Practical Interpretation of Metrological Traceability on Gauge

Practical Interpretation of Metrological Traceability on Gauge Block as to VIM 3

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Practical Interpretation of Metrological Traceability onGauge Block as to VIM 3

LUNG-HEN CHOW*, YI-TING CHEN, LIANG-HSING CHEN and GWO-SHENG PENGCenter for Measurement Standards (CMS), Industrial Technology Research Institute (ITRI)

Bldg. 16, 321, Sec. 2, Kuang Fu Road, Hsinchu City, 30011, Taiwan (ROC)*e-mail: [email protected]

[Received: 05.02.2011 ; Revised: 02.03.2011 ; Accepted: 03.03.2011]

AbstractIn ISO/IEC Guide 99:2007, i.e. the International Vocabulary of Basic and General Terms in Metrology-3rd edition (VIM 3), the term "traceability" is replaced by "metrological traceability", giving it a newdefinition as property of a measurement result which can be related to a reference. In essence, "metrologicaltraceability" can offer an evidence of measurands tracing to the primary standards which can realizethe SI units, and offer a documented unbroken chain of calibrations, thus considered as one of the mostimportant terms in VIM 3. National Measurement Laboratory (NML, Chinese Taipei) has long operatedits main mission of calibration implemented along with peer assessed traceability of its measurementsystems, which demonstrate a calibration hierarchy conventionally in schematic approach. In dealingwith definition of the new term "metrological traceability" in VIM 3, this paper elaborates in takingadditionally a newly mathematical approach rather than schematic approach only to realize the practicalinterpretation of "metrological traceability" to show how the unbroken calibration chain is functioningseamless and robust on the gauge block measurement system in NML. Through such study activities,we well assure our strong confidence on technology inheritance of gauge block and the other measurementsystems with sufficient metrological know-how in NML, which can continually pass to each entry levelmetrologist.

© Metrology Society of India, All rights reserved 201.

1. Indroduction

Towards increasing demands of metrologicalstandards with associated metrological traceability,measurement uncertainty and nominal properties inemerging industrial and societal applications, suchas material metrology and biological metrology, theInternational Organization for Standardization andthe International Electrotechnical Commissionpublishing ISO/IEC Guide 99:2007 [1] cancels andreplaces the second edition of the VIM and it isequivalent to the third edition of the VIM (VIM 3). In

VIM 3, the term "traceability" is replaced by"metrological traceability", giving it a new definitionas property of a measurement result which can berelated to a reference. In essence, "metrologicaltraceability" can offer an evidence of measurandstracing to the primary standards which can realizethe SI units, and offer a documented unbroken chainof calibrations, thus considered as one of the mostimportant terms in VIM 3. International LaboratoryAccreditation Cooperation (ILAC) also proposed siximportant elements to confirm the definition of"metrological traceability" [2].

MAPAN - Journal of Metrology Society of India, Vol. 26, No. 1, 2011; pp. 79-86ORIGINAL ARTICLE

Lung-Hen Chow, Yi-Ting Chen, Liang-Hsing Chen and Gwo-Sheng Peng

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National Measurement Laboratory (NML,Chinese Taipei) has long operated its main missionof calibration implemented along with peer assessedtraceability of its measurement systems, whichdemonstrate a calibration (traceability) hierarchyconventionally in schematic approach. In dealing withdefinition of the new term "metrological traceability"in VIM 3, a newly mathematical approach is taken inaddition to the schematic approach to realize practicalinterpretation of "metrological traceability" to reviewhow the unbroken calibration chain can befunctioning seamless and robust on differentmeasurement systems in NML. Gauge blockmeasurement system is typically demonstrated forsuch purpose of metrology study activity at NMLduring the year 2010.

2. Definition of the Metrological Traceability in VIM 3

Metrological traceability is defined in 2.41 of VIM 3as "property of a measurement result whereby the resultcan be related to a reference through a documented

unbroken chain of calibrations, each contributing to themeasurement uncertainty", within which measurementresult, calibrations and measurement uncertainty are alsoclearly defined in VIM 3. While "a documented unbrokenchain of calibrations" is not formally defined, it needs toaddress more, which is clearly illustrated in Fig. 1, as agraphical interpretation of metrological traceability.

For the definition shown in Fig. 1, metrologicaltraceability requires an established sequence ofcalibrations, i.e. calibration hierarchy, starting from areference to the final measuring system, with welldocumentation applying to calibration procedure andmeasurement uncertainty, and finally obtains ameasurement result from the measuring system. Ameasurement result is generally expressed as a singlemeasured quantity value and a measurement uncertainty.As to such definition, a 'reference' can be a measurementstandard, or a measurement procedure, or a definition ofa measurement unit through its practical realization.

Fig.1. A graphical interpretation of metrological traceability as to VIM 3


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It is also noted that the specification of the reference mustinclude the time at which this reference was used inestablishing the calibration hierarchy, along with anyother relevant metrological information about thereference, such as when the first calibration in thecalibration hierarchy was performed. Nevertheless,metrological traceability should be the property of ameasurement result, instead of the traceability of ameasuring system previously misunderstood at NML.

Similar to aforementioned definitions, ILACproposes six important elements to confirm thedefinition of metrological traceability [2] as; i) anunbroken metrological traceability chain to aninternational measurement standard or a nationalmeasurement standard, ii) a documentedmeasurement uncertainty, iii) a documentedmeasurement procedure, iv) accredited technicalcompetence, v) reference to the SI units, such that thetraceability chain must, where possible, end at primarystandards for the realization of the SI units and vi)calibration intervals at which calibrations must berepeated depending on such factors of uncertaintyrequired, frequency of use, way of use, stability of the

equipment etc. Thus, a measurement well equippedwith above six key elements will suffice to give acomplete interpretation of metrological traceability inorder to relate a measurement result to a reference.

3. Conventional Metrological Traceability Diagram

NML is a renowned national metrology Institute(NMI) in Taiwan and a registered calibrationlaboratory accredited by Taiwan AccreditationFoundation (TAF) which performs its assignedcalibration work in compliance with ISO 17025:2005[3]. Since the chapter 5.6 Measurement traceability of[3] gives requirement for calibration laboratorycomplying traceability, in 5.6.2.1 Calibration-thatmentions "For calibration laboratories, the programfor calibration of equipment shall be designed andoperated so as to ensure that calibrations andmeasurements made by the laboratory are traceableto the SI units", NML then designs approach to sketchmetrological traceability diagram for their measuringsystems in order to enable the concept of measurementrealized through a complete metrological traceabilitychain.

Fig. 2. Hardness traceability chain


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Conventional metrological traceability diagramrequested by MSVP at NML is initiated based on theviewpoint of measurement system since the majorpurpose of MSVP is designed to validate themeasurement system and claim its evaluateduncertainty. Thus, a simple and conceptualtraceability illustration in Fig. 3(a), or even a little moredetailed traceability explanation in Fig. 3(b) cannotfully cover the aforementioned six key elements ofmetrological traceability. Such conventional approachof metrological traceability diagram is obsolete andcannot comply with the new definition of metrologicaltraceability.

4. New Metrological Traceability Diagram in Mathematical Approach

In order to really focus the property ofmeasurement result as metrological traceability isdefined in VIM 3, we shall intend to measure only theoutput quantity Y in the measurement model orequation h(Y, X1, …, Xn) = 0, i.e. the measurand, thequantity value of which is to be inferred frominformation about input quantities in themeasurement model X1, …, Xn, instead of theconsideration of all the affection factor (e.g.temperature, coefficient of thermal expansion etc.)during the whole measurement process. After a closediscussion in the metrology study group at NML thebeginning of year 2010, we propose another new wayof mathematical approach combined withconventionally schematic approach to draw a newmetrological traceability diagram for practicalinterpretation of metrological traceability incompliance with VIM 3.

Measurement result is actually measurementresult of measurand, in which measured quantity willbe expressed usually as a number and a unit(reference), and that is a mathematical representationin itself. Thus we propose to insert "mathematicalmeasurement equation" into conventional traceabilitydiagram to reinforce "unbroken chain of calibrations"at each node of connection between sequence ofcalibrations as quantitatively and clear documentedevidence, where measurement (calibration) systemchanges as the process. In such approach, themeasurand associated with measurement result may

A lately disclosed diagram of traceability chainfor hardness measurement traceability in industry [4],shown in Fig. 2 can be referred to investigate how thesix key elements of metrological traceability are wellpresented in such hardness traceability chain, wherethere are some issues that are worthy of discussionand to be clarified;

i) Reliable hardness values, hardness testingmachines and hardness calibration machines aremixed placing in the same line of traceability,which we can not make sure whether themeasured target is "hardness values" or"machines". The definition tells us: metrologicaltraceability is the property of measurement resultthat is interested in the quantity intended to bemeasured, and here shouldn't be "machines;

ii) In traceability chain, no explanation is describedor illustrated to give appropriate evidence of "anunbroken metrological traceability chain";

iii) No documentation is mentioned forimplementing measurement procedure, claimedmeasurement uncertainty, and final measurementresult recorded in each stage of traceability chain;

iv) As capable laboratories or institutes for operating"Direct calibration", no direct evidence ordocumentation is shown or mentioned intraceability chain to demonstrate their accreditedtechnical competence.

3.1 Conventional Approach of NML's Metrological Traceability Diagram

During the development of each measurementsystem for a specific measured quantity of calibrationat NML, there will produce two documents; one isInstrument Calibration Technique (ICT) used as adocumented calibration procedure, the otherMeasurement System Validation Procedure (MSVP)used as a documented calibration system evaluationreport, within which the claimed uncertainty isrecorded. It requires of MSVP that a newly developedor modified measuring system draw a measurementsystem traceability diagram at NML as part of adocumented traceability. Figure 3(a) illustrates ameasurement traceability diagram for NML's gaugeblock comparator, and for small mass measurementsystem shown in Fig. 3(b).


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return back to play obviously a main role ofmetrological traceability. Gauge block comparatormeasurement system then is taken as a typical case inthis study to demonstrate how this new approach andmetrological traceability diagrams (shown in Figs.4-6)practically comply with the new definition ofmetrological traceability.

Figure 4 shows gauge block metrologicaltraceability diagram in mathematical approach,where measurement equations are placed in the righthalf of figure. In Eq. (1),

Lx = Lr+ d1 (1)

where Lx at the left of equality, the measurement resultof calibrated gauge block is unknown value, Lr, themeasurement result of standard gauge block and d1,the measured difference from gauge block comparatorat the right of equality being known values. Similarly,in Eq. (2),

Lr=LN+ d2 (2)

where Lr at the left of equality is unknown value, LN,the nominal value of standard gauge block and d2, themeasured deviation from gauge block interferometer

at the right of equality being known values of inputquantities. Then again, d2 becomes an unknownmeasurand, obtained from and at the left of equalityin Eq. (3),

d2= λ(ε-ξ)/2 (3)

where ε is the interference stripe number from themeasurement, ξ, the interference stripe number fromcalculation and the laser vacuum wavelengthmeasurand λ, finally trace and relate to Mise enPratique, (MeP) of the metre, ƒr, the frequency value ofstandard laser (iodine stabilized He-Ne laser) and Δƒ,the measured frequency deviation of beat frequencymeasurement from Eq. (4),

λ = c0 / (n x ƒ ) and ƒ = ƒr + Δƒ (4)

where f is the frequency value of calibrated laser, n isthe refractive index, and c0 is the velocity of light invacuum.

In mathematical approach and the expression ofmeasurement equations, Fig. 4 has clearlydemonstrated a quantitatively unbroken chain ofmetrological traceability diagram, where themeasurement result of each calibration step depends

Fig. 3(b). Small mass measurement system traceabilitydiagram

Fig.3(a).Gauge block comparator measurementtraceability diagram


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on and traced to the measurand and measurementresult of the previous step. The measured quantitiesto be traceable, from the right of equality in thisequation to the left of equality in the previousmeasurement equation are tail-to-head interconnectedin green line, finally connected to the practicalrealization of a measurement unit for checkingwhether the element of an unbroken chain is achievedboth graphically and in mathematical approach.Figure 6 shows complementary illustration onto gaugeblock metrological traceability in documentation forother important traceability elements, includingdocumented expanded uncertainties associated withdocumented ICT and MSVP in each traceability stepat NML. Figure 5 illustrates gauge block system'sauxiliary measurement parameter traceabilitydiagram at NML, where the laboratories operatingcalibrations of relevant auxiliary parameters are allinner laboratories of NML and accredited by TAF, andthat means all such inner laboratories' technicalcompetence accredited too, with calibration intervalsindicate on their calibration certificates issued bythem.

In summary, NML's gauge block metrologicaltraceability in new approach combined with differentdiagrams complementary each other shown in Figs. 4 -6,fully explicitly presents six important elements ofmetrological traceability.

5. Further Discussion on Measurement Equationfor the Interpretation

Comparing with previous viewpoint on theevaluation of measurement uncertainty towardsmeasuring system and from NML's gauge blockcalibration system evaluation report or MSVP,measurement equation in Fig. 4 was originallyexpressed in a more complicated form;

αθ α θ= + − +1 s s s(1 ) (1 )d L L (5)

where L is the dimension of calibrated gauge block at20ºC , α is thermal expansion coefficient of calibratedgauge block, θ is temperature difference of calibratedgauge block with respect to that 20ºC and Ls,αs and θsare similar ones symbolized for standard gauge block.

Fig. 4. Gauge block metrological traceability diagram (in mathematical approach)


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Fig. 5. Gauge block system's auxiliary measurement parameter traceability diagram-

Fig.6. Gauge block metrological traceability diagram (in documentation)


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Equation (5) is then deduced to obtain as;

α θα θ αθ

αθ+ +

= = + + − ++

s s s 1s 1 s s s

(1 ) ( )(1 )

L dL L d L (6).

In Eq. (5), it is of much confusion in finding whichparameter is the measurand or output quantityintended to be measured, and which ones are inputquantities. In Eq. (6), the measurand L though placedcorrectly in the left-hand side of equation, the addingcomplicated affection factors, α and θ … seeminappropriately to become among many inputquantities, such that it is so difficult to trace theoutcome of each calibration to the outcome of theprevious calibration in a calibration hierarchy. Thus,a simple and correct mathematical equation torepresent a measurement model such as Eqs. (1-4)indicated in Fig. 4 of the gauge block traceability willplay an important role as giving complementary meritsthat conventional metrological traceability diagramcannot address about for practical interpretation andchecking of an "unbroken" metrological traceabilitychain.

6 Conclusion

Through the study activities for drawing newmetrological traceability diagrams in mathematicalapproach that new edition of VIM 3 requires, we

will well assure ourselves on technology inheritanceof gauge block and the other measurement systemswith sufficient metrological know-how in NML,which can continually pass to each entry levelmetrologist. Besides, since "reference to the SI units"is one of metrological traceability elements, thedegree of complexity for derived quantity such asfluid flow would be much more significant than thatfor base quantity. We will keep elaborating to furtherand deepen the concept of unbroken chain inmetrological traceability to every measurementsystem of any kind quantities operating at NML.

References

[1] ISO/IEC GUIDE 99:(E/F), InternationalVocabulary of Metrology - Basic and GeneralConcepts and Associated Terms (VIM), (2007).

[2] ILAC P-10, ILAC Policy on Traceability ofMeasurement Results, (2002).

[3] ISO 17025, General Requirements for theCompetence of Testing and CalibrationLaboratories, (2005).

[4] Alessandro Germak, Konrad Herrmann andSamuel Low, Traceability in HardnessMeasurements: from the Definition to Industry,Metrologia, 47 (2010) S59-S66.

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Practical Interpretation of Metrological Traceability on Gauge