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The positioning influence of dial gauges on theircalibration results

Marcelo Kobayoshi a,1, Queenie Siu Hang Chui b,*

a Centro SENAI de Metrologia do Departamento Regional de Sao Paulo, Rua Bento Branco de Andrade Filho 379,

Sao Paulo, SP, CEP 04757-000, Brasilb Universidade Sao FranciscoPPGECM, Itatiba, Sao Paulo, Rua Alexandre Rodrigues Barbosa,

45, Itatiba, SP, CEP 13.251-900, Brasil

Received 17 July 2003; received in revised form 24 November 2004; accepted 10 December 2004Available online 29 April 2005

Abstract

In Brazil dial gauges are among the mostly used measurement instruments in industrial dimensional metrology. Theobjective of this work is to study the positioning effect of the dial gauge in the vertical position and in the horizontalposition on the uncertainty of their results in tests and measurements. By using a system with optical solution (laser),

with an interferometer method of displacement control, calibrations were performed in six new dial gauges, from twodifferent manufacturers, with scale interval of 0.01 mm and measuring range of 10 mm. All differences between theobtained values were below the values of the calculated uncertainties of the involved calibration processes. No mean-ingful differences are noticed, when the dial gauge is either in vertical or horizontal position. This factor produces aneffect that does not deserve being considered as a source of meaningful contribution to the final uncertainty of theresults of measurements. 2005 Elsevier Ltd. All rights reserved.

Keywords: Dial gauges; Mechanical comparator; Measuring instrument; Dimensional metrology; Measuring uncertainty

1. Introduction

Mechanical dial gauges belong to the categoryof dimensional measuring instruments known asmechanical indicators [1,2], which are among themostly used instruments in the metal mechanicproducing area, as well as electro-electronics, plas-tics and construction[3].

0263-2241/$ - see front matter 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.measurement.2004.12.001

* Corresponding author. Tel.: +55 11 4534 8025; fax: +55 114524 1933.

E-mail addresses: [email protected](M. Kobayoshi),[email protected](Q.S.H.Chui).1 Tel.: +55 11 5641 4072.

Measurement 38 (2005) 6776

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In studies for a new materials, when a favorablecombination of properties is required, such as ten-sile strength, compression, toughness, flexibility,

wear resistance and hardness, dial gauges are usedin their characterization tests with the purpose ofdetecting the presence of eventual dimensionalvariations [4].

It is known that in most of its applications,either for research and development or for indus-trial purposes, the positioning of the dial gauge,regarding the direction of the action of gravity, de-pends on the conditions of physical space for itsassembly, usually performed with devices, basesand supports.

Regarding its calibration, it is offered to theBrazilian market[5]a remarkable variety of equip-ment that makes possible the calibration of dialgauges. Most of these systems follow an orienta-tion positioning parallel or close to the directionof the action of gravity (vertical), or an orientationorthogonal to the direction of gravity (horizontal).

Analyzing the procedures adopted by the Labo-ratories of Calibration of dial gauges belonged tothe Brazilian Calibration NetworkRBC, that iscordinated by the National Metrology InstituteINMETRO in Brazil, it is observed that the

positioning of the dial gauge during its calibrationis normally defined according to the type andmodel of calibration equipment available in thelaboratory.

Moreover, technical standards and referencedocuments from different countries cover themethods of production and calibration of the dialgauges, but there is no consensus relating theirpositioning during the calibration.

The Brazilian standard NBR 6388[6] mentionsin its item 6, sub-item 6.1 that: All the test

requirements should be guaranteed for any posi-tioning of the movable stem regarding thedirection of gravity. In the official documentDOQ-DIMCI-004Orientations for the perfor-mance of calibrations in the area of dimensionalmetrology [7]the standard JIS B7503[8], is men-tioned as a reference for the determination of thesepoints and states in its item 8Methods of mea-suring of performance,Table 2, the following ori-entation: Holding the plunger of the dial gaugevertically and downward, carry out the following

procedure. . .. It is noticed therefore the applica-tion of different concepts regarding the positioningrequirements of the dial gauges during their

calibration.Other standards and international recommen-dations such as ISO R463 [9], DIN 878 [10] andASME/AINSI B89.1.10M[11], do not either pres-ent a consensus about this subject making clearthe nonexistence of an unique criterion regardingthe positioning procedure during the calibration.

The present work aims at pursuing a discerningstudy about the variability of the calibration re-sults of a dial gauge as a function of its verticaland horizontal positioning.

2. Methodology

In the study mechanical and analogical dialgauges were used, with a scale interval of0.01 mm and a measuring range of 10 mm. Threemodel 2046F dial gauges, manufactured by Mitu-toyo Corporation, made in Japan and three gaugesmodel 3025-481, manufactured by Starret Indu-stria e Comercio Ltda and assembled in Brazil,were utilized. All these dial gauges complied with

the maximum permissible error required by theDIN 878 standard for each of the parameters:the span of error, fe 6 15lm, the total span oferror, fges 6 17lm and the hysteresis error,fu 6 3lm.

By ethical reasons, and also because it was notthe focus of this work to evaluate possible differ-ences between the products used, it was decidedto do not identify the manufacturer of each dialgauge assessed. It was only stated that the dialgauges were identified by the numbers 1, 2, 3, 4,

5 and 6.The experiments were performed at the Labora-tory of Metrology of the Escola Suco-Brasile-ira, belonging to the Servico Nacional deAprendizagem Industrial (SENAI), BrazilianNational Service of Industrial Learning.

For the development of the calibration appara-tus, the following premises were adopted:

Develop an apparatus that minimizes the possi-bility of the occurrence of variations in theobtained results, due to the positioning of its

68 M. Kobayoshi, Q.S.H. Chui / Measurement 38 (2005) 6776


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components regarding the action of gravity. Theuse of an optical system was the chosen option.

The temporal stability should be studied for the

validity of the results obtained during the wholephase of the experiments.Possible errors due to positioning flaws, rigidity

lack, misalignment, clearances and others shouldpreviously be studied and solutions should beproposed to avoid them.

The reference conditions of the laboratoryshould be provided, in order to guarantee theminimum necessary requirements. Deviations tothe ideal conditions should be corrected.

The remaining items of possible influence, suchas alignment flaws, reference point variations andtemperature gradients should be studied, correctedor considered in the mathematical equation andconsequently in the uncertainty analysis andcalculations.

Once these pre-requirements were identified, ef-forts were devoted to the development and assem-bly of the apparatus, for which the following itemswere considered:

A device for the measurement of coordinates,where its main contributions to the apparatus areits mechanical rigidity, the straightness of the dis-

placements and the orthogonality between the axesXand Z.

A displacement measurement system operatingby laser interferometry, where its main contribu-tion is the accuracy of the displacement indication,

which should be adequate or superior to the onestudied. Fig. 1 shows schematically the measure-ment system being applied to the spindle of a

machine.Devices for the positioning and fastening of thereflecting mirrors, interferometers and the refer-ence points and the studied objects should bemanufactured with the necessary accuracy fortheir application, allowing the best adequacy ofthe available physical space and eventual position-ing adjustments and alignments.

Fig. 2shows the apparatus that is mounted andconfigured for the calibration of a dial gauge inhorizontal position aiming to minimize the Abbeoffset.

The vertical position is shown in Fig. 3.The calibrations were performed at the Labora-

tory of Metrology/SENAI Suco-Brasileiralocated at Sao Paulo, Brasil. The results obtainedin the experiments were determined with threemeasurement cycles, in the increasing and decreas-ing directions within the measuring range ofthe instruments. The parameters fe, fges and fu(Fig. 4) were determined according to the instruc-tions of the DIN 878 standard [10] and forthe determination of the measurement points

the JIS B7503 standard [8] was followed, accor-ding to the guidelines of the document DOQ-DIMCI-004Orientations for the performanceof calibrations in the area of dimensionalmetrology [7].

Fig. 1. Scheme of the measurement system.

M. Kobayoshi, Q.S.H. Chui / Measurement 38 (2005) 6776 69


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3. Results

3.1. Assessment of the temporal stability of theapparatus

Once the experiments involved an assembly ofdifferent metrological systems and auxiliary ele-ments, it was considered necessary to carry outthe analysis of the stability of the results suppliedby the calibration apparatus along the time. Thus,it was investigated the presence of a drift thatmight influence the data obtained within the timeperiod of the experiments.

Two calibrations were made in the dial gaugesidentified by the numbers 1 and 6. The apparatus

was configured at the vertical position for the firstcalibration and at the horizontal position for thesecond calibration. Both calibrations were per-formed and repeated after an interval of 15 days,in the dates that marked the beginning and theend of the experiments.

The assessment of the temporal stability wasaccomplished by means of the comparison be-tween the shape and the positioning of the twobias curves obtained in the different dates. Theevaluation took also into account the analysis of

Fig. 2. Apparatus mounted and configured for the calibration with a dial gauge in the horizontal position.

Fig. 3. Apparatus mounted and configured with a dial gauge in the vertical position.



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the differences obtained between the values foundfor the parameters the span of error (fe), the totalspan of error (fges) and hysteresis error (fu), at thebeginning and at the end of the experiments.

Fig. 5compares the bias curves of the calibra-tions performed in the two dates, with the dialgauge # 1, with the apparatus configured at thevertical position.

Analyzing the graphs obtained it was observedthe similarity of the shape and the position be-

tween the appraised bias curves, both for thevertical and the horizontal calibrations.

With the values obtained for the parameters fe,fges and fu, it was observed that no meaningfuldifferences were found that could indicate the non-stability of the system during the whole period

of performance of the experiments, because thedeviations presented during the period indicatedby the dates of the beginning and of the end ofthe experiments involved in the calibrationsremained within the range of expanded un-certainties.

Therefore, it was possible to conclude that theapparatus was shown to be properly stable duringall the period of the performance of the experi-ments, and it did not present any drift mistakes

that might influence the results obtained.

3.2. Method validation

The reliability of the measuring results obtainedwith this apparatus was verified by comparing our

Graph of Bias

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(

Bias

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fu

fges

fe

Fig. 4. Graph exemplifying the determination of thefe, fgesand fu, parameters, according to instructions of the standard DIN 878.

Repeatability Study of the Calibration Results

Gauge # 1 at the Vertical Position

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Indication (mm)

March 8, 2002 Increasing March 8, 2002 Decreasing

March 22, 2002 Increasing March 22, 2002 Decreasing

IndicationError

(m)

Fig. 5. Bias curves demonstrating the temporal stability of the apparatus configured for calibrations performed at the vertical position.



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experimental results with the results obtained bytwo laboratories accredited by INMETRO andbelonging to the Brazilian Calibration Network

RBC.The evaluation considered the differences of thevalues obtained for the parameters of the span oferror (fe), the total span of error (fges) and thehysteresis error (fu), in the calibrations carriedout by the three different laboratories.

Fig. 6 shows the bias curves of gauge # 1,obtained in our experiments and at theINMETRO accredited laboratories (RBC-031and RBC-087).

Analyzing the obtained graphs it was observedthat all the other gauges presented a similarity ofshape and positioning in regard to the three biascurves.

The values obtained in the parameters fe, fgesand fu demonstrated that there were no differ-ences when compared to the values obtained bythe other two laboratories. Only one evaluationparameter of one of the gauges analyzed pre-sented a deviation higher than the expanded uncer-tainties determined in the calibration resultsinvolved. As it deals with divergences found be-tween results from two laboratories of RBC, this

will not be discussed here since it is out of thescope of this work. Therefore, it was possible toconclude that the assembled system was satisfac-torily appropriate for the performance of theexperiments.

3.3. Evaluation of the results obtained in the two

positions

The calibrations were made in the vertical posi-tion and in the horizontal position. This decisiontook into account the fact that most of the com-mercially available calibration systems followed apositioning orientation of the dial gauge that waseither parallel to the direction of the action ofthe gravity (vertical), or orthogonal to the direc-tion of the action of the gravity (horizontal).

The study was accomplished by means of thecomparison of the shape and the relative positionof the bias curves obtained in the calibrations ofthe experiments.

Fig. 7 presents the comparison of the biascurves of gauge # 1, obtained in the calibrationexperiments, carried out in the vertical and hori-zontal positions.

Similarly to the gauge # 1 it was observed thatall the bias curves of remaining gauges presented asimilarity of shape and position in the vertical andhorizontal positions.

The differences obtained for the parameters ofmaximum deviation in the direction of advance-ment (fe), maximum deviation in the two direc-

tions (fges) and hysteresis error (fu), in thecalibrations were observed with the dial gaugesin the two different positions.

For the determination of the uncertainties ofthe results recommendations for the expression

Comparison between the Calibration Results - Gauge # 1

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Vertical Increasing Vertical Decreasing RBC-087 Increasing

RBC-087 Decreasing RBC-031 Increasing RBC-031 Decreasing

IndicationErr

or(m)

Fig. 6. Bias curves of the gauge # 1 obtained in the experiments and in other two calibration laboratories accredited by INMETRO.



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of the uncertainty of measurement [12,13] werefollowed.

Eq.(1) was determined as representing the var-ious factors that could influence the final uncer-tainty to be associated to the experimentalmeasuring result.

Iins Ipad Dpad Dres.i Dres.p Dalin Dzer

Dtem dtem 1

where Iins, indication in the instrument undercalibration (dial gauge); Ipad, indication in thestandard (laser interferometer system); Dpad,correction due to standard errors; Dres.i, correc-tion due to the resolution presented by the instru-ment; Dres.p, correction due to the resolutionpresented by the standard; Dalin, correction dueto the alignment error between the instrumentand the standard; Dzer, correction due to theerror upon the return to the point zero; Dtem, cor-rection due to the deviation to the reference

temperature; and dtem, correction due to the tem-perature difference between the instrument andthe reference.

By considering these terms the combined stan-dard uncertainty,uc, was calculated using equation(2), as the sum of squared relative standarduncertainties:

whereuAanduBindicate respectively the type Aand type B evaluation of standard uncertainties;the expanded uncertainty (U=kuc) was obtainedby multiplying the combined standard uncertaintywith a coverage factor (k) as recommended by ISOGUM instructions.

Table 1presents the results obtained for each ofthe influence factors and the estimation ofmeasurement uncertainties for the gauge # 1 inthe vertical position.

It was assumed a rectangular distribution for thetermsDres.p,Dzer,Dtemand dtem; forDres.ia triangu-lar; for Dalina U type and for Dpad, the normaldistribution as it was indicated on a calibration cer-tificate issued by a calibration laboratory.

It can be noted that the type A evaluation ofstandard uncertainty was a dominant term fol-lowed by the resolution of the gauge readoutswhen assessing type B standard uncertainties.

The same calculation was performed for all thesix gauges in both calibration positions, although

the details are not being presented in this paper.Table 2presents the values of each parameter in

the two positions, obtained with the six gauges andtheir respective calculated uncertainties.

Observing the results obtained for the gauge # 1for the span of error (fe), it is noticed thatthe difference between the results of 12.4lm

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Vertical Increasing

IndicationErro

r(m)

Vertical DecreasingHorizontal Increasing Horizontal Decreasing

Comparison between the Calibration Results - Gauge # 1

Indication (mm)

Fig. 7. Bias curves of the gauge # 1 obtained with the calibrations made in the vertical and horizontal positions.

uc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu

2A u

2BDpad u

2BDres.i u

2BDres.p u

2BDalin u

2BDzer u

2BDtem u

2Bdtem

q 2



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(horizontal) and 12.8lm (vertical) is of 0.4lm,value that is smaller than the uncertainties of2.5lm obtained in the former position and2.4lm obtained in the latter position.

Fig. 8ac demonstrate the variations in eachone of these parameters in the calibrations per-formed with gauge # 1. Similar responses were ob-tained for the other five gauges, although they arenot presented.

4. Discussion and conclusion

It is observed that the bias curves demonstrate asimilarity of shape and position, in the vertical andin the horizontal positions.

The results in the horizontal position for bothparameters fe and fges are within the (9.914.9lm) interval. For the vertical position, the re-sults are within the (10.415.2lm) interval.

Table 1Uncertainties budgetgauge # 1 in vertical position

Symbol Source of uncertainty Probabilitydistribution

Standarduncertainty

Sensitivitycoefficients (ci)

Uncertainty(ui) lm

Degrees offreedom (mi)

Ipad Uncorrected standard errors (type B) Normal 0.01lm 1 0.01 1Iins Repeatability (type A) Normal 0.61lm 1 0.61 5Dres.i Instrument resolution (type B) Triangular 0.43lm 1 0.43Dres.p Standard resolution (type B) Rectangular 0.03lm 1 0.03 1Dalin Alignment error (type B) U type 0.003lm 9.9895 0.03 1Dzer Return to the point zero (type B) Retangular 0.29lm 1 0.29 1Dtem Deviation to the reference

temperature (type B)Rectangular 0.57735 K 0.000135 0.08 1

dtem Temperature difference between theinstrument and reference (type B)

Rectangular 0.11547 K 0.000115 0.01 1

uc Combined standard uncertainty Normal 0.80 14U95 Expanded uncertainty Normal (k= 2.1) 1.7U95 Parameters uncertainty 2.4

Table 2Resultsa of the calibration experiments of the six gauges in the horizontal and vertical positions

Calibration (lm) Span of error, fe Total span of error,fges Hysteresis error,fu

Gauge 1 H 12.4 2.5 12.4 2.5 2.2 2.5V 12.8 2.4 12.8 2.4 2.6 2.4

Gauge 2 H 8.9 2.5 9.1 2.5 2.4 2.5V 8.4 2.4 9.4 2.4 2.6 2.4

Gauge 3 H 8.3 2.5 11.2 2.5 2.7 2.5

V 8.2 2.2 10.6 2.2 3.3 2.2

Gauge 4 H 4.7 2.4 5.2 2.4 1.2 2.4V 4.8 2.0 5.2 2.0 1.0 2.0

Gauge 5 H 7.4 2.2 8.1 2.2 1.4 2.2V 7.6 1.9 8.1 1.9 1.7 1.9

Gauge 6 H 6.5 2.4 7.5 2.4 1.5 2.4V 6.8 2.3 7.2 2.3 1.8 2.3

H= Horizontal position; V= Vertical position.a Results expressed with respective expanded uncertainties.



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The result of the measurement in the horizontal

position for the parameter fu is within the (04.7lm) interval. For the measurement in the verti-cal position, the result is within the (0.25lm)interval.

As it occurred with the gauge # 1, it is observedthat, for all the other gauges studied, the values ofthe evaluation parameters, fe, fges and fu, in thevertical and horizontal positions are comparable.In other words, they are within the respectiveintervals presented; consequently it can be under-

stood that they are not each other different. For

all studied gauges, in both conditions, the domi-nant uncertainty terms were represented by theresolution of the gauge readouts (type B evalua-tion standard uncertainty) and the random errorof measurements (type A evaluation standarduncertainty).

Therefore, it can be understood that there wereno differences that indicated that the variation ofthe vertical or horizontal positioning for the per-formance of the calibration of these dial gauges

Gauge # 1 - Total Span of Error(fges)

Gauge # 1 - Total Span of Error (fges)

10.49.9

15.214.9

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Deviation(m

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Deviation(m)

Gauge # 1 - Hysteresis Error (fu)

0.20.0

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2.62.2

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Horizontal Vertical

Error(m)

a

b

c

Fig. 8. (a) Comparison between the values of the (fe) parameter of gauge # 1 obtained with the calibrations in the horizontal andvertical positions. (b) Comparison between the values of the (fges) parameter of gauge # 1 obtained with the calibrations in thehorizontal and vertical positions. (c) Comparison between the values of the (fu) parameter of gauge # 1 obtained with the calibrationsin the horizontal and vertical positions.



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could influence the results; the deviations foundwere smaller than the expanded uncertaintiesdetermined in the involved calibration processes

and were also smaller than the maximum permissi-ble error required by the DIN 878 standard.Due to the magnitude of the values of the

uncertainties obtained in the calibrations, it canbe understood that, when dial gauges presentingcharacteristics similar to the ones studied in thiswork are used, the different positions used in theirassembly (vertical or horizontal) do not representuncertainty sources that need to be taken into ac-count for the determination of the final uncer-tainty of the results of measurements.

Acknowledgement

To Mitutoyo Corporation and StarrettIndustria e Comercio Ltda for the dial gauges.

To the two accredited laboratories byINMETRO coded as RBC-031 and RBC-087.

References

[1] F.F. Farago, M.A. Curtis, Handbook of DimensionalMeasurements, third ed., Industrial Press, New York,1994, 580 p.

[2] J.A. Bosch, Coordinate Measuring Machines and Systems,Marcel Dekker, New York, 1995, 444 p.

[3] M. Kobayoshi, Calibracao de relogios comparadores,relogios apalpadores e comparadores de diametros inter-nos, SENAI, Sao Paulo, 2002, 106 p.

[4] R.S. Figliola, D.E. Beasley, Theory and Design for

Mechanical Measurements, John Wiley & Sons, Republicof Singapore, 1991, 516 p.

[5] MITUTOYO SUL AMERICANA. Departamento deplanejamento. Estudo da participacao nas vendas dafamlia dos relogios comparadores. Electronic publicationeletronica [personal communication]. Message receivedfrom on July 23, 2001.

[6] ABNT (Associacao Brasileira de Normas Tecnicas), NBR6388 : Relogios comparadores com leitura de 0,01 mm,1983, Sao Paulo, 6 p.

[7] INMETRO (Instituto Nacional de Metrologia, Normal-izacao e Qualidade Industrial), DOQ-DIMCI-004: Ori-entacoes para a realizacao de calibracoe s n a area demetrologia dimensional. Rev. 00.[s.l], Rio de Janeiro, 1999,6 p.

[8] JIS (Japanese Industrial Standard), JIS B7503: Dialgauges.Tokyo:JSA, 1997, 14 p.

[9] ISO (International Organization for Standardization), ISOR463: Dial gauges reading in 0.01 mm, 0.001 in and0.0001 in, Switzerland, 1965, 8 p.

[10] DIN (Deutsches Institut fur Normung), DIN 878: dialgauges, Berlin, 1983, 5p.

[11] ASME & ANSI (American Society of Mechanical Engi-neers), ASME/ANSI B89.1.10M: Dial indicators (forlinear measurements), New York, 1987, 14 p.

[12] ISO (International Organization for Standardization), ISOGUM: Guide to the Expression of Uncertainty in Mea-

surement First Edition 1993 (corrected and reprinted,1995), 91p.[13] INMETRO (Instituto Nacional de Metrologia, Normal-

izacao e Qualidade Industrial), Expressao da incerteza demedicao na calibracao. Rio de Janeiro, 1999, 34 p.


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