Oiml Bulletin April 2002

K Editorial

MAA 9CD

The OIML Mutual Acceptance Arrangement (MAA)continues to make good progress thanks to the contri-butions of OIML TC 3/SC 5 Members, and especiallyas a result of the considerable amount of work that has beendone by the US Secretariat of this SC. A Ninth CommitteeDraft (9CD) for the MAA has now been sent to the SCMembers and is likely to be presented for postal voting byCIML Members before the 37th CIML Meeting later thisyear in Saint Jean de Luz.

It is both the BIMLs and the Subcommittees expecta-tion that the MAA can be adopted in Saint Jean; indeed, it isnow of crucial importance for this to happen in order forthe OIML to be able to continue its work. We must nowdevelop our experience of implementing declarations ofmutual confidence for different categories of instruments inorder to be able to revise and improve this MAA in the futu-re and to start working on the other issues that have beenidentified in the OIML Action Plan.

Conformity to type is certainly the most important issuethat we have to address. It has been strongly recommendedthat a high level of priority be allocated to this topic by a

number of individuals and groups: representatives of indus-try, the Eleventh OIML Conference in London (in particu-lar), several RLMOs and most developing countries all agreethat this area is a key one for the future.

Fundamental ideas are now emerging on this issue, butto start such work requires that the OIML CertificateSystem be highly consistent throughout all the MemberStates, which is the intended outcome of implementing theMAA.

When the technical aspects of conformity to type havebeen agreed on, we shall be able to develop and extend theOIML Certificate System to include certification of indi-vidual measuring instruments. This must be our goal inorder to contribute to the free circulation of measuringinstruments and to support developing countries in exertingtighter control of the instruments placed on their markets.

We look forward to seeing this first step completed, toseeing the MAA adopted and implemented, and to wit-nessing first hand the commencing of further work in thisfield. K

BIML

Abstract

A general technique for the calibration of metricinstruments developed at the Measurement StandardsLaboratory of New Zealand is applied to the verificationof vehicle weighbridges. The technique, called thecombinatorial technique, is used to determine both theerrors in the weighbridge scale over the verificationrange and the associated measurement uncertainty. Usingsuitable equipment, the measurements can be carriedout in a time comparable to that of current techniques.The technique has the advantage that the total mass ofthe standard weights used can be between 5 % and 50 %of the capacity of the weighbridge. Although reducingthe proportion of standard weights increases theuncertainty in calculated scale errors, the technique hassufficient statistical rigor to allow a determination of thedegree of confidence in any compliance/non-compliancedecision. Examples of the verification of road weigh-bridges, up to 40 t, using the technique are given.

Keywords: Mass, Weighbridge, Verification

1 Introduction

Ongoing verification of road and rail weighbridges formarket surveillance requires regular maintenance,transportation and use of standard weights of largenominal values, typically between 0.1 t and 1 t. A weigh-bridge can have a capacity of up to 120 t or more, so thatverification requires the use of specialized lifting and

transportation equipment. Recent developments [1,2]have focused on designing such equipment to minimizethe number of personnel required to carry out verifica-tion and to improve the efficiency of the verification.Such equipment consists of a truck/trailer system thatcan transport the standard weights required as well as aforklift and hydraulic hoist for manipulating theweights.

Often it is not possible, practical or legal to transportstandard weights that reach the capacity of the weigh-bridge, in which case verification is achieved by usingsubstitution material [3] instead of standard weights. Ingeneral the truck/trailer unit itself is designed to be ofsufficient mass to be used as a substitution weight. Forexample the Rhineland-Palatinate vehicle [2] is a self-contained verification system consisting of a 12.5 ttractor, 15 t trailer, and 27.5 t of standard weights, allow-ing verification of weighbridges of up to 55 t. Oftenvehicles or material present at the weighbridge site atthe time of the verification are also used as substitutionmaterial.

OIML R 76-1 [3] allows the quantity of standardweights required for use in the substitution technique tobe as small as 20 % of the capacity of the weighbridge.The use of the substitution technique can therefore be ofconsiderable advantage to a Verification Authority withlimited resources. However, as the quantity of standardweights used is reduced, the cumulative effect of errorsdue to measurement reproducibility increases. Tightconstraints are therefore placed on the allowable limitsfor repeatability error [3], so that the use of the substitu-tion technique in accordance with OIML R 76-1 is oftennot possible.

In this paper the authors describe the application ofa relatively new technique in which the total mass ofstandard weights required can be reduced to 5 % of thecapacity of the weighbridge, while at the same timeproviding a rigorous analysis of uncertainties in the veri-fication to allow an assessment of the risk arising fromusing a smaller total mass of standard weights. Thistechnique, called the combinatorial technique, wasoriginally developed for the calibration of resistancebridges used in thermometry [4], but its application tometric instruments in general soon became apparent[5]. The combinatorial technique has practical advan-tages in large mass and balance calibration [6], andthese advantages, with particular regard to weighbridgeverification, are discussed here.

In Section 2 of this paper the authors describe theprinciple of the combinatorial technique. In Section 3they illustrate the use of the technique with threeexamples and compare the results of measurements onweighbridges using the combinatorial technique and thesubstitution technique. In Sections 4 and 5 the practicaland theoretical aspects of the technique are considered,and conclusions are given in Section 6.

5O I M L B U L L E T I N V O L U M E X L I I I N U M B E R 2 A P R I L 2 0 0 2

t e c h n i q u e

VERIFICATION/WEIGHING

A combinatorial techniquefor weighbridge verification

MARK T. CLARKSONMeasurement Standards Laboratory of New ZealandIndustrial Research Ltd.P O Box 31-310, Lower Hutt, New Zealand

TERRY COLLINS and BARRIE MORGANTrading Standards Service, Ministry of Consumer AffairsP O Box 33308, Petone, New Zealand

In this paper the term reproducibility rather thanrepeatability is used to describe apparent randomvariations in measurements. Repeatability, in relation toweighbridges, is defined in OIML R 76-1 as the abilityof an instrument to provide results that agree one withthe other when the same load is deposited several timesand in a practically identical way on the load receptorunder reasonably constant test conditions. This defini-tion is based on that given in the Guide to the expressionof uncertainty of measurement [7]. However, in the com-binatorial technique, the loads used are loaded indifferent positions and sequences, so that measurementvariability is influenced by instrument repeatability aswell as eccentric loading and discrimination. Thesefactors combined influence what is referred to here asreproducibility. Also, in this paper the authors usemass to mean conventional value of mass [8].

2 Description of the technique

The combinatorial technique involves placing m distinctloads in all possible combinations onto the weighbridge.Only one of these loads need consist entirely of standardweights, and the remaining loads are made up withsuitable material and vehicles that are available on-site.This gives a total of 2m possible loading combinations,including the weighbridge zero where no load is used.The masses of the loads are chosen so that the range ofcombinations covers the operating range of the weigh-bridge. If Max is the maximum capacity of the weigh-bridge, then a binary sequence of loads having masses ofapproximately 0.5 Max, 0.25 Max, 0.125 Max, ... gives auniform coverage of the scale range. In practice 5 loadsare usually sufficient, ranging in mass from approx-imately 0.05 Max to 0.5 Max. Although the binarysequence is ideal, any sequence of loads that gives asuitable distribution of measurements over the requiredrange is sufficient to give a rigorous assessment of errorsover the range of the weighbridge scale.

The basis of the combinatorial technique is that acomparison of scale indications for different combina-tions of loads can give information on the non-linearityof the scale without the need for standard weights. As anillustration, consider the following measurementscarried out on a weighbridge with scale intervald = 20 kg. A load of approximate mass 20 t gave areading of

r1 = 20358 kg (1)

and a load of approximate mass 10 t gave a reading of

r2 = 10082 kg (2)

A third measurement using these two loads in com-bination gave a reading of

r1+2 = 30426 kg (3)

so that

r1+2 (r1 + r2) = 14 kg (4)

Note that each reading has been corrected using themethod described in [3] in which weights of mass 0.1 dare applied to determine the value at which the indica-tion changes. If the scale response was linear one wouldexpect (4) to equal zero. The observation that this is notthe case demonstrates these three measurements provideinformation about the non-linearity of the weighbridgescale. Analysis of readings for all 16 possible combina-tions of 4 loads, nominally 20 t, 10 t, 5 t and 2.5 t, usingleast-squares estimation, gives information on the non-linearity of the scale over its entire range up to 40 t. Ifone of the loads consists of standard weights of knownmass, scale errors with corresponding uncertainties ofmeasurement can be determined [5,6]. Note that thenon-zero result of Equation (4) may also includecomponents due to instrument repeatability, discrimina-tion and eccentricity errors. However, with the largenumber of different measurements involved in thecombinatorial technique, the effect of these componentsis randomized to some extent, and consequently thesecomponents are accounted for in an evaluation ofmeasurement reproducibility from the residuals of theleast-squares estimation.

In the combinatorial technique, the dependence ofthe scale error E(r) on the scale indication r is modeledby a polynomial equation, normally a cubic polynomialof the form

E(r) = Ar + Br2 + Cr3 (5)

where A, B and C are constants that are calculated in theleast-squares analysis. Figure 1 illustrates the form ofresults obtained with the combinatorial technique. Thesolid curve is the calculated cubic polynomial E(r), andthe dashed curves (with light shading between)represent the confidence interval associated with theexpanded uncertainty U(r) [7], normally calculated for a95 % level of confidence. The bold solid lines are speci-fied values of maximum permissible error (MPE) for thedevice. In the unshaded region of Figure 1, the envelopeE(r) U(r) of probable error values lies entirely withinthe MPE, so that compliance to the MPE can be assertedwith a high degree of confidence. Conversely, in theheavily shaded region on the right hand side of Figure 1,the envelope of probable error values lies entirely out-side the MPE, so that non-compliance can be assertedwith a high degree of confidence. In the shaded regionin between, a decision on compliance or non-compliance can only be made with a lesser degree ofconfidence. However, it is not within the scope of this

6 O I M L B U L L E T I N V O L U M E X L I I I N U M B E R 2 A P R I L 2 0 0 2

t e c h n i q u e

paper to discuss the assessment of the risk associatedwith such decisions. The important point to note is thatthe combinatorial technique gives sufficient statisticalinformation to allow an evaluation of the risk associatedwith any compliance/non-compliance decision, particu-larly in situations where the total mass of standardweights available is much less than the capacity of theweighbridge.

3 Examples

The three examples presented here describe measure-ments done during verifications of three different truckweighbridges, each having a scale interval d = 20 kg. Ineach example, MPE values shown are for a Class IIIdevice on subsequent verification, as described in [3]. Allweighbridges were verified up to 40 t, which is currentlythe legal limit for road usage in New Zealand. Also, foreach example, measurements using the substitutiontechnique were carried out on the same day, in order todemonstrate the validity of the combinatorial technique.For both techniques, all readings were corrected usingthe method described in [3], in which weights, of mass0.1 d, are applied to determine the value at which theindication changes.


t e c h n i q u e

Figure 1 Schematic illustration of the form of results obtained using thecombinatorial technique, showing calculated error (solid curve) with associated expanded uncertainties (dashed curves, generally for a 95 % level of confidence). The bold solid lines are the relevantvalues of MPE.

Figure 2 Loads used in the measurements in Example 1.

Figure 3 Results of measurements using the combinatorial technique asdescribed in Example 1, using 2 t of standard weights. The datapoints indicate the variation of the data about the calculated error (solid curve). The dashed curves are the expanded uncertainty in thecalculated error, for a 95 % level of confidence. The solid bold linesare the relevant values of MPE.

Standard weights (2 t)Forklift (4 t)

Truck + material (20 t)

Weights (partlyobscured, 8 t)

Forklift + material(partly obscured, 6 t)

3.1 Example 1

For this weighbridge, of capacity 60 t, measurementswere carried out using the combinatorial technique upto 40 t with m = 5 loads, made up from vehicles andmaterial available on site, as well as standard weights.Apart from the standard weights, the masses of the loadsonly need to be known approximately in order to ensurethat the combinations are suitable. The only otherrequirement of the loads is that they be stable over theperiod of measurements. The loads used in this examplewere: truck + material (approximate mass 20 t), spareweights (8 t), forklift + material (6 t), 2nd forklift (4 t) and

standard weights (2 t). These are shown in Figure 2.Figure 3 shows the results using the combinatorial tech-nique, based on the known mass of the 2 t load ofstandard weights only. In Figure 3 the solid curve is theleast-squares estimate (the calculated error E(r)). Thedata points indicate the variations in the data about E(r)(the residuals of the least squares estimation), andthese variations are used to determine the reproducibil-ity of the measurements [5,6]. For these measurements,the reproducibility, calculated as a standard uncertainty[7], is uR = 3.1 kg. The reproducibility and the uncer-tainty in the combination of standard weights areincorporated into the least-squares analysis to calculateuncertainties in the calculated errors E(r) [6]. All otherpossible uncertainty contributions are negligible, and inthe three examples in this paper the uncertainty is domi-nated by the reproducibility component. This is notentirely obvious from Figure 1, particularly at highervalues of scale indication where the variation in the dataabout the least-squares estimate is small compared tothe expanded uncertainty (dashed lines in Figure 3). Aninherent characteristic of the combinatorial technique isthat the uncertainty in the calculated scale error at agiven scale indication is proportional to the product ofthe reproducibility and the ratio of the indication to themass of standard weights (see Equation (6) later).

Clearly, from Figure 3, one can assert to a high levelof confidence that the errors in the weighbridge indica-tion are within the specified values of MPE. This is aremarkable result, given that the mass of the standardweights used corresponds to 5 % of the capacity of theweighbridge. To demonstrate the dependence of results


t e c h n i q u e

Figure 4 Re-calculated error (solid curve) for the measurements in Example 1,based on 8 t of standard weights, and associated uncertainty (dashedcurves). The data points with uncertainty bars are the errorscalculated using the substitution technique. All uncertainties areexpanded uncertainties for a 95 % level of confidence. The solid bold lines are the relevant values of MPE.

Figure 5 Loads used in the measurements in Example 2.

Forklift + material (9 t)

Forklift + material (6 t)

Standard weights (4 t)

Weights (2 t)

Truck + material (20 t)

on the total mass of standard weights, the data was re-analyzed based on the 8 t combination of standardweights, and the results are shown in Figure 4 (datapoints have been omitted for clarity). ComparingFigures 3 and 4, the uncertainty has been reduced by afactor of four through using 8 t rather that 2 t of stand-ard weights, and the two results show excellent agree-ment within the calculated uncertainties. Figure 4 alsocompares the results for the combinatorial techniquewith those for measurements carried out using thesubstitution technique. For the substitution technique,10 t of standard weights were used in 4 substitutions,and the uncertainty limits shown are calculated fromthe reproducibility determined by the combinatorialtechnique (see reference [6]). There is excellent agree-ment between the two techniques. However, it is impor-tant to realize that without the estimate of the repro-ducibility obtained from the combinatorial technique, aproper comparison of the two techniques would not bepossible.

3.2 Example 2

For this weighbridge, of capacity 60 t, measurementswere carried out using the combinatorial technique upto 40 t with m = 5 loads, made up from vehicles andmaterial available on site, as well as standard weights.The loads were: truck + material (approximate mass20 t), forklift + material (9 t), 2nd forklift + material (6 t),standard weights (4 t) and spare weights (2 t). These areshown in Figure 5. This verification was based on the 4 tload of standard weights, and although measurementswere hindered by windy conditions at the time, thereproducibility was good (uR = 4.2 kg). Results areshown in Figure 6, along with the results from the sub-stitution technique using 10 t of standard weights. Basedon the results of the combinatorial technique, one canassert with a high degree of confidence that theweighbridge complies with the specified MPE. This isconfirmed by the excellent agreement with the results ofmeasurements using the substitution technique.

3.3 Example 3

For this weighbridge, of capacity 60 t, measurementswere carried out using the combinatorial technique upto 40 t with m = 4 loads, made up from vehicles andmaterial available on site, as well as standard weights.The loads were: truck + material (approximate mass20 t), 2nd truck (10 t), forklift + material (6 t), and stand-ard weights (4 t). Results are shown in Figure 7, alongwith the results from the substitution technique. The

calculated reproducibility was uR = 4.9 kg. In thisexample, for the results obtained using the combina-torial technique, the uncertainty is much larger com-pared with the earlier examples, exceeding the MPE atlarger load. This is largely due to the fewer number ofcombinations used and also the poorer reproducibility.Based on these results, one can only assert that theweighbridge complies with the specified MPE up toaround 20 t. As in the previous examples, there is goodagreement with the results obtained using the substitu-tion technique.


t e c h n i q u e

Figure 7 Results of measurements using the combinatorial technique asdescribed in Example 3, using 4 t of standard weights, showing thecalculated error (solid curve) and associated uncertainty (dashedcurves). The solid bold lines are the relevant values of MPE, and thedata points with uncertainty bars are results of measurements usingthe substitution technique. All uncertainties are expandeduncertainties for a 95 % level of confidence.

Figure 6 Results of measurements using the combinatorial technique asdescribed in Example 2, using 4 t of standard weights, showing thecalculated error (solid curve) and associated uncertainty (dashedcurves). The solid bold lines are the relevant values of MPE, and thedata points with uncertainty bars are results of measurements usingthe substitution technique. All uncertainties are expandeduncertainties for a 95 % level of confidence.

4 Practical aspects

4.1 Calculations

The least-squares analysis required in the combinatorialtechnique uses matrix algebra for calculation of scaleerrors and corresponding uncertainties [6]. Thesecalculations can easily be implemented in computerspreadsheet software such as Microsoft Excel. Thecalculations for the examples presented here were doneusing a spreadsheet that is set up so that, once all dataare entered into the appropriate cells, the scale errorsare automatically calculated. This implementation hasthe advantage that the operator does not need to fullyunderstand the details of the calculation.

An important advantage of the combinatorial techni-que is that the reproducibility is assessed from a largenumber of different combinations of loads. This gives areliable estimate of the weighbridge reproducibility, as itincludes variations that occur due to such effects asrepeatability, discrimination and eccentric loading.

4.2 Loading sequences

Table 1 shows the sequence of measurements inExample 2, in the order in which they were carried out.This order was designed to reduce the amount of timeand manipulation of loads required. For convenience,the sequence was divided into sub-sequences involving 3or 4 loadings. The strategy was to keep the larger loadsin place while going through the combinations ofsmaller loads. For example, for the first 4 sub-sequencesthe truck was left in position on the weighbridge whilethe other loads were moved on and off and measure-ments made.

4.3 Resources required

A critical aspect in assessing the practicality of thecombinatorial technique is the resources required, inparticular time, equipment and number of personnel. Inthe case where the total mass of standard weightsavailable is less than 10 % of the capacity of the weigh-bridge, the combinatorial technique requires a similarnumber and similar types of loadings as the substitutiontechnique [6]. In general, the efficiency of the combina-torial technique is greatly increased if rolling loads areused. For example, the use of two forklifts (with skilleddrivers) and a truck in examples 1 and 2 allowedefficient manipulation and interchanging of loads. The

ideal requirements for a weighbridge verification usingthe combinatorial technique are given in Table 2. Withsuch equipment available, measurements on a weigh-bridge using the substitution technique followed by thecombinatorial technique were completed within half aday, including the time taken to organize suitablevehicles and material for the loads required. With suitableequipment, measurements using the combinatorialtechnique can be carried out in a similar time to othercurrent techniques.

5 Theoretical aspects

Although the least-squares analysis will always produceuncertainties for a given set of measurements, it isuseful to know in advance what uncertainties can beachieved in a given situation. This can be achieved usingthe following equation, which gives an approximationfor the standard uncertainty u(r) in the calculated errorE(r) at a given indication r,

(6)

where uM is the standard uncertainty in the mass M ofstandard weights. This equation was derived empiricallyby numerical analysis, and is a slightly better approxi-mation than that given in [6]; it gives values ofuncertainty that are within 10 % of those calculated byleast-squares analysis, provided that the load of stand-ard weights is either of the two smallest loads used.

Equation (6) can be simplified with the followingconsiderations. It is usually best to use m = 5 loads, andthe uncertainty uM in the standard weights is generallysmall enough to be disregarded. For a properly installedand serviced weighbridge, based on the results pre-sented here, one would expect that uR = 0.25 d in theworst case. Equation (6) then becomes, for m = 5,

(7)

or as an expanded uncertainty (for m = 5),

(8)

A common criterion used in designing measure-ments for determining compliance or non-compliance isthat U(r) should be less than or equal to one-third of the


t e c h n i q u e

u(r) rM

u2R2

m3.6 + u2MABBBBB

u(r) 0.084 rdM

U(r) 0.17 rdM

Weights used 1 2 3 4 5Identifiers 20truck 9fork 6fork 4stds 2stds


t e c h n i q u e

Loadings Indication Delta Corrected

20truck+9fork+6fork 35000 16 3499420truck+9fork+6fork+2stds 36980 12 3697820truck+9fork+6fork+4stds 38980 10 3898020truck+9fork+6fork+4stds+2stds 40980 12 40978

20truck+9fork 28800 4 2880620truck+9fork+2stds 30800 2 3080820truck+9fork+4stds 32820 18 3281220truck+9fork+4stds+2stds 34820 16 34814

20truck+6fork 25960 8 2596220truck+6fork+2stds 27960 6 2796420truck+6fork+4stds 29960 4 2996620truck+6fork+4stds+2stds 31960 4 31966

20truck 19800 20 1979020truck+2stds 21800 18 2179220truck+4stds 23800 18 2379220truck+4stds+2stds 25800 20 25790

9fork+6fork 15180 8 151829fork+6fork+2stds 17180 8 171829fork+6fork+4stds 19180 4 191869fork+6fork+4stds+2stds 21180 2 21188

9fork 9020 10 90209fork+2stds 11020 10 110209fork+4stds 13020 10 130209fork+4stds+2stds 15020 6 15024

6fork 6180 16 61746fork+2stds 8180 18 81726fork+4stds 10180 14 101766fork+4stds+2stds 12180 14 12176

2stds 2000 10 20004stds 4000 8 40024stds+2stds 6000 6 6004

Table 1 The sequence of loading combinations used in Example 2, and corresponding indications and mass Delta of extra weightsrequired to change each indication (all in kg).

Equipment 10 t truck2 forklifts1520 t of material to make up loads28 t standard weights

Personnel 2 forklift/truck drivers1 verifying officer

Table 2 Ideal requirements for theverification of a weigh-bridge, up to 40 t, using thecombinatorial technique(see Examples 1 and 2).

MPE. Considering the case where r = Max, for whichMPE = 2 d (for subsequent verification), then thiscriterion would be met for M > 0.25 Max. That is, basedon the assumptions given here, this criterion would besatisfied for a total mass of standard weights that is assmall as 25 % of the weighbridge capacity.

6 Conclusions

This paper describes the application of the combina-torial technique to the verification of truck weigh-bridges. The combinatorial technique can be used in anyweighbridge verification, and is particularly suited to

situations where it is not feasible to have standardweights that cover the full range of the weighbridgescale. This technique enables a rigorous determinationboth of the errors in the weighbridge scale and also ofthe associated uncertainties, and can be easily andefficiently implemented with the use of rolling loads.Comparisons of the results of the combinatorial tech-nique with those of the substitution technique, madepossible through use of the reproducibility dataobtained from the combinatorial technique, demon-strate the validity of the combinatorial technique. Thecombinatorial technique provides sufficient informationto allow a quantitative assessment of the risk associatedin making a compliance/non-compliance decision,particularly when the total mass of standard weightsused is much less that the capacity of the weigh-bridge. K


t e c h n i q u e

References

[1] R.C. Goldup: A new weighbridge test unit for Hampshire County Council, OIML Bulletin No. 121, December 1990, pp.4749.

[2] W. Ggge and D. Scheidt: Vehicle for verification of truck scales, OIML Bulletin Vol. XLI, No. 3, July 2000, pp. 58.

[3] OIML R 76-1: Nonautomatic weighing instruments Part 1: Metrological and technical requirements - Tests, 1992.

[4] D.R. White, K. Jones, J.M. Williams and I.E. Ramsey: A simple resistance network for calibrating resistance bridges, IEEE. Trans. Instrum. Meas. Vol. IM-46, No. 5, pp. 10681074, 1997.

[5] D.R. White and M.T. Clarkson: A general technique for calibrating metric instruments, Proc. Metrology Society of Australia 3rd Biennial Conf., Sydney, pp. 179183, 1999.

[6] M.T. Clarkson and D.R. White: A technique for large mass and balance calibration, Proc. 5th Asia-Pacific Symposium on Measurement of Force, Mass and Torque, Tsukuba, Japan, 78 Nov. 2000, pp. 6166.

[7] Guide to the expression of uncertainty in measurement (GUM), BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, Corrected & Reprinted Edition, 1995.

[8] OIML R 33: Conventional value of the result of weighing in air, 1973.

MARK T. CLARKSON TERRY COLLINS BARRIE MORGAN

1 Introduction

This paper deals with the verification of nonautomatic,single interval weighing instruments from a statisticalpoint of view.

On the basis of the verification test results obtainedfor weighing instruments, the verification officer makesthe decision as to whether or not an instrument can beverified.

The test results are estimates, i.e. their values areassociated with uncertainties and due to them theofficer may make incorrect decisions.

The aim of this paper is to investigate these decisionsand to make suggestions about how to avoid them. Aformula is given for the uncertainty of the errors in theindication of the instrument observed in the weighingtest (R 76-1, A.4.4.1). It is used in the study of incorrectdecisions and also to judge some of the requirementslaid down for verification.

In Section 2 a short note on the verification tests isgiven. Sections 3 and 4 deal with incorrect decisions. InSection 5 a formula for the uncertainty associated withthe results of the weighing test is presented.

2 Notes on verification tests

The flow chart at the bottom of this page shows some ofthe verification tests and checks for the instruments.

The test results in 2) must be within the MPEs, themaximum permissible errors on initial verification(R 76-1, 3.5), and the differences between the results ofthe weighings in 3) must meet the permissible differ-ences (R 76-1, 3.6).

3 Uncertainty and a quality indicator for verification

3.1 True E

For a certain load let E be the error of the instrumentobtained in the weighing test and U the value of theuncertainty of that error. The interval E U covers thetrue value of E with a high confidence level. Thetrue value of E is here called the true E.

According to the requirements of R 76-1, 3.5 theabsolute value of the error E must satisfy the condition

E MPE

for all the loads. The question is, what is the probabilitythat

true E MPE

is true when

E MPE

is met and U takes on different values?

3.2 Probability that ||true E || || MPE || is true *)

Case 1: U 1/3 MPE

If E 2/3 MPE and U 1/3 MPE , then substi-tuting these values for E and U in E U (which includesthe true E) it is easy to see that true E MPE istrue.


t e c h n i q u e

WEIGHING

Verification of weighinginstruments from astatistical point of view

TEUVO LAMMI, The Finnish Association ofTechnology for Weighing, Helsinki, Finland

1) 2) 3)

Checks before the tests, e.g. Weighing test where the indications Repeatability and eccentricity testsleveling, connection to are compared with the values of the where differences between thethe power supply and test loads (standard weights) - the results of several weighings oftemperature stability true values of the indications the same load are investigated

*) A similar discussion of this subject is given in the authors paper Calibration of Weighing Instruments and Uncertainty of Calibration, OIML Bulletin, October 2001.

In general, if E MPE and U 1/3 MPE , theprobability P that true E MPE is true is approxi-mated by the fraction

MPE / ( MPE + 1/3 MPE ).

Now MPE is half the length of the interval wherethe true E should be and

MPE + 1/3 MPE

that where it is. If U < 1/3 MPE , P is greater than thefraction and if U = 1/3 MPE , P equals the fraction.So:

P MPE / ( MPE + 1/3 MPE ) == MPE / (4/3 MPE ) = 75 %

Case 2: U < MPE

U = k MPE (k < 1). In a similar way as in Case 1 theprobability P that true E MPE is true is:

P = MPE / ( MPE + k MPE ) == 1 / (1 + k) > 50 % (k < 1)

Example:

Let the observed E be

E = + 0.4 MPE .

If k = 0.9, then the true E is in the interval

E 0.9 MPE (its length is 1.8 MPE ).

In order for the condition

true E MPE

to be true, the true E should be in the interval

from 0.5 MPE to MPE

the length of which is 1.5 MPE . Thus P = 1.5 MPE / (1.8 MPE ) 83 %.

Case 3: U MPE

U = k MPE (k 1). The probability P that true E MPE is true is:

P = MPE / ( MPE + k MPE ) == 1 / (1 + k) 50 % (k 1)

On the basis of the previous cases one can draw theconclusion that the smaller the value U assumes, thebetter the chances are that true E MPE is truewhen E MPE .

3.3 Quality indicator U

If U < MPE (P > 50 %), the quality of the verificationis here regarded as good enough. Obviously values of

U 1/3 MPE (P 75 %)

are ideal but may sometimes be difficult to achieve.Practical conditions for U < MPE are given in 5.3.2and for U 1/3 MPE in 5.3.3.

If U MPE (P 50 %), the values of U should bereduced by having the instrument serviced and adjusted.As stated in 5.3.2 the adjustment should primarily aimto reduce the eccentric errors and the repeatability error,if possible. The intention is: U < MPE .

4 Type I and II errors and OC-curves

4.1 Type I and II errors

Consider Type I in Figure 1 where the observed E (3.1)is E > +MPE. If the true E in the interval E U is trueE < +MPE, it complies with the requirements (a goodresult). However, the observed E is E > +MPE and doesnot comply with the requirements. Because E is thebasis for decision, a Type I error is committed (thegood result cannot accepted).

Consider Type II in Figure 1 where E < +MPE. Ifthe true E in the interval E U is true E > +MPE, itdoes not comply with the requirements (a poor result).However, the observed E is E < +MPE and complies withthe requirements. Because E is the basis for decision, aType II error is committed (the poor result isaccepted).

Type I and II errors can also be brought about bysome defects in the tests (Section 2). For example:

A) If in the eccentricity test the variations in the zeropoint are not taken into account accurately enoughbefore the test load is applied to the different posi-tions on the load receptor, then the results of the testmay be misleading and the decisions made on theirbasis may be incorrect.

B) Suppose that the errors of the indications obtainedin the weighing test vary in a non-linear way and thatthey are within the MPEs. However, the errors of thenet values may exceed the MPEs. If in this case theerrors of the net values are not investigated as theyshould be, an instrument not complying with therequirements might be verified and a Type II error iscommitted.


t e c h n i q u e

4.2 OC-curves

In the following the effect of Type I and II errors isillustrated with the aid of OC-curves (see textbooksdealing with statistical quality control) showing theprobability that the instrument is verified.

4.2.1 Ideal OC-curve

Let us deal with an imaginary case where E is within theMPEs but U equals zero. Thus the observed E equals thetrue E. It is thus possible to perform the verificationwithout the effect of Type I and II errors. This isillustrated by the ideal OC-curve in Figure 2.

4.2.2 Actual OC-curve

In real situations the uncertainty associated with theobserved E differs from zero. When this E is used toinvestigate whether or not the condition |E| | MPE| (3.1)is met, incorrect decisions can be made due to Type Iand II errors as explained in 4.1.

Consider Figure 3 where two example OC-curves areshown. Their ordinates show the probability P that theinstrument is verified. Now let a Type I error mean thata good instrument (all the true E values are withinthe MPEs) is not verified and a Type II error that apoor instrument (all the true E values are not withinthe MPEs) is verified.

In order to avoid these errors P should be as large aspossible when |true E | | MPE| and as small as possiblewhen |true E | > |MPE|.

Curve a) in Figure 3

Type I errors may be committed because P < 1 for thevalues of true E which are just below MPE . Sogood instruments may sometimes not be verified. Ifthe true E is small or near zero, then P 1 andType I errors can very likely be avoided.

Type II errors can be committed because P > 0 for thevalues of true E which are slightly greater than MPE . So a poor instrument may be verified,although in this case quite rarely. P decreases as true E increases and assumes zero if true E isgreat enough. So the chances of Type II errors graduallydecrease as true E increases.


t e c h n i q u e

Figure 1

Type I: Let the true E be < +MPE. Decisions are made according to theobserved E which is E > +MPE. So a Type I error is committed.

Type II: Let the true E be > +MPE. Decisions are made according to theobserved error E which is E < +MPE. So a Type II error iscommitted.

Figure 2

If | true E| MPE (U = 0), the probability P that the instrument is verified is 1.

If | true E| > MPE , the probability is 0.

Curve a) is considered to be a good fit to the stepcurve (the ideal OC-curve). The fit is better the smallerthe values U assumes. On the other hand, the better thefit the more unlikely Type I and Type II errors are.

Curve b) in Figure 3

For the values of true E which are slightly smallerthan MPE , P assumes values zero. So Type I errors arevery likely and good instruments are in practice notverified. However, if true E is near zero, P 1 andthe very good instruments ( true E 0) can beverified.

kn R is the standard deviation of the results of therepeatability test. kn assumes the following valuesaccording to the number n (n 3) of results in thetest: k3 = 0.591, k4 = 0.486, k5 = 0.430, k6 = 0.395, k7 = 0.370, k8 = 0.350, k9 = 0.337, k10 = 0.325.

u is the standard deviation of the errors of theverified weights used. u = 0.4 (the sum of the mpe s of the weights for the load which corres-ponds to the load used in the repeatability test).

D is the greatest eccentric error noted in theeccentricity test (R 76-1, A.4.7). Frequently, thetest load is 1/3 MPE of the instrument. If D isless than or equal to the smaller of D < MPE or D < e for the load used in the test, set D = 0 in U.In this case the errors in the weighing test can beregarded as independent of the positions of theweights on the load receptor. Otherwise, D 0 and0.4 D is the standard deviation of the errorsbrought about by the eccentric positions of theweights on the load receptor during the weighingtest.

r is a coefficient and assumes the values 0.3, 0.4, 0.7and 1 which are associated with the values of theMPEs of the instrument as given in Table 1. r isused to evaluate U for the loads where the MPEstake on the different values 0.5 e, 1 e and 1.5 e or 0.5 e and 1 e or only 0.5 e.

The formula for U can be used if:

A) digital rounding errors included in digital indica-tions are eliminated (R 76-1, 3.5.3.2),

B) readings of the indications are unambiguous (R 76-1, 4.2.1),

C) the verification is performed at a steady ambienttemperature (R 76-1, A.4.1.2),

D) verified weights are used in the verification, and

E) the buoyancy effect of the air density on weightsdoes not need to be taken into account (note that thiseffect should also be considered on the load meas-uring device (load cell) and the load receptor).

5.2 Determination of U

The values of kn R, u and D are determined as mentionedin 5.1 and are inserted in the formula for U. Thereafter,according to r (Table 1) the values of U are sequentiallyevaluated for the loads where the MPEs take on thedifferent values.

Type II errors are practically impossible and poorinstruments are not likely to be verified at all. This isachieved at the expense of committing Type I errors.

Curve b) could represent a situation where instead of E MPE the requirement E U MPE isapplied to verification. The fit of curve b) to the stepcurve is considered to be very poor.

5 Practical evaluation of the uncertainty and requirements

5.1 Formula for U

The uncertainty U associated with the errors E (3.1)obtained in the weighing test is evaluated here with theaid of the following formula for U:

U = 2r [(kn R)2 + u2 + (0.4 D )2 ]1/2

Where: *)

R is the repeatability, i.e., the difference between thelargest and the smallest results in the repeatabilitytest. The test load is the largest load used in thetest. Frequently, it is near Max (R 76-1. A.4.10).


t e c h n i q u e

*) Explanations of kn R, u, D and r are presented in the authorspaper Calibration of Weighing Instruments and Uncertainty of Calibration, OIML Bulletin, October 2001.

Figure 3

If |true E | MPE (U > 0), the probability P (curve a) that the instrument is verified is 1. Only if the values of |true E | are near zero, then P = 1. If |true E | > MPE , P (curve a) is > 0 and cannot be 0 until the values of |true E| are great enough. The fit of curve a) to the step curve (the ideal OC-curve) is quite good but that of curve b) is not.

The values of r associated with the values of the MPEs for the instrument.

MPE: 0.5 e 1 e 1.5 e

r: 0.3 0.7 1

r: 0.4 1 -

r: 1 - -

For example, let the instrument be of class III andMax/e = n = 2000. Thus the MPEs assume the values 0.5 e and 1 e. U is as follows:

U = 2 0.4 [ (kn R)2 + u2 + (0.4 D )2 ]1/2

for the loads where

MPE = 0.5 e (r = 0.4)

U = 2 [ (kn R)2 + u2 + (0.4 D )2 ]1/2 for the loads where

MPE = 1 e (r = 1).

5.3 Requirements and values of U

5.3.1 Values of U expressed in terms of e

Let us deal with instruments with MPEs which take onthe values 0.5 e and 1 e.

According to the requirements of R 76-1 the values ofR, u and D could be as follows:

- R can be at most e, if the test load is near Max. Thenumber of weighings is supposed to be six. Sok6 = 0.395 and k6 R 0.4 e (R 76-1, 3.6.1 and 8.3.3).

- In order to obtain u, calculate the sum of the mpe sof the weights S mpe for the test load used for R. Soaccording to u in 5.1 and R 76-1, 3.7.1, u = 0.4 S m p e 0 . 4 1 / 3 M P E = 0 . 4 1 / 3 ebecause MPE = e of the instrument for the load inquestion.

- The value of D can be at most e (R 76-1, 3.6.2).


t e c h n i q u e

Insert these greatest values for kn R, u and D in U.Thus, the value of U for the loads for which MPE = 0.5 e (r = 0.4) is:

U = 2r[(kn R)2 + u2 + (0.4 D )2]1/2 == 2 0.4 [ (0.4 e)2 + (0.4 1/3 e)2 + (0.4 e)2 ]1/2 =

= 2 0.4 0.58 e 0.46 e (U MPE )

The value of U for the loads for which MPE = 1 e (r = 1) is:

U = 2r[(kn R)2 + u2 + (0.4 D )2]1/2 = = 2 [ (0.4 e)2 + (0.4 1/3 e)2 + (0.4 e)2]1/2

= 2 0.58 e 1.2 e (U > MPE )

In a similar way the values of U can be approximatedif the MPEs of the instrument assume the values 0.5 e, 1 e and 1.5 e or only 0.5 e.

5.3.2 Conditions for U < MPE and suggestions for R, D and errors of the weights

In order to arrive at values of U which are smaller than MPE (see 3.2 and 3.3), the following values aresuggested for R, D and the errors of the weights:

- R should be R < MPE or R < e for the applied testload, whichever is smaller. The number n of weighingsin the repeatability test should be n 5 (the values ofkn (5.1) are quite stable for these values of n and thusthe information from the test could be good enough).

- D should be D < MPE or D < e for the appliedtest load, whichever is smaller. In this case set D = 0 inU.

- The weights for the weighing test should, if possible,be selected so that their errors are not greater than 1/5(instead of 1/3) of the MPE of the instrument for theapplied load.

5.3.3 Conditions for U 1/3 MPE

If U should be U 1/3 MPE and the MPEs assumethe values 0.5 e and 1 e, then R should be R 0.35 efor the applied test load while D is as given in 5.3.2. Theweights should preferably be selected so that their errorsare at most 1/5 (instead of 1/3) of the MPE for theapplied load.

Table 1 Coefficient r

If U should be U 1/3 MPE and the MPEs takeon the values 0.5 e, 1 e and 1.5 e, R should beR < 0.55 for the applied test load, D is as given in 5.3.2and 1/5 should be used in the selection of the weights.However, if the weights are selected using 1/3, R shouldbe R < 0.4 e for the applied test load while D is as givenin 5.3.2. K


t e c h n i q u e

References

OIML Recommendation R 76-1: Non-automatic weighing instru-ments. Part 1: Metrological and technical requirements - Tests (1992)

Guide to the Expression of Uncertainty in Measurement, BIPM, IEC,IFCC, ISO, IUPAC, IUPAP, OIML (1995 corrected and reprintededition)

Abstract

The method used to decide whether an instrumentconforms with the requirements for legal metrology hasan important impact on the accuracy that can besubsequently achieved. There are two approaches todeciding on conformity, the classical approach that doesnot take uncertainty directly into account, and a moremodern approach that is consistent with the industrialdecision rules for proving conformity with specifica-tions.

On the basis of a consistent mathematical treatment,the consequences of using the different approaches aredemonstrated, along with their influence on theuncertainty contribution of verified instruments that arebeing used.

Introduction

The accuracy of measuring instruments must beconsistent with their intended use. ISO 9001: 2000 andISO / IEC 17025: 2000 standards [1] [2], require thattraceability of measuring and test results to national orinternational standards must be given in order to allowthe necessary statements about their metrologicalquality. The most important methodologies used toensure that measuring instruments are giving thecorrect indication are:

In industrial metrology: regular calibration of themeasuring instruments according to the qualitysystem in use; and

In legal metrology: type testing and periodic verifica-tions of the measuring instruments according to legalregulations.

Both methodologies are closely related and are basedsubstantially on the same measuring procedures. Overthe years, however, they have become established withseparate rules and metrological infrastructures, andthey aim at different areas of application.

Legal verification of the conformity of measuringinstruments is a method of testing covered by legalregulations. It is part of a process of legal metrologicalcontrol that in many economies requires type evaluationand approval of some types of instruments as a firststep.

However, the use of legally verified instruments with-in the framework of quality management sometimespresents problems, since only the maximum permissibleerrors (MPE) for the instruments are stated, without themeasurement uncertainties being explicitly given. Therelationship of legally prescribed error limits andmeasurement uncertainty is insufficiently understood.The most important concern for the instrument usertherefore is the equivalence and relationship of meas-urement results which have been obtained from verifiedand from calibrated instruments.

In order to answer this concern, the understandingof the role of measurement uncertainty in decidingconformity plays a central role, along with the estima-tion of the uncertainty contributions of verified or con-formity tested instruments when they are being used.

Verification and measurement uncertainty

Constituents of legal conformity verification

The constituents are:

Qualitative tests, predominantly for the state of theinstrument and the applicable safety requirements;

Quantitative tests which are consistent with thedefinition of calibration (see VIM 6.11 [3]);

Evaluation of the results of the qualitative and quanti-tative tests to ensure that the legal requirements arebeing met; and

If the evaluation leads to the instrument being accepted:placing a verification mark on the instrument, and, onrequest, issuing a certificate.

Measurement uncertainty associated withthe results of the quantitative tests

The aim of the quantitative tests is to determine theinstrumental errors together with the associated un-


t e c h n i q u e

UNCERTAINTY

Role of measurementuncertainty in decidingconformance in legalmetrology(*)

KLAUS-DIETER SOMMER and MANFRED KOCHSIEK

(*) This article was first published in the Proceedings of the 10th International Metrology Congress held in Saint Louis,France, from 2225 October 2001. Reprinted with permission.

certainty of measurement at prescribed testing values.The tests are carried out according to well-establishedand standardized testing procedures. These proceduresare mostly identical to those which are used forcalibration in industrial metrology. Following thedefinition of calibration (see VIM 6.11 [3]), a quanti-tative test may be considered a calibration. Comparisonmethods are predominantly used for these tests.

Figure 1 shows the block diagram of a typical com-parison of an instrument under test and a standardwhich, in the given example, is a material measure [3].The standard reproduces or supplies known values ofthe measurand XS.

From the block diagram, the measurement error D Xof the instrument under test may be described by theequation:

D X = XINDX XS d XCS d XP (1)

d XCS is the unknown error of the standard due to animperfect calibration of the standard itself;

XINDX is the indication of the instrument under test;

d XP may be the combination of all other unknownmeasurement errors due to imperfections of themeasuring procedure and of the instrumentunder test.

d XP = d XDS + d XPS + d XCPL + d XPX + d XINDX (2)

Where:

d XDS is the unknown error of the standard due to drifteffects;

d XPS is the unknown error of the standard due to itssusceptibility to the (incompletely known)environmental conditions;

d XCPL is the unknown error due to the imperfectcoupling of the measurand with the instrumentunder test, e.g. caused by temperature differ-ence, pressure loss, electrical mismatch, etc.;

d XPX is the unknown error due to the imperfection ofthe instrument under test and its susceptibilityto the (incompletely known) environmental con-ditions;

d XINDX is the unknown error due to the digital resolu-tion or the need to estimate an analoguereading.

The expectation of the measurement error E[D X] = D x is:

D x = E[XINDX] E[XS] E[d XCS] E[d XP] (3)

where the capital E symbolizes the expectation value ofthe respective quantity in brackets.

Assuming that all quantities are independent, thesquare of the standard uncertainty associated with theexpectation value of the measurement error can becalculated by:

u2(D x) = u2(d xCS) + u2(d xDS) + u

2(d xPS) + u2(d xCPL) +

+ u2(d xPX) + u2(d xINDX) (4)

The uncertainty contribution u(d xCS) can be derivedfrom the uncertainty statement given on the calibrationcertificate of the standard, and the contribution u(d xDS)from the existing knowledge about its long-termstability. All other contributions can be estimated fromthe knowledge about the quantitative test or calibration.

Figure 2 illustrates the relationship between the ex-pected value of the measurement error and theassociated (expanded) uncertainty of measurement Uwhen presenting a (single) calibration result.

Equation (4) demonstrates the key problems associ-ated with calibrations:

The result is valid only for the moment of calibration. The result is valid only for the specific calibration

conditions.


t e c h n i q u e

Fig. 2 Calibration result: Illustration of the relationship betweenthe expected value of the measurement error, D x, and theassociated (expanded) uncertainty, U, U = k u(D x) [5]

a) when stating the conventional true value together withthe indicated value,

b) when stating the conventional true value or theindicated value together with the error D x.

Fig. 1 Comparison method for quantitative testing and calibrationusing a material measure [3] as a standard. SRC - source ofthe quantity XS ; other quantities - see text

The result and, therefore, the quality of disseminationof a physical unit, depend on the performance of theindividual instrument under test.

It must be accepted that instruments are often usedin environments that are different from the calibrationor test conditions.

Therefore, the measurement uncertainty that hasbeen evaluated for laboratory conditions will often beexceeded if the instrument is susceptible to environ-mental influences. A problem can also arise if the instru-ments performance degrades with prolonged use. Theinstrument user must, therefore, consider all theseproblems on the basis of his technical knowledge.

Assessment of compliance in legal metrology

Specification limits and uncertainty of measurement

If an instrument is tested for conformity with a givenspecification or to check that it meets a requirementwith regard to error limits, this test consists of com-parisons of the calibration results, that give the meas-urement errors, with the specified values and limitsrespectively. The uncertainty of measurement associatedwith the calibration result (see Fig. 2 and equation (4))inevitably then becomes an uncertainty of the con-formity decision. Measurement results affected by meas-urement errors lying close to prescribed error limits,MPE- and MPE+, cannot definitely be regarded as being,or not being, in conformance with the given tolerancerequirement. Figure 3 (taken from the standard ISO14253-1 [4]) makes this problem quite clear: apparently,between the conformance zone and the upper and lower

nonconformance zones there are uncertainty intervalsthat are also called zones of ambiguity. The uncertaintyintervals are defined by:

IMPE- = [MPE- U; MPE- + U] and

IMPE+ = [MPE+ U; MPE+ + U].

According to the explanation of the expanded uncer-tainty of measurement given in the Guide to theexpression of uncertainty in measurement (GUM) [5], itcan be expected that values lying outside the uncertaintyintervals, can be assigned with a high probability, eitherto the conformance or to the nonconformance zones.When instruments are bought and sold, this conclusionforms the basis for demonstrating conformity or non-conformity.

Decision criteria

Classical approach of legal metrology

The classical approach of legal verification does not takemeasurement uncertainty directly into consideration.Measuring instruments are normally considered tocomply with the MPE requirement if they meet thefollowing criteria:

(a) The value of the instrumental error of the instru-ment under test is found to be equal to or less thanthe value of the prescribed maximum permissibleerror on verification (MPE):

| D x| MPE (5)

(b) The expanded uncertainty of measurement associ-ated with the value of the measurement error, for acoverage probability of 95 %, is small comparedwith the legally prescribed error limits.

In verification, the expanded uncertainty of meas-urement U95 is usually considered to be small enough ifit does not exceed 1/3 of the value of the respective errorlimit:

U95 Umax = 1/3 MPE (6)

where Umax is the maximum acceptable value of theexpanded uncertainty of measurement associated withthe value of the measurement error.

On type testing, the maximum acceptable value ofthe expanded uncertainty of measurement is reduced to:

U95type Umaxtype = 1/5 MPE (6a)


t e c h n i q u e

Fig. 3 Specification and measurement uncertainty, U(D x), which isassociated with the value of the measurement error, D x,according to ISO 14253-1 [4].

IMPE- and IMPE+ are the lower / upper uncertainty intervals(see text)

The decision criteria for verification are illustrated inFig. 4. The legally prescribed error limits, MPE- andMPE+, are equal to the acceptance limits of the instru-mental error D x.

Because of the associated uncertainty, which mayextend up to the value Umax, it can be expected that, inthe worst case, the given error limits on verification willbe exceeded by the value of Umax, i.e. by 33 % (see equa-tion (6)).

It should be noted that in many economies withdeveloped legal metrology systems, a second kind oferror limits has been defined: the maximum permissibleerrors in service (MPES). These are normally twice themaximum permissible errors on verification. For theinstrument user, the maximum permissible errors inservice are the error limits that are legally relevant [6].Therefore, there is only a negligible risk in the sense thatno measured value under verification, even if themeasurement uncertainty is taken into account, will beoutside the tolerance band which is given by the errorlimits in service (see Fig. 4).

Modern approach to deciding on conformity

In todays metrology, another approach is widely usedtoo. In the regulated area, it is applied to testing ofworking standards, e.g. weights [7]. This approach isconsistent with the prescribed procedures for state-ments of conformance of calibration results in industrialmetrology [8] and with the decision rules given to ISO14253-1 [4].

Here, instruments are considered to comply with agiven specification or with the legal requirements forerror limits if they meet the following criteria:

(a) The value of the instrumental error D x of theinstrument under test is found to be equal to or lessthan the difference between the value of theprescribed error limits, MPE, and the actualexpanded uncertainty of measurement, U95:

| D x| MPE U95 (7)

where U95 is the actual expanded uncertainty of meas-urement associated with the value of the instrumentalerror D x.

(b) The expanded uncertainty of measurement associ-ated with the value of the instrumental error, for acoverage probability of 95 %, is small comparedwith the prescribed error limits.

When verifying weights [7], the expanded uncertain-ty of measurement, U95, is usually considered to be smallenough if it does not exceed 1/3 of the respective errorlimit. Therefore, equation (6) also applies.

In practice, this means that with respect to measure-ment errors, D x, an acceptance interval is defined that issignificantly reduced when compared with the rangebetween the prescribed error limits. The magnitude ofthis interval may be defined by:

[MPE- + U95; MPE+ U95].

This approach is illustrated in Fig. 5.


t e c h n i q u e

Fig. 4 Illustration of the decision criteria according to the classicalverification approach. MPE- and MPE+ are the lower / upper maximum permissible errors on verification; MPES- and MPES+ are the lower / upper maximum permissible errors in service;D x value of the instrumental error; I

D x error acceptance interval; Umax see equation (6)

Fig. 5 Illustration of the decision criteria according to the modern approachof evaluating conformity. MPE- and MPE+ are the lower / upper maximum permissible errors on verification; D x value of the instrumental error; I

D x error acceptance interval; U95 actual expanded uncertainty of measurement associated with D x

This approach ensures that there is a high prob-ability that the prescribed error limits are hardly everexceeded. But, when compared with the classicalapproach of legal metrology, its practical result is areduction in the given error limits. Due to the com-mercial impact of such a de-facto reduction, commonuse in legal metrology seems to be unlikely.

Furthermore, it should be noted that, according toequation (7), the acceptance limits of the error value D xdepend on the value obtained for the expanded uncer-tainty U95 by the performing laboratory. This means thatthe acceptance limits are not constant, but may varydepending on the competence of the laboratory.

Use of legally verified instruments

In practice, it is often necessary or desirable to deter-mine the uncertainty of measurements that are carriedout using legally verified instruments.

The uncertainty of measurement attributed to themeasurand is to be estimated according to the GUM [5].Figure 6 shows the block diagram of a typical directmeasurement for which the following equation can bederived:

Y = XIND d XM XDelta (8)

Where:

Y is the measurand, XIND the indication of themeasuring instrument;

d XM represents a combined unknown measurementerror that comprises all unknown measurementerrors due to the imperfection of the measure-ment procedure and of the measuring instrumentin use; and

XDelta is the output quantity either from the instru-ments verification or from a calibration.

As an aid to understanding, the uncertainty contri-bution of a calibrated instrument may first be evaluated.In this case, the output quantity XDelta of the previouscalibration of the instrument is the measurement error,and equation (8) becomes:

Y = XIND d XM D X (8a)

d XM comprises the result of at least the followingerror sources (see Fig. 6):

d XPM the susceptibility of the instrument toenvironmental conditions and incompleteknowledge of the actual operating conditions;

d XDM instrument drift;

d XCPLY imperfect coupling of the measurand to theinstrument; and

d XINDM digital resolution or errors in reading theindication.

From equation (8a), the expectation value of themeasurand becomes:

y = E [Y] = E [XINDM] E [D X] E [d XM] (9)

The following standard uncertainty may be attrib-uted to the value of the measurand:

u(y) = u2(d xM) + u2(D x) (10)

Both contributions can be assumed to be independ-ent of each other. The contribution u(D x) and the valueD x are known from the result of the previous calibration.The contribution u(d xM) must be estimated on the basisof existing knowledge about the measurement.


t e c h n i q u e

Fig. 6 Direct measurement of the quantity Y (measurand).SRC is the source of the measurand; other quantities - see text

Fig. 7 Suggested probability distributions for evaluating the standarduncertainty contributions of verified measuring instruments.

Plot a: for the classical verification approach; Plot b: for the modern approach.

MPE value of the maximum permissible errors;xIND indicated value;Umax see equation (6).

ABBBBBBBBBB

In the case of a verified or conformity tested instru-ment, only the positive statement of conformity, thelegally prescribed error limits and the decision criteriaare known. With regard to the quantity XDelta (seeequation (8)), the following is known:

Classical verification approach to deciding on con-formity:

| D x| MPE and Umax = MPE / 3

Modern approach to deciding on conformity:

| D x| MPE U95 and Umax = MPE / 3

In both cases, the quantity XDelta (see equation (8))may be understood as an unknown measurement error,d XDelta, inside the above given limits.

For verified instruments, equation (10) becomes:

u(y) = u2(d xM) + u2(d xDelta) (10a)

The contribution u(d xM) must be estimated in thesame way as for calibrated instruments.

u(d xDelta) can be estimated on the basis of the follow-ing knowledge:

Indications in the ranges of values

[y MPE; y + MPE], for the classical approach,

or

[y MPE + Umax; y + MPE Umax], for the modernapproach, can be assumed to be equally probable.

The probability of indications beyond these intervalsdeclines in proportion to the increase in distance fromthese limits. Indications outside the intervals [y MPE Umax; y + MPE + Umax], for the classical approach,and [y MPE; y + MPE], for the new approach, areunlikely.

This knowledge corresponds more or less to atrapezoidal probability distribution as shown in Fig. 7.

Therefore, the uncertainty contribution of newlyverified measuring instruments may be estimated by

u(d xDelta) = a (1 + b2) / 6 [5] (11)

Where:

for the classical approach, a = Umax + MPE; b = 0.75

, and,

for the modern approach,a = MPE; b = 0.60 ... 0.80.

As a result we obtain u (d xDelta) 0.7 MPE (classicalapproach) and 0.5 MPE (modern approach).

It should be emphasized that in comparison withcalibration results, simplicity and confidence inconformity statements which are provided to the instru-ment user must be bought by keeping a considerableerror reserve. This error reserve corresponds to theratio of maximum permissible errors to the maximumacceptable expanded uncertainty. It also depends on themethodology used to consider the measurementuncertainty.

References

[1] ISO 9001: Quality management systems Requirements,International Organization of Standardization (ISO),Geneva 2000.

[2] ISO/IEC 17025: General requirements for the competenceof testing and calibration laboratories, 2000.

[3] International Vocabulary of Basic and General Terms inMetrology, BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML,1993.

[4] Geometrical Product Specification (GPS) Inspection bymeasurement of workspieces and measuring equipment;Part 1: Decision rules for proving conformance ornonconformance with specifications, ISO 14253 1,1998, International Organization for Standardization(ISO), Geneva 1998.

[5] Guide to the Expression of Uncertainty in Measurement,BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, Geneva1995 (corrected and reprinted).

[6] K.-D. Sommer and S.E. Chappell and M. Kochsiek,Calibration and verification: Two procedures havingcomparable objectives and results, OIML Bulletin, Vol.XLII, pp. 5 12, January 2001.

[7] OIML R 111: Weights of classes E1, E2, F1, F2, M1, M2, M3,OIML, 1994.

[8] The Expression of Uncertainty in Quantitative Testing,EA 3 / 02, Ed. 1, European Cooperation for Accredita-tion (EA), April 1997

Acknowledgement: The authors wish to thank Charles D. Ehrlich(NIST, USA) for useful discussions.


t e c h n i q u e

KLAUS-DIETER SOMMERLandesamt fr Mess- und Eichwesen ThringenUnterpoerlitzer Str. 2, PF 10 01 55, 98693 Ilmenau, Germany

MANFRED KOCHSIEKPhysikalisch-Technische BundesanstaltBundesallee 100, PF 33 45, 38116 Braunschweig, Germany

ABBBBBBBBBBB

ABBBBBB

25

e v o l u t i o n s

O I M L B U L L E T I N V O L U M E X L I I I N U M B E R 2 A P R I L 2 0 0 2

This paper was presented at the 13th International Fair ofMedical Techniques Health For All held in Havana,

Cuba, on April 2327, 2001.

Although still considered a developing economy, Cubais recognized by many countries as being an authorityin the medical domain on account of a number offactors:

Its success with the educational program for trainingmedical, paramedical and electro-medical servicepersonnel;

The progress made in creating teaching and health-care units;

The introduction of free national medical andhospital care; and

The existence of health indicators which are com-parable to (and in some cases better than) those ofdeveloped countries.

The concept of medical authority includes not onlythe above elements, but also the assurance that bothimported and domestic equipment used within thenational health system operate in a safe and reliableway.

Medical equipment, many of which are in factmeasuring instruments, plays an important role withinthe national health system since many of the para-meters used as supports for clinical diagnosis areobtained as a result of measuring processes. It is nothard to imagine the negative impact of a measurementresult intended to be used for a diagnosis or a therapytreatment if the instrument fails to operate correctly.Just by way of example one could mention:

A lack of accuracy in radiotherapy equipment maylead to harmful radiation emissions or may causenegative effects on a tumor;

A sphygmomanometer registering unequal figures ofmaximum and minimum blood pressure values, orshowing an error that is outside the maximum per-missible values established, has a negative influenceon the determination of a patients blood pressurepattern;

If the electrical impulse for cardiac muscle stimula-tion is not properly quantified, an energy value loweror higher than the correct one is likely to be applied,thus paving the way for alterations in the impulseand irreversible damage being done to the patient.

In brief, the essence of safety and reliability in theuse of medical equipment lies in the assurance of itscorrect performance and the accuracy of its measure-ments, aspects contained within the object of study ofthe metrological science and, particularly, of theactivities related to metrological control.

Each country takes care of the coordinated develop-ment of these aspects depending on its own (state ornon-state) metrological activity. In this regard, theCuban government is responsible for ensuring thecorrect operation of the said metrological infrastructureto protect the population, but the factors that con-tribute to the design, development, manufacture,import, marketing and ultimate use of measuringinstruments - in the present case medical instruments -are also involved.

Cubas level of development in medical equipmentproduction and the fact that the majority of thisequipment is currently imported triggered the decisionto create and develop a methodological, organizationaland scientific-technical infrastructure which allows thetrueness of the technical, metrological and safety-related characteristics stated by the manufacturers tobe assessed.

Testing also provides information about:

The technical level of the equipment according tomodern-day technological developments;

The behavior with regards to external influencequantities;

The possibility to carry out metrological control ofthe equipment; and

The facilities for the maintenance and repairactivities, among others.

The main objective is clearly to ensure the highestpossible level of product quality and to this end theOIML, with its 107 Members (among which Cuba, oneof the founders) attempts to guarantee a propercredibility level concerning test results and thus facili-tate international harmonization of regulations andmetrological controls applied by national metrologyservices, promote international cooperation andcontribute to the elimination of technical barriers totrade. A significant role is played therein by OIML D 19

CUBA

Regulations for themetrological control of measuring instruments in the Republic of Cuba

DR. YSABEL REYES PONCEHead of INIMET Testing LaboratoryNational Metrology Research InstituteNational Bureau of Standards, Cuba

26

e v o l u t i o n s


NC OIML D 19 (1994) Pattern Evaluation andApproval, and

Joint Resolution 1-95 of the Ministry of Economicsand Planning and the Ministry of Foreign Trade onProcedure for Measuring Instrument Pattern Evalua-tion and Approval, published in the Official Gazette ofthe Republic of Cuba, June 28, 1995.

The Normative Document NC OIML D 19 is a gen-eral document that contains:

Introduction; Definitions; Instruments submitted for pattern approval; Procedures for pattern approval; Pattern evaluation plan and examination; and Pattern approval decision.

The procedure for measuring instrument patternevaluation and approval is laid down in a separatedocument with a view to the nationwide implementa-tion of NC OIML D 19, and it contains:

Evaluation and approval bodies; Responsibilities for pattern approval; Procedure for pattern approval and evaluation; Annex 1: Content of the pattern approval certificate;

and Annex 2: List of measuring instruments submitted for

pattern approval.

In the case of medical science, the list given inAnnex 2 includes measuring instruments the legalnature of which refers to measuring the characteristicsof human beings and animals, therapy uses, instru-ments used in chemical, biological and biochemicalanalyses, identification of biological and chemicalsubstances and species, and definition of contents,concentrations, etc.

This document is mandatory for all state and privateentities operating in the country in the development,production, importation, marketing and use of measur-ing instruments comprised within their scope.

Likewise, it is mandatory for state and privateinvestment entities that import into the country anymeasuring instruments covered by this procedure. Theprocedure establishes that:

Assessment bodies and testing laboratories mustmeet the requirements laid down in NC ISO 9002 onQuality management and assurance and NCISO/IEC 17025 on General requirements for thecompetence of testing and calibration laboratories.

The assessment bodies are the laboratories located inentities that belong to the system of the NationalBureau of Standards, namely the National MetrologyResearch Institute and the Territorial MetrologyCenters. Other laboratories outside the system of the

Pattern Evaluation and Pattern Approval, adopted byCuba and discussed in further detail later on.

Decree-Law 183 on Metrology, which came intoforce in Cuba as of July 2, 1998, contains two chaptersdirectly linked to our object of study:

Chapter VI: On metrological control; and

Chapter VII: On the manufacture, repair and sale ofmeasuring instruments.

Metrological control

Metrological control addresses measuring instrumentsand methods as well as the conditions under which theresults are obtained, expressed and used. Measuringinstruments in use or to be used in specified regulatorymeasurements are subject to metrological control,including:

Standard instruments used in the verification andcalibration of measuring instruments;

Instruments used in public health; Commercial transactions; Environmental protection; Technical safety; Official registers; Instruments used in consumer-related activities; and Others of public interest.

Only those measuring instruments that have beensubmitted to metrological control with satisfactoryresults can be used.

Any measuring instrument submitted to metrolo-gical control that fails to meet the regulatory require-ments will be declared unfit for use or sale until it does.If the instrument cannot be conditioned to meet therequirements of this Decree-Law, its provisions will bewithdrawn or confiscated, as applicable.

The metrological control of measuring instrumentsis a group of activities comprising:

Pattern approval; Initial and subsequent verification; and Supervision of use.

For the moment, pattern approval and supervisionof use (metrological supervision) will be dealt with.

Pattern approval

Pattern approval is regulated in Cuba according to theprovisions laid down in:

27

e v o l u t i o n s


National Bureau of Standards may be used providedthey meet the above-mentioned requirements.

The pattern approval body is the National Bureau ofStandards, which has put the National MetrologyResearch Institute in charge of approving, registeringand issuing the certificates.

The approval body can accept pattern approvalsissued by any other country(ies) as long as there arebilateral or regional agreements signed to this end. Itcan also accept pattern approvals emanating fromother competent bodies, after a case-by-case discus-sion with the applicant.

Measuring instruments imported before both NCOIML D 19 (1994) and the Procedure for MeasuringInstrument Pattern Evaluation and Approval cameinto effect, and put into use in places of strategic eco-nomic importance or where a very stringent safetylevel is required, must remain under the metrologicalcontrol of the National Bureau of Standards, andtheir importation is prohibited until they are evalu-ated and approved.

So far the OIML Technical Committee for MedicalInstruments (TC 18), together with other TCs, haveissued twelve International Recommendations whichare very useful for the evaluation of various types ofmedical measuring instruments, among whichelectrocardiographs, electroencephalographs, sphygmo-manometers, audiometry equipment, dosimeters,ergometers and clinical thermometers.

Metrological supervision

State inspectors carry out metrological supervision on:

Production, testing, calibration and verification ofmeasuring instruments;

Proper use and application of measuring instru-ments;

Maintenance, reparation or modification of measur-ing instruments;

Production, control and sale of prepacked and pre-packaged products; and

Importation of measuring instruments and pre-packed and prepackaged products.

Manufacture, repair and sale of measuringinstruments

Decree-Law 183 on Metrology establishes, amongothers, the following provisions:

Any measuring instrument importer shall provide, asapplicable and together with the final user and otherrelevant parties, the necessary means for the assemb-ling, use, maintenance and repair of the instruments.

It also points out that:

Any manufacturer, importer, renter, trader or user ofmeasuring instruments of a new pattern shall ensurethat they are included in the block diagram of thecorresponding hierarchy. Otherwise, they areresponsible for guaranteeing their traceabilitythrough the National Metrology Research Institute orthe Territorial Metrology Centers.

It is important to underline the fact that Chapter Xof this Decree-Law includes the means available fordealing with offences.

Decree-Law 271 of the Executive Committee of theCouncil of Ministers on Contravention of regulationsestablished on Metrology, January 10, 2001, will comeinto force in the country ninety days after its publica-tion in the Official Gazette of the Republic of Cuba.

Any offences concerning the above regulations willlead to administrative sanctions being taken, in addi-tion to any civil, legal or other liabilities which mayarise.

In the event that any of the above offences areimputable to a physical person, he/she will be partiallyor totally, temporarily or definitively banned fromcarrying out the specific activity he/she had beenauthorized to carry out, as applicable. The incumbentwill be personally liable in accordance with the relevantcontravention.

Finally, as additional information on the level ofperformance of Cuban metrological control activityregarding pattern evaluation with a view to approval, itcan be stated that the Testing Laboratory of theNational Metrology Institute ranks among the entitiesthat have offered this service by assessing various typesof medical measuring instruments, such as:

Line of electrocardiographs; System for cardiac rhythm recording and processing; Baby scales; Dosimeter readers; Blood pressure monitor; and Bone density measurer. K

METROLOGY 2002810 May 2002 - Havana (Cuba)

On May 8 to 10 2002, Havana (Cuba) will host the internationalmeeting METROLOGY 2002

For more information, please visit www.oiml.org

29

u p d a t e


OIML technical activities

A 2001 ReviewA 2002 Forecasts

Activits techniques de lOIML

A Rapport 2001A Prvisions 2002

WD Working draft (Preparatory stage)Projet de travail (Stade de prparation)

CD Committee draft (Committee stage)Projet de comit (Stade de comit)

DR/DD/DV Draft Recommendation/Document/Vocabulary (Approval stage)Projet de Recommandation/Document/Vocabulaire (Stade dapprobation)

Vote CIML postal vote on the draftVote postal CIML sur le projet

Approval Approval or submission to CIML/Conference for approvalApprobation ou prsentation pour approbation par CIML/Confrence

R/D/V International Recommendation/Document/Vocabulary (Publication stage) For availability: see list of publicationsRecommandation/Document/Vocabulaire International (Stade de publication)Pour disponibilit: voir liste des publications

Postponed Development of project suspended pending completion of relevantdocument by other international organization(s)Dveloppement du projet suspendu en attendant lachvement dundocument correspondant par une (d)autre(s) organisation(s) internationale(s)

KEY TO ABBREVIATIONS USED

Les informations donnes en pages3036 sont bases sur les rapports

annuels de 2001, fournis parles secrtariats OIML. Lesthmes de travail sontdonns pour chaque comittechnique ou sous-comitactif qui a produit et/ou

distribu un WD ou un CDpendant 2001, avec ltat

davancement la fin de 2001 etles prvisions pour 2002, si appropri.

The information given on pages 3036is based on 2001 annual reports

submitted by OIML secretariats.Work projects are listed for

each active technicalcommittee and sub-

committee that producedand/or circulated a WD or

CD during 2001, together with the state of progress at the endof 2001 and projections for 2002,

where appropriate.

30

u p d a t e


OIML TECHNICAL ACTIVITIES 2001 2002

TC 2 Units of measurement

Amendment* D 2: Legal units of measurement WD 1 CD*(harmonized with resolution of 22nd CGPM (Paris, 1999)

TC 3 Metrological control

Revision D 1: Law on metrology WD 1 CD

TC 3/SC 1 Pattern approval and verification

Initial verification of measuring instruments utilizing D -the manufacturers quality system (D 27)

TC 3/SC 2 Metrological supervision

Revision D 9: Principles of metrological supervision 2 CD 3 CD/DD

TC 3/SC 3 Reference materials

Revision D 18: General principle of the use of certified reference Vote Dmaterials in measurements

TC 3/SC 4 Application of statistical methods

Applications of statistical methods for measuring WD 1 CDinstruments in legal metrology

TC 3/SC 5 Conformity assessment

Mutual acceptance arrangement on OIML type evaluations 8 CD DD

Expression of uncertainty in measurement WD 1 CD in legal metrology applications

OIML Certificate System for Measuring Instruments 2 CD DD/Vote

OIML procedures for peer review of laboratories to enable mutual WD 1 CDacceptance of test results and OIML certificates of conformity

Checklists for issuing authorities and testing laboratories 2 CD DDcarrying out OIML type evaluations

TC 4 Measurement standards and calibration and verification devices

Revision D 5: Principles for establishment of hierarchy systems 1 CD 2 CD/DDfor measuring instruments (Questionnaire

on revision)

Revision D 6 + D 8: Measurement standards. 2 CD DD/VoteRequirements and documentation

31

u p d a t e


OIML TECHNICAL ACTIVITIES 2001 2002

Revision D 10: Guidelines for the determination of calibration DD DD/Voteintervals of measuring equipment (Developed

by ILAC)

Principles for selection and expression of metrological characteristics WD 1 CDof standards and devices used for calibration and verification

TC 5/SC 1 Electronic instruments

Revision D 11: General requirements for electronic WD 1 CDmeasuring instruments

TC 5/SC 2 Software

Software in legal metrology WD WD/1 CD

TC 6 Prepackaged products

Revision R 87: Net content in packages 2 CD 3 CD/DR

TC 7 Measuring instruments for length and associated quantities

Revision R 35: Material measures for length for general use WD 1 CD

TC 7/SC 1 Measuring instruments for length

Revision R 30: End standards of length (gauge blocks) WD 1 CD

TC 7/SC 3 Measurement of areas

Instruments for measuring the areas of leather WD/1 CD

TC 7/SC 4 Measuring instruments for road traffic

Electronic taximeters WD 1 CD

TC 8 Measurement of quantities of fluids

Vessels for public use(Combined revision of: WD WD/1 CDR 4: Volumetric flasks (one mark) in glass;R 29: Capacity serving measures;R 45: Casks and barrels; andR 96: Measuring container bottles) E

32

u p d a t e


2001 2002

TC 8/SC 2 Static mass measurement

Annex to R 125: Test report format for evaluation of massmeasuring systems for liquids in tanks WD

TC 8/SC 3 Dynamic volume measurement (liquids other than water)

Revision R 86: Drum meters for alcohol and their supplementary devices WD

Revision R 118: Testing procedures and test report format for pattern 2 CD 3 CDevaluation of fuel dispensers for motor vehicles

Revision R 117: Measuring systems for liquids other than water WD 1 CD(combined with revision R 105)

TC 8/SC 4 Dynamic mass measurement (liquids other than water)

Revision R 105: Direct mass flow measuring systems for quantities WD 1 CDof liquids (with the intention of incorporating R 105 into R 117)

TC 8/SC 5 Water meters

Water meters intended for the metering of cold water - Amended R 49-1(including requirements for electronic devices) (R 49-1) to be published

R 49-2: Test procedures Approval R R 49-3: Test report format WD 1 CD/2 CD

TC 8/SC 6 Measurement

Date post:	22-Nov-2015
Category:	Documents
Upload:	libijahans
View:	82 times
Download:	12 times

Oiml Bulletin April 2002

Documents