmarizes the differences in the eqipment sed at each NMI and in their calibration procedres. All participants carried ot their task by adopting the hydrostatic weighing in a single liqid, the density of which was known for the test temperatre (Cckow s method). For laboratories: KRISS, NMIJ, NMIA and LATU sed two different balances for weighing the tested hydrometer in air and immersed in the boyant liqid, respectively. The weighing method was the direct reading of the balance for INRiM, MKEH, NIST, NMIJ and LATU while the laboratories CENAM, KRISS, PTB, GUM, LNE and NMIA sed the balance as a comparator and the sbstittion weighing by means of calibrated weights was performed to achieve the balance readings within a narrow electronic range. Straight chain alkanes sch as n-pentadecane, n-nonane, n-tridecane and n-tetradecane were sed by the different laboratories as boyant liqids. Each participant measred the density of the sed liqid by hydrostatic weighing, oscillating-type density meter, and sensitive standard hydrometers. However each laboratory monitored the stability of the density of the boyant liqid at least before and after the hydrometer calibration by sing the same instrments and standards sed to determine the density of the boyant liqid. The majority of participants measred the srface tension of the boyant liqid by commercial available tensiometers by applying different measring methods, CENAM sed the stem measrement with the hydrostatic weighing and the MKEH knew the vales of interest from reference data. The mean of the parameters contribting to the air-density calclation were recorded dring calibration, i. e. pressre, temperatre, relative hmidity (or dew point). With the eception of KRISS, all laboratories assmed a constant vale of 0.04% for the CO content. The mean of the air-density vales was calclated by the CIPM formla (CIPM007) [] and reported. Accrate calipers or sitable instrments with a resoltion between 0.0 and 0. mm were sed to measre the diameter of the stem of the hydrometer to be calibrated. PTB sed an atomatic measring device by means of which the separation between gradation mark and the stem diameter throghot the whole scale of each hydrometer to be calibrated were measred. In general, the alignment of the liqid horizontal plane with the selected scale-mark is identified by CCD camera servo-assisted with a desktop compter or by monitor, a few laboratories sed a magnifier. The alignment principles by CCD camera were independently based on [3, 4, 5] althogh technical modifications were made by the sers.

11 CCM.D-K4 Hydrometers Page of 45 Table 5. Smmary of the eperimental facilities operated at the different NMIs. Institte Balance Ma capacity [g]/readability [g] Hydrostatic Weighing in air weighing Boyant liqid INRiM 505 / n-nonane Thermostat type, capacity Doble-walled glass vessel, 30 litre Thermometer for liqid temperatre Pt00 Ohm, ASL F7 CENAM* 405 / n-pentadecane Tamson TV7000, 70 litre Pt00 Ohm, ASL F50 KRISS* 405 / / n-tridecane Lada RP840, litre Pt00 Ohm, ASL F300 PTB* 09 / n-tridecane Tamson TVBX 70, 70 litre MKEH 000 / n-nonane Tamson TMV70, 70 litre NIST 05 / n-tridecane Hart 70, 0 litre NMIJ 50 / / n-tridecane Doble-walled PVC and alminim vessel, 30 litre GUM* 09 / n-nonane Tamson TV7000, 70 litre LNE* 405 / n-tetradecane Tamson TV7000, 70 litre NMIA* 000 / / / n-nonane Colora NB33498, 5 litre SPRT 5 Ohm, PAAR MKT5 Pt00 Ohm, Hart Sci Black Stack 560 YSI Thermistor, Keithley 95A Pt00 Ohm, ASL F00 5 Ohm PRT, ASL F700B Pt00 Ohm, HP3440A Pt00 Ohm, Hewlett Packard LATU 00 / / n-tridecane Tamson TV7000, 70 litre Pt00 Ohm * Weighing procedre: By sbstittion method Alignment CCD camera PC aided CCD camera PC aided CCD camera PC aided CCD camera PC aided Magnifier hand-operated laser sheet + laser power meter Magnifier hand-operated Magnifier electronically controlled spport Magnifier hand-operated CCD camera hand-operated Magnifier hand-operated Srface tension method Plate Stem method, hydrostatic weighing Ring Plate Reference data D Noüy & Wilhelmy ring Plate Ring D Noüy & Wilhelmy ring Ring Ring

12 CCM.D-K4 Hydrometers Page of 45 Mechanical devices were sed for sinking the tested hydrometer or additionally, sinkers adjstable in height were sed in order that the liqid level corresponds to the scale mark concerned..4. Uncertainty claims of NMIs In addition to the ncertainty contribtions proposed in the worksheet by the coordinating laboratories [], several laboratories have inclded the contribtion de to standard deviation of the mean of corrections or reprodcibility of measrements. Moreover PTB also took into accont the contribtion de to the inflence of the temperatre distribtion in the bath, NMIJ the contribtions de to the weighing vale of sspension and the density of sed weights and NIST considered tridecane density changing, srface tension, and positioning the liqid srface at the mark to be calibrated (contribtion de to the contact angle of the boyant liqid on the hydrometer stem). 3. RESULTS After the participating laboratory completed its own measrements, all information concerning the calibration was sbmitted to the pilot laboratory sing the sheets Report Form and Report Form anneed to []. 3. Data received from participants The INRiM collected and analysed anything related to: a) Details of the instrmentation sed by each participant in the project, inclding the origin of their traceability to the SI. b) Details of the relevant information on the measrements and parameters sed for the comparison sch as local gravity, mass measrements, density of working flid and, finally, the ambient conditions inclding data on air density, air temperatre, air pressre, hmidity and CO content. c) Calclated vales of the three corrections for each transfer standard at the specified reading marks and srface tension vales. d) Uncertainty bdget of the twelve calclated corrections, which were estimated and combined following GUM [6] nder the responsibility of each participating institte. Each laboratory also reported the ncertainty of all measred qantities as well as the effective degrees of freedom eff of the combined standard ncertainty c, the t-factor

13 CCM.D-K4 Hydrometers Page 3 of 45 t 95 ( eff ) taken from the t-distribtion for a 95% confidence level and the epanded ncertainty for the corrections as U 95 = t 95 ( eff ) c. e) Analysis of reported data, INRiM elaborated all laboratory data as soon as they were available. Some participants were also invited to check for reslts that appeared to be anomalos before the Draft A was sent to them in agreement with the CIPM MRA-D-05, March 04 [7]. 3. Commnication from the participating laboratories The alcoholometer S/N broke dring the circlation and as a reslt, it was decided that the calibration reslts obtained by NMIA and INRiM wold be presented as a bilateral comparison. LATU detected some problems with their apparats dring the calibration of the three hydrometers in the range from 000 kg/m 3 to 000 kg/m 3 ; the epected reslts of the transfer standards identified with the Serial Nmbers 93407, and were not sbmitted. After the first isse of the draft A circlated among the participants, the MKEH and the NIST sbmitted new reslts. Before the isse of the draft A the MKEH staff sspected that the bilding reconstrction in the laboratory dring the comparison measrements cold have affected its reslts. The MKEH was able to detect the possible case after the conclsion of the draft. The inflence of temperatre changing in the room dring the immersion was the main problem. A density correction becase of the temperatre inflence has been made. NIST made a mistake abot the nits sed for the ncertainties, as reported in in the data report (Form). NIST thoght the nits were parts per million when they were actally g/cm In addition the laboratory sspected that density changes of the boyant liqid over time de to evaporation of less dense imprities affected the own measrements and gave commnication to pilot laboratory that: NIST reslts show differences between g/cm 3 and g/cm 3 from the KCRVs. Note that the crrently approved NIST CMC ncertainty is 00 ppm, bt smaller, cstomized ncertainty vales were sed for this KC. SIM.M.D-K covered density range 60 kg/m 3 to 300 kg/m 3 and NIST s degrees of eqivalence with the reference vales ranged from -5 ppm to 30 ppm. Moreover, NIST sspects that density changes of their tridecane over time de to evaporation of less dense imprities is the sorce of the larger degrees of eqivalence in this comparison.

14 CCM.D-K4 Hydrometers Page 4 of 45 Therefore NIST wrote that NIST will: employ a higher resoltion check standard to better reveal changes in their Cckow s apparats. (Presently, a check standard is sed before each batch of cstomer calibrations and the reslts mst agree with prior reslts within 00 parts in 0 6, the NIST CMC ncertainty). measre the properties of the tridecane more freqently to track changes de to evaporation. not seek a lower CMC than or crrent vale of 00 ppm ntil ftre comparisons spport sch redctions. 3.3 Interpretation of the comparison: the degree of eqivalence DoE According to the CIPM MRA, the degree of eqivalence (DoE) mst be established for each comparison, which can provide traceability for a calibration measrement capability annonced in the Key Comparison Data Base, KCDB, Appendi C, by the laboratory. DoE mst be calclated as the deviation of the vale reported by the laboratory from the key comparison reference vale evalated in the framework of an internationally accepted key comparison. Twelve Key Comparison Reference Vales (i= to ) have been obtained at the tested density mark of the for transfer standards for each petal by the reslts of participants in the range 600 kg/m 3 to 000 kg/m 3. To qantify the discrepancies, tests of eqivalence of the measrements are based on a recommended method sed for key comparisons [8]. The reslts from each of the n laboratories of the j petal (j=a or B) have then been characterized in terms of a degree of eqivalence representing the deviation D jni of its reslt jni from the estimated Key Comparison Reference Vale (KCRV ji ) at the tested density mark i as D jni = jni KCRV ji () with the associated ncertainty (D jni ) = ( ( jni ) + (KCRV ji ) ( jni, KCRV ji )). (3) In eqation (3), the (KCRV ji ) is interpreted as an estimate of the reference vale ncertainty made on the basis of the measrements provided by the participating instittes, and ( jni, KCRV ji ) is the possible covariance term between the laboratory reference vale. reslts and the

15 CCM.D-K4 Hydrometers Page 5 of 45 The Reference vale firstly was determined by weighted mean of the instittes measrements (Procedre A), sing the inverses of the sqares of the associated standard ncertainties as the weights: jni KCRV ji n. (4) n jni jni The individal reslt jni of each of the n laboratory reslts was considered consistent with the Reference vale at the 95 % of the level of significance if D jni (D jni ). (5) Sch a reference vale, however, is not applicable if some of the instittes measrements appear to be anomalos or discrepant. To identify the overall consistency of the claimed reslts, a chi-sqared test was then applied considering the consistency check as failing if where Pr denotes probability of, n is the nmber of degrees of freedom and Pr obs ref n ref obs is the observed chi-sqared vale. n If the test was not satisfied, the KCRV ji is the median vale amongst the sbmitted measrement reslts (Procedre B). By means of a Monte Carlo simlation, random samples were generated, each made of N vales drawn from the distribtions representing the reslts from each laboratory (N, here, is the nmber of the laboratories of the relevant petal). In this way, vales for the median of the drawn samples were obtained. The mean of sch vales was taken as the KCRV ji of the single tested mark i. Also the corresponding simlated deviation terms of the degrees of eqivalence were obtained for each laboratory and sed to determine a 95% coverage interval for the laboratories deviations from the KCRV ji. (6) 3.4 Key Comparison Reference Vales (KCRVs) and degrees of eqivalence The crrent reslts of the key comparison corresponding to the involved A and B j petals are reported in the Appendi A relating to each tested hydrometer. The measrement reslts with the corresponding ncertainties claimed by the participants are listed in the odd table A or B which also provides the KCRVs with their own etended ncertainty, the lower and pper limits of the coverage interval if procedre B was applied and the χ obs vale at each tested mark. The even table A or B for the same artefact shows at

16 CCM.D-K4 Hydrometers Page 6 of 45 each tested mark of each n laboratory of the petal the degree of eqivalence to the KCRV with the coverage interval. Moreover the table reports the arithmetic mean of the three degree of eqivalence corresponding to the k tested hydrometer jnk = i D jni 3 standard ncertainty jnk = ( Djni + (D jnima D jnimin ) with its estimated ). Corresponding to the same tested artefact, the figre also shows the degree of eqivalence with respect to the KCRV of each participant of the relevant petal related to each calibrated mark and their arithmetic mean with their own epanded ncertainties. The average of the three degrees of eqivalence to the KCRVs, jnk and the corresponding estimated standard ncertainties are a good indicator of the ability of the laboratory n in the calibration of hydrometers, becase it shows the laboratory repeatability. The estimated standard ncertainty jnk takes into accont the associated ncertainty of the individal degree of eqivalence Djni calclated by (3), and the reprodcibility in the calibration of the laboratory by assming a rectanglar distribtion from the dispersion of the individal degrees of eqivalence with respect to the three KCRVs for each transfer standard. Table 6 shows the jnk at the corresponding petal j of each k tested hydrometer for each n participant to the comparison, its ncertainty, and finally information abot the consistency of each claimed reslt from the laboratory, according to eqation (5): A the reslt is consistent, B the reslt is not consistent. In general it was observed that: Petal A shows that all data are rather close to the weighted mean vales. The eperimentally observed obs vales are always lower than.07 with 5 degrees of freedom and 9.47 with 4 degrees of freedom. The LATU reslts were not considered in the KCRV calclations with the eception in the range g/cm 3 and 0.60 g/cm 3. Petal B shows that some laboratories ehibit a largest deviation related to the reference vales. In sch inconsistent case, the mean of medians was taken as the KCRV ji. In particlar that was de to the reslts of NIST and MKEH at 0.60 g/cm 3, LNE at g/cm 3 and 0.99 g/cm 3, and again MKEH at.98 g/cm 3. The NMIA reslts were not considered in the reference vale calclations in the range g/cm 3 and g/cm 3.

17 CCM.D-K4 Hydrometers Page 7 of 45 Table 6. Arithmetic mean vale of the three degrees of eqivalence of the NMIs with respect to the KCRVs jnk, at the corresponding petal j of each k tested hydrometer for each n participant to the comparison and the relevant ncertainty. Table also shows information abot the consistency of each laboratory reslt i with the individal Key Comparison Reference Vale in the range of the tested hydrometer: A the reslt is consistent, B the reslt is not consistent, the different colors give a level of attention (orange: medim attention, yellow: low attention)

18 CCM.D-K4 Hydrometers Page 8 of 45 Table 7. Differences of the average of the degree of eqivalence of the INRiM, CENAM and PTB who measred all Transfer standards. Division of the scale g cm -3 in the density range g cm -3 and.500 g cm -3. Division of the scale g cm -3 in the density range.980 g cm -3 and.000 g cm -3. Frthermore the stability of the circlated standards was confirmed from the difference of the average between the INRiM, CENAM and PTB measrements who tested them in both petals and can be estimated as approimately one tenth (/0) of a division of the scale, Table Continos fnctions of DoEs Individal degrees of eqivalence DoEs between the vales reported by participants and the corresponding KCRVs, as well as the average vale related to the range of each tested hydrometer for both petals, have been introdced in the above sections. As each participating laboratory reported a total of density vales for the for hydrometers, it is better to epress a set of DoEs of each participant as a fnction of nominal density vales ρ i, sch as 600 kg/m 3, 000 kg/m 3, 500 kg/m 3, etc. A regression crve (i.e. first order crve) for corresponding DoE is therefore proposed for each participant n from its own set of DoEs. In order to introdce all sets of vales, a matri eqation takes the following form where Dn is the colmn vector of the degrees of eqivalence of the participant n, ρ i is the matri of the i tested nominal vales of density, ε n the residal vector of the fitting and, β n is the colmn vector which contains the slope m n and the intercept b n of the proposed straight line fitting: D n ρ β i n ε n (7) D n Dn Dn Dn Dn n m n n ρ i β ε n n bn n ; ; ;. n

19 CCM.D-K4 Hydrometers Page 9 of 45 The weighted least sqare method (WLS) can be sed for calclating the regression crves, the soltion of (7) by WLS is βˆ T ρ ψ ρ where concerning the participant n the weighting matri (8) ψ D n, is formed by the variance (and covariance) of the corresponding DoEs ncertainties given in Table 6 and the term ˆ n ρ T ψ ψ β i D i is assmed to be the variance-covariance matri of the best fit parameters βˆ n. n ρ For the correlation coefficient 0.9 for DoEs corresponding to the calibration of same hydrometer can be assmed and 0.3 for DoEs corresponding to the calibration of different hydrometers. An additional test, i.e chi-sqare test, can be sed to indicate agreement between the observed and predicted vales as well as between the estimated variance of the fit and the inpt ncertainties. 3.6 Degree of eqivalence between pairs of NMIs According to the 4th CCM meeting (Febrary, 03) pair-wise degrees of eqivalence shold no longer be pblished in the KCDB. Information on pair-wise degrees of eqivalence pblished in KC reports shold be limited to the eqations needed to calclate them, with the addition of any information on correlations that may be necessary to estimate them more accrately. In brief, mathematically the pair-wise degree of eqivalence for each pair of laboratories p and q is the difference d pq of the comparison reslts of the two laboratories: Both laboratories p and q are in the same loop. The degree of eqivalence d pq of each petal at the stated density vale or range of i is the difference between the comparison reslts i of the two independent laboratories Its standard ncertainty is n T i D i ρi ψ D Dn d pq with the epanded ncertainty is U. n n D D i d pq p q p d q p pq d pq Note. The implication of this condition is that there is no mtal dependence of the institte s measrements. q i (9) (0) Anyway, in the sal cases in which the laboratories are shifted in separate loops and different TSs are sed, eqation (9) shold take into accont an offset given by the difference

20 CCM.D-K4 Hydrometers Page 0 of 45 between the set of the reference vales of the different loops. Defining by the continos relations f and KCRV A d pq and the ncertainty is d pq g the offset to be considered, the d pq is KCRV B f g D D i where D p, D q is the correlation term of the DoEs with respect to the KCRVs of the corresponding loops. The soltion of D p, D q can be resmed as follows: The independent laboratories p and q worked respectively in the A and B petals, contribting to determine each one the reference vales KCRV A and KCRV B by means of the two different set of transfer standards. The degree of eqivalence between two laboratories can be obtained for a stated density vale or range of i ; the correlation term is given by D, D KCRV, KCRV p p k D k q q p, D q k A A B k i KCRV A i D, D p q i B j () (), (3) where i and j represent the laboratories participating in the two loops A and B, respectively. Note. The three laboratories k (INRiM, CENAM and PTB) make an important contribtion in the correlation determination since they worked in both loops. Appendi A eplains how to evalate the degrees of eqivalence and their ncertainties between the two instittes, p and q, who participated in the two different loops, A and B. KCRV B i p i q i 3.7 Linkage of international comparisons to the CCM.D-K4 A nmber of linked comparisons have already been pblished in the KCDB sing different methods. The procedre described in [9] to link SIM NMIs to the EURAMET key comparison of EURAMET.M.D-K4 is sitable for linking the reslts of regional, spplementary and bilateral comparisons to the KCRVs of CCM.D-K4 Hydrometer throgh the DoEs between the reslts reported by the joint participation of each participant at this CCM comparison and in the concerning comparisons. In sch cases, degrees of eqivalence are compted for the participants in the previos and sbseqent comparison with respect to all other participants and to the previos key comparison reference vale. By the continos fnction participants in the spplementary comparison D D the individal DoE to the KCRV are compted for the d d D pq RMO bil link (4)

21 CCM.D-K4 Hydrometers Page of 45 where link D is the continos fnction concerning the DoEs between reslts reported by the linking laboratory (laboratories) with respect to the KCRVs in the CCM.D-K4; d pq RMO is the continos fnction concerning the degree of eqivalence between pairs of NMI laboratories, in the Regional comparison; bil d is the continos fnction concerning the difference between the reslt measrement of the two laboratories, the linking laboratory and the laboratory that took part in the Regional and/or spplementary comparison. In order to calclate the ncertainty of eqation (4), nmerical simlations by the Monte Carlo method can be performed for each estimated vale of D [0]. 3.8 The Bilateral comparison INRiM - NMIA and its linkage to CCM.D-K4 Dring the circlation of the transfer standards, the alcoholometer S/N , belonging to petal B, was broken and replaced with the S/N 93407, having the same characteristics in the density range of 000 kg/m 3. Anyway the calibration reslts obtained by NMIA and INRiM concerning the broken standard S/N were handled as a bilateral comparison between the two participants inside this key comparison. Table 8 shows the measrement reslts of the two laboratories, the reference vales determined by the weighted means with ncertainties at 95 % of the level of confidence and finally the normalized error ratio E n which, if reslts between - and +, generally indicates that the measred vales are considered consistent. Alcoholometer S/N Range (0-0) % vol g/cm3 RV (weighted mean) U ( RV ) E n , , , 0-6 / g cm -3 INRiM NMIA Combined std ncertainty of corrections c Epanded ncertainty of corrections U 95 =t 95 c Stdent t-factor t Table 8. Measrements reslts as reported by INRiM and NMIA concerning the alcohol hydrometer S/N Last colmn reports the normalized error for each calibrated gradation marks

22 CCM.D-K4 Hydrometers Page of 45 Table 9, DoEs of the NMIA with respect to the CCM. D-K4 KCRVs of the Petal B at the three tested density marks with the corresponding epanded ncertainties. Moreover the table shows the mean average of the three tested vales in the range and with its ncertainty at the 95 % of the confidence level D INRiM UD 0 NMIA g cm -3 d bil D NMIA , Figre. Degrees of eqivalence respect to the KCRV of each laboratory of the relevant petal identified by the alcohol hydrometer The lengths of the bars show the epanded ncertainty of the degree of eqivalence related to each calibrated mark and of their average. This Figre replaces the Figre B in Appendi Hydrometer S/N Djni 0-6 g cm g cm INRiM NMIA CENAM NIST 4 LNE GUM 6 MKEH PTB 8 Participants In order to link the NMIA reslts to KCRV vales of the CCM.D-K4 Hydrometer for each reslt at the three tested marks in the range of 000 kg/m 3, eqation (4) is re-written as where d bil NMIA INRiM (5) is the difference of the measrands as reported by INRiM and NMIA at each tested mark in the bilateral comparison; INRiM D NMIA d D INRiM D is the individal DoE of INRiM with respect to the KCRV concerning the CCM.D-K4 at the density related to tested mark. The variance of each DoE of NMIA at the density related to the tested mark reslt where the term of correlation is assmed to be bil D D dbil DINRiM INRiM, NMIA INRiM (6)

23 CCM.D-K4 Hydrometers Page 3 of 45, D,, KCRV INRiM INRiM INRiM INRiM 0.9 j INRiM j where is the ncertainty claimed by each participant belonging to petal B. j D INRiM The linkage reslts concerning the NMIA with respect to the KCRV vales of the CCM.D-K4 Hydrometer in the range 000 kg/m 3, as they were calclated by eqations (5) and (6) are shown in Table 9. The Table also shows the average of the three NMIA DoE vales and the ncertainty at the 95 % level of significance, vale which takes into accont the repeatability of the calibration reslts on the three tested marks. Figre replaces the Figre B in Appendi. It shows the degree of eqivalence with respect to the KCRVs of the concerned NMIs inclding the determined vales of NMIA. 4. DISCUSSION and CONCLUSION The Key comparison CCM.D-K4 Hydrometer, which covered the density range 600 kg/m 3 to 000 kg/m 3 at 0 C, comes after varios comparisons in Hydrometry performed since the 90s by regional metrology organizations. So, the main prpose of it was not only to evalate the degree of eqivalence between NMI participants in the calibration of hydrometers of high accracy, bt also to establish a base to link, were it is possible, the reslts of previos comparisons to the Key Comparison Reference Vales (KCRVs) of CCM.D-K4. In order to reach sch objectives, two similar sets of three high-accracy hydrometers for liqid density determinations and an alcoholometer were circlated to the NMI participants as a travelling standard in the time interval from Janary 0 to April 0. The eleven participating NMIs were divided into two grops which to form two loops (petals). The three density laboratories of INRiM, CENAM and PTB performed calibrations in both petals. The calibration measrements of each hydrometer were carried ot at three specified division marks at atmospheric pressre. Each laboratory sed their own hydrostatic weighing system with their own respective standard liqid sch as: n-pentadecane, n-nonane, n-tridecane and n-tetradecane. Two sets concerned twelve KRCVs, for each petal, have been obtained at the tested density marks by the reslts of participants. The KRCVs and corresponding ncertainties were calclated by the weighted mean in the case of consistent reslts, otherwise the median was sed. D INRiM B (7)

24 CCM.D-K4 Hydrometers Page 4 of 45 The DoE with respect to the corresponding KCRV was determined for each participant and also, in this particlar comparison, the Weighted Least Sqares (WLS) method to link the individal DoE of each participant by a continos fnction has been proposed. Frthermore, information on pair-wise degrees of eqivalence was provided: the eqations needed to calclate them, and any information on correlations that may be necessary to estimate them more accrately. We also eplained the procedre for linking international comparisons to the CCM.D-K4. Finally an eample of linkage to the CCM.D-K4 is given by dealing with the reslts of the bilateral comparison between INRiM and NMIA, which was added to this comparison so that all participants were engaged after the breakage of the artefact. The overall reslts have shown a very satisfying agreement among the reslts provided by most of the participants. Technical improvements can be made in some laboratories and, in general, on the ncertainty evalation. With the eception of few cases, the deviations of the laboratory reslts to the KCRVs are within of /3 to /4 of a division of scale and the ncertainty at 95% is sally within half a division. Anyway some systematic differences and either nderestimated or overestimated ncertainties of the sbmitted reslts have been identified with respect to the KCRVs which had the responsibility to fail the consistency test of the Reference vale of this comparison. Dring the analysis of the sbmitted reslts, a systematic difference between the first and last immersed mark was also noted, possibly de to a temperatre gradient along the stem and/or wetting of the stem close to the tested mark []. A corrected claimed ncertainty from each laboratory is epected according Table 6. However this comparison may help the laboratories to solve some residal or marginal problems as well as to better nderstand the ncertainty components. The CCM.D-K4 Hydrometer key comparison flly spports the calibration measrement capabilities table in the BIPM key comparison database (KCDB). The reslts can be sed to link regional comparisons to this CCM key comparison.

25 CCM.D-K4 Hydrometers Page 5 of 45 References [] Lorefice S., Becerra O. L., Toth H. 00 Technical Protocol for CCM.D- K4 Hydrometer, [] Picard A., Davis R. S., Gläser M. and Fjii K. 008 Revised formla for the density of moist air (CIPM- 007), Metrologia, 45, [3] Lorefice S. and Malengo A. 004 An image processing approach to calibration of hydrometers, Metrologia 4, L7 L0 [4] Lee Y J, Chang K H, and Oh C Y 004 Atomatic Alignment Method for Calibration of Hydrometers, Metrologia 4, S00-S04 [5] Agilera, J., Wright, J., and Bean, V. 008, Hydrometer Calibration by Hydrostatic Weighing with Atomated Liqid Srface Positioning, Meas. Sci. Technol. 9, 0504 [6] JCGM 00:008 - Evalation of measrement data Gide to the epression of ncertainty in measrement [7] CIPM MRA-D-05, Measrement comparisons in the CIPM MRA, March 04 [8] Co M. G. 00, The evalation of key comparison data, Metrologia, 39, [9] Becerra L.O., Lorefice S. and Pennecchi F. Hydrometer calibration: Linking SIM NMIs to the EURAMET key comparison reference vale of EURAMET.M.D-K4, Ingeniería (): 95-05, ISSN: ; 0. [0] JCGM 0. (008). Evalation of measrement data. Spplement to the Gide to the epression of ncertainty in measrement. Propagation of distribtions sing a Monte Carlo method [] Lorefice S. and Malengo A. 006 Calibration of hydrometers, Meas. Sci. Technol., 7, 560 Acknowledgements The athors wold like to acknowledge the kind assistance of all the colleages in the participating laboratories for helping this comparison to rn so smoothly. A special thanks to A. Daed and L.M. Peña of CENAM and S. Gerdesmann of PTB for their great competence to measre both sets of the travelling standards sed in this key comparison. Or thanks are also de to Dr Kenichi Fjii, chairman of the CCM WG on Density and Viscosity, for all his efforts.

26 CCM.D-K4 Hydrometers Page 6 of 45 Appendi A This section deals with the measrement reslts and the standard ncertainties as reported by the participants. For each artefact, the calclated CCM Key-Comparison Reference Vale (KCRV) at each calibrated mark concerning with each of the two petals, with the related ncertainty or the lower (U l ) and pper (U r ) limits of the confidence interval if procedre B was applied [8]. Moreover, for each petal and for each artefact the three degrees of eqivalence to the KCRVs and their average with the corresponding estimated standard ncertainties concerning each of the NMIs are listed and shown.

27 CCM.D-K4 Hydrometers Page 7 of 45 Hydrometer S/N The KCRVs for the petal A, identified by the hydrometer 93435, have been calclated by applying the weighted mean method according to the reslts of the consistency check Pr Appendi A Petal A obs 0. 05of the measrement reslts and standard ncertainties of the participants reported in Table A.. The Table shows also each calclated KCRV with the epanded ncertainties and the obs vales. Table A. and Figre A. present the degrees of eqivalence to the KCRVs and their average of the concerned NMIs. Table A.. Measrements reslts as reported by the participants for the petal identified by the hydrometer and the KCRV with its epanded ncertainty and the vale at each calibrated mark. obs Hydrometer S/N Range ( ) g/cm / g cm -3 INRiM CENAM LATU NMIJ KRISS KCRV A (weighted mean) U (KCRV A ) PTB Combined std ncertainty of corrections c Epanded ncertainty of corrections U 95 =t 95 c Stdent t-factor t Pr (ν)>χ obs } <0,05? (5)=.07>χ = (6.; 6.03; 8.47) obs The consistency test doesn't fail: procedre A Table A.. Degree of eqivalence to the KCRV and epanded ncertainty at each tested mark of each laboratory and average of the petal identified by the hydrometer NMI (n ) mark (i )/range (k ) Djni 0-6 U (Djni ) 0-6 Djni 0-6 U (Djni ) 0-6 Djni 0-6 U (Djni ) 0-6 jnk 0-6 U ( jnk) 0-6 INRiM CENAM LATU NMIJ g cm KRISS PTB

28 CCM.D-K4 Hydrometers Page 8 of 45 Appendi A Petal A Figre A.. Degree of eqivalence with respect to the KCRV of each laboratory of the relevant petal identified by the hydrometer The lengths of the bars show the epanded ncertainty of the degree of eqivalence related to each calibrated mark and of their average.

29 CCM.D-K4 Hydrometers Page 9 of 45 Hydrometer S/N The KCRVs for the petal A, identified by the alcohol hydrometer 93407, have been calclated by applying the weighted mean method according to the reslts of the consistency check Pr Appendi A Petal A obs 0. 05of the measrement reslts and standard ncertainties of the participants reported in Table A.3. The Table shows also each calclated KCRVs with the epanded ncertainties and the obs vales. Table A.4 and Figre A. present the degrees of eqivalence to the KCRV and their average of the concerned NMIs. Table A.3. Measrement reslts as reported by the participants for the petal identified by the alcohol hydrometer and vale of the KCRV with its epanded ncertainty and the vale at each calibrated mark. obs Alcoholometer S/N Range (0-0) % vol g/cm 3 KCRV A (weighted mean) U (KCRV A ), , , Combined std ncertainty of corrections c Epanded ncertainty of corrections U 95 =t 95 c Stdent t-factor t / g cm -3 INRiM CENAM NMIJ KRISS PTB Pr (ν)>χ obs } <0,05? (4)=9.49>χ = (.39;.5;.58) obs The consistency test doesn' t fail: procedre A Table A.4. Degree of eqivalence to the KCRV and epanded ncertainty at each tested mark of each laboratory and average of the petal identified by the hydrometer NMI (n ) mark (i )/range (k ) Djni 0-6 U (Djni ) 0-6 Djni 0-6 U (Djni ) 0-6 Djni 0-6 U (Djni ) 0-6 jnk 0-6 U ( jnk) 0-6 INRiM CENAM NMIJ g cm KRISS PTB