White Paper - Mettler Toledo€¦ · White Paper to Select and Test Weighing Instruments ... If the...

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A Risk Based Approach to Select and Test Weighing Instruments

Contents

1 Summary

2 Selection of a Weighing Instrument

2.1 Specifications&Uncertainty

2.2 Essentials to Select a Weighing Instrument

2.3 Example

2.4 Safety Factor

3 Testing Procedures and Frequencies

3.1 Regulatory Requirements

3.2 Test Procedures

3.3 Test Frequencies

3.4 Test Limits

3.5 Test Weights

3.6 UserTests

3.7 Instruments with Automatic Test and Adjustment Features

4 Appendix

5 Glossary

6 Literature References

Good Weighing Practice™ (GWP®) is a universal approach to selecting and testing weighing instruments based on user require-ments. GWP® allows to reduce measurement errors and ensures reliable weighings in a straightforward and efficient way.

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2 White Paper METTLER TOLEDO

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aper 1 Summary

Selection of a Weighing Instrument

Each weighing instrument has limits to its performance. While for the evaluation of a weighing instrument vari-ous criteria are to be considered, GWP® uses two key issues for a successful choice:• Theweighingcapacitymustbelargerthanthelargestgrossloadexpectedtobeweighedbytheuser;• theminimumweight1) of the weighing instrument for the accuracy required must be smaller than the small-

est sample expected to be weighed by the user.

Test Procedures and Frequencies

To achieve verification of laboratory weighing instruments effectively, GWP® recommends the following types of procedures to be carried out with a weighing instrument:• Calibrationbyauthorizedpersonnel(aservicetechnician,forexample);• routineteststobecarriedoutbytheuser;• automatictestsoradjustmentseffectedbytheinstrument.

The testing procedures and corresponding frequencies recommended by GWP® are based on• therequiredweighingaccuracyoftheapplication;• theseverityofimpact(e.g.onbusiness,consumerandenvironment),incasethattheweighinginstrument

shouldnotdeliverthecorrectweighingresult(malfunction);• thedetectabilityofsuchamalfunction.

The recommended test frequencies are increased with higher accuracy (i.e., more stringent requirements) and with increasing severity of impact, and are decreased with detectability of a malfunction. The frequencies extend between yearly to daily. Sensitivity should be tested most often, followed, with decreasing frequency, by repeat-ability (if at all) and eccentricity (if at all). The user does not need to test nonlinearity, because this property is calibrated with sufficient frequency through maintenance.

For the user tests, two test weights are recommended: • Alargeweightpreferablywithamassequaltothenominalcapacityoftheweighinginstrument,and• asmallweightpreferablywithamassequaltoafewpercentofthenominalcapacityoftheweighinginstru-

ment.

Theusertestsofsensitivityandeccentricityshouldbecarriedoutwiththelargeweight;thetestofrepeatabilitywith the small weight.

The test limits recommended by GWP® are based on• theweighingaccuracyrequiredbytheapplication;• thesafetyfactorchosenbytheuser,establishingawarninglimit,ortheexpansionfactorchosen;• themassofthesmallestsampletobeweighed(whereapplicable);• themassofthetestweightused(whereapplicable).

1) If the minimum weight specification of a weighing instrument is not known, it can be calculated from its repeatability specification, according to mmin = (k/Areq)·sRP , where Areq is the required weighing accuracy, k is the expansion factor, and sRP is the stan-dard deviation of the repeatability.

3White Paper METTLER TOLEDO

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aper 2 Selection of a Weighing Instrument

2.1 Specifications&Uncertainty

“ I buy an analytical balance with a readability of 0.1 mg, because that is the accuracy I need for my application. “Statements like this are often heard. In the wake of this requirement, a user may select an analytical balance with a capacity of 200 g and a readability of 0.1 mg, because it is believed that this balance is “accurate to 0.1 mg”. This is a misconception, for the simple reason that the readability of an instrument is not equivalent to its weighing accuracy.

There are several properties, quantified in the specifications of the weighing instrument, which limit its perfor-mance.Themostimportantarerepeatability(RP),eccentricity(EC),nonlinearity(NL)andsensitivity(SE).Howdo they influence the performance, and hence, the selection of a weighing instrument?To answer this question, the term “weighing uncertainty” must first be discussed. The “International Vocabulary of Metrology” [VIM] defines uncertainty as a parameter which expresses the dispersion of the values of a mea-surement.

The weighing uncertainty, i.e., the uncertainty when an object is weighed on a weighing instrument, can be estimated from the specifications of a weighing instrument (typically the case when performing a design qualifi-cation), or from test measurements with the weighing instrument (typically the case when carrying out an opera-tional qualification or performance qualification), or from a combination of both. The essential influences can be combinedaccordingtostatisticalmethodstoobtaintheweighinguncertainty[GUM].

Uncertaintycanbeexpressedeitherasstandarduncertaintyu (corresponding to the standard deviation of a sta-tistical process), or as expanded uncertainty U 2). To obtain the expanded uncertainty, the standard uncertainty must be multiplied with the expansion factor k. Figure 1 shows uncertainties of various balances which were estimated according to these rules from their typical specifications.

2) also referred to as “uncertainty interval”

Relative Weighing Uncertainty

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1E-05 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000

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Various Balance Models, Without Tare Load (@ k=2)

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Figure 1: Relative weighing uncertainties of various balances, from an ultra-microbalance with a readability of 0.1 µg to a precision balance with 1 g. Shown is the relative uncertainty U (in %) versus sample mass mS(ing).Uncertaintiesareestimated from typical specifications of the balances, and are expanded with a factor k=2,withtheassumptionofzerotareload (i.e., gross load = sample mass).

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Figure.2:Relativeweighinguncertaintyversussamplemass(withzerotareload)ofananalyticalbalancewithacapacityof200gandareadabilityof0.1g(U_tot,thickblackcurve).Thecontributingcomponentstouncertaintyarealsoshown:repeatability(U_RP,orange),eccentricity(U_EC,green),nonlinearity(U_NL,blue)andsensitivityoffset(U_SE,pink).Uncertaintiesareexpandedwithafactorofk=2.Repeatabilitydominatesuncertaintyinyellow-ish region, sensitivity or eccentricity in greenish region.

What can be deduced from figure 1 is that the uncertainties as a function of the sample mass behave similarly for all balances models. It is their “position”, i.e., their location relative to the axes of sample mass and uncer-tainty, which is dependent on the model of balance. The characteristics of this behavior become more obvious from figure 2, where the individual contributing components are shown. The uncertainty as a function of the sample mass can be separated into three distinctive regions: 1. Region 1 with sample masses less than the lower rollover limit mass 3) (about 10 g in this example 4), yel-

lowish in figure 2, where the relative uncertainty is dominated by repeatability. As repeatability is a weak function of gross load (if at all), the relative uncertainty decreases inversely proportional to the sample mass.

2. Region 2 with sample masses larger than the upper rollover limit mass 5) (about 100 g in this example 6), greenish in figure 2, where the relative uncertainty is dominated by sensitivity (offset) or by eccentricity 7). Therelativeuncertaintiesofthesepropertiesareindependentofsampleload;consequently,thecombinedrelative uncertainty remains (essentially) constant.

3. Region 3 is the transition region with sample masses between the lower and upper rollover limit mass, where the uncertainty rolls off from inverse proportionality to a constant value.

Moreover, nonlinearity hardly contributes a significant part to uncertainty, as its relative uncertainty, over the entire range of sample mass is smaller than any other contribution 8).

2.2 Essentials to Select a Weighing Instrument

With these facts in mind, and with the knowledge of the weighing accuracy required for an application, and the mass of the sample to be weighed, two essential selection criteria for a weighing instrument can be formulated:

3) Largest sample mass, at which the contribution of repeatability dominates uncertainty.4) The value given (10 g) for the lower rollover limit mass is valid for the analytical balance, the uncertainty of

which is depicted in fig. 2. Other weighing instruments will exhibit other limit masses.5) Smallest sample mass, at which the contributions of sensitivity offset and eccentricity dominate uncertainty.6) The value given (100 g) for the upper rollover limit mass is valid for the analytical balance, the uncertainty of

which is depicted in fig. 2. Other weighing instruments will exhibit other limit masses.7) Again, this is dependent on the model of weighing instrument: there are balances, where eccentricity is domi-

nant and sensitivity is of inferior importance.8) Thismaynotbetrueforallweighinginstruments.However,theprobabilitythatthisappliesforamajorityof

instruments is rather high.

Relative Weighing Uncertainty

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U_totU_RPU_ECU_NLU_SE

Model XP204 Individual Uncertainty Contributions (@ k=2)

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aper 1. The capacity of the weighing instrument must be larger than, or equal to, the largest gross load, i.e., the sum

of the tare load and the sample (or net) load, to be handled in the application.2. The uncertainty when weighing the smallest sample must be smaller than, or equal to, the accuracy required

(Areq) by the user’s application.

If a weighing instrument meets these two conditions, it is in principle suitable for the application. The second condition is also known as “minimum weight condition”. For a small sample mass, repeatability is the dominat-ing contribution (region 1, figure 2), from which the smallest mass, satisfying the required uncertainty condi-tion, can be calculated. This amount of mass is referred to as “minimum sample weight”, or simply “minimum weight”. If the minimum weight of a balance is unknown, it can be determined from repeatability. Because a small sample weight lies in region 1, repeatability (sRP) is the only balance property on which the minimum weight depends 9). mmin = (k/Areq)·sRP .As discussed above, it is not the readability that determines the accuracy of a weighing instrument, but rather its repeatability, or depending on it, its minimum weight capability.

2.3 Example

AfoodcompanyneedsabalancefortheirQCdepartment.Ataspecificpointinthisprocess,themassofsam-ples as small as 20 mg must be determined with a relative weighing accuracy of 1%. The gross load is limited to 180 g. What balance suits this application?

From these givens, it can be concluded that any balance with a capacity of 180 g or more (rule 1), and a mini-mum weight capability of 20 mg or lower (rule 2) is a candidate for this application.If the minimum weight of the balance would not be known, the equivalent repeatability can be calculated instead. With an expansion factor of k = 2, and the required accuracy of 1%, the equivalent required repeatabil-ity is sRP = mmin (Areq/k) = 20 mg (1%/2) = 0.1 mg.

For example, the METTLER TOLEDO XP204 analytical balance would fit this application. This balance has a (maximum) capacity of 220 g and a typical repeatability of 0.05 mg at 200 g. Figure 1 confirms this: the uncer-tainty curve (at k = 2) of an XP204 with a 20 mg sample mass passes below the 1% level 10).

2.4 Safety Factor

Repeatabilities determined from a limited number of on site weighings will vary, even if the setup is left unal-tered 11). Besides these statistical variations, environmental conditions, labware used, or the operator may change, influencing the performance of the weighing instrument 12). It is therefore recommended to apply a safety factor 13), which establishes a safety margin between the warning and the control limit. The safety fac-tor is the quotient between the (accuracy) control limit and the (accuracy) warning limit. GWP® recommends a safety factor of 2 by default to compensate for the variation in the determination of repeatability.

Revisiting our example and applying a safety factor of 2, both the required minimum weight and the repeatability decrease by this factor. The required repeatability thus amounts to 0.05 mg, a value that an XP204 may not be

9) an appropriate expansion factor k must be chosen10) Thisdiagrambasesonatypicalrepeatabilityof0.04mgatzerotare.With200gtare,thetypicalrepeatabil-

ity increases to 0.05 mg. Even though, it can be concluded from the diagram that the uncertainty margin at 20 mg is large enough to accommodate for this increase.

11) The standard deviation of a random variable is itself a random variable. For example, the standard deviation calculated from the readings of 10 weighings of the same object may accidentally exceed the true value of repeatability by as much as 180% or underestimate the true value by as low as 70% on a 95% confidence level (see appendix “Estimating the Standard Deviation of a Stochastic Process”).

12) see 'reproducibility' in glossary13) not to be confounded with the expansion factor k

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able to provide. As an alternative, the XP205 semimicro balance with a typical repeatability of 0.007 mg (at low load) could be used instead.

3 Procedures and Frequencies

3.1 Regulatory Requirements

“ Measuring equipment shall be calibrated or verified at specified intervals […] against measurement stan-dards traceable to international or national measurement standards. “ISO9001:7.6ControlofMonitoringandMeasuringDevices

“ Apparatus used in a study should be periodically inspected, cleaned, maintained, and calibrated according to Standard Operating Procedures. It is the responsibility of test facility management to ensure that instruments are adequate and functioning according to their intended use. “OECDPrinciplesofGLP,4.2Use,Calibration,andMaintenanceofEquipment

The statements cited above delegate the responsibility for the correct operation of equipment to the user. This applies also for weighing instruments. Statements like these are usually formulated vaguely, as they are meant as general guidelines. They can therefore not be put to work for daily routine. Questions like

“ HowoftenshouldItestmybalance?“emerge in situations, where guidance is needed to design standard operating procedures that neither are too exhaustive, and thus are costly and time consuming, nor are too loose to assure the proper functioning of a weighing instrument.

3.2 Test Procedures

Most likely, the majority of all samples being weighed on laboratory weighing instruments, especially in labo-ratory applications, satisfy the condition of being “small samples” 14), i.e., samples with a mass considerably smaller than the capacity of the weighing instrument, a few percent of capacity, say. When discussing the rela-tive uncertainty versus sample mass, it was already mentioned that weighing uncertainty is governed by repeat-ability, if a small sample is weighed (figure 2).

Consequently,withthemajorityofweighings,repeatabilityisthemostimportantcontributiontouncertainty.Thiswouldbeagoodreasontorecommendrepeatabilitytobetestedmostfrequently.However,thistestcom-prises repeated weighings of the same test weight multiple times, usually around 10 times. To perform this test properly, considerable effort and elaborated skills are required. On the other hand, the test of sensitivity can be carried out with one single weighing of a test weight, certainly less of an effort. What is more, the sensitivity test wouldrevealanyseriousproblemwiththeinstrument,oriftheresultweretodrift;inshort,itmayberegardedas an elementary test of the functionality of the weighing instrument. Although sensitivity is not the most critical property of a weighing instrument by far, the sensitivity test is proposed to be carried out with the highest fre-quency for the reasons cited, followed by repeatability with a lower frequency.

Revisiting figure 2 and its explanations, it was said that eccentricity influences only weighings of samples with a considerable mass compared to the capacity of the weighing instrument, larger than a few percent, say 15). Besides, placing containers and samples in the center of the weighing platform, or at least in the same place for the tare and the gross readings, the influence of eccentricity can be avoided entirely. This is the reason, why GWP® recommends to test for eccentricity less frequently than for repeatability or sensitivity. For less demand-

14) i.e., net load, not gross load15) i)massisdependentonthemodeloftheweighinginstrument;

ii) eccentricity may be superseded by sensitivity, making it negligible (also dependent on the model)


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aper ing applications, it can even be dropped, as eccentricity is tested when the weighing instrument is calibrated by

authorizedpersonnel.Fortheleastdemandingapplications,eventhetestofrepeatabilitycanbedropped.

Nonlinearityisnotrecommendedtobeingtestedbytheuseratall,asitsinfluenceonweighinguncertaintyisinferiorandhardlydominantwithanymodelofweighinginstrument;besides,itisbeingtakencareofwhentheweighinginstrumentiscalibratedbyauthorizedpersonnel.

GWP® recommends test procedures for weighing instruments as follows:i) Calibrationbyauthorizedpersonnel,includingthedeterminationofweighinguncertaintyorminimumweight,

ifapplicable;theaimistoassessthecompleteperformanceoftheinstrumentbytestingallrelevantweighingparameters of the instrument.

ii) Routine test of sensitivity, repeatability and eccentricity (but not nonlinearity), to be carried out by the user withindefinedintervals;theaimistoconfirmitssuitabilityfortheapplication.

iii) Automatic tests or adjustments, such as those of the sensitivity, carried out automatically by the weighing instrument;theaimistoreducetheeffortofmanualtesting.

3.3 Test Frequencies

GWP® thus recommends testing procedures and corresponding frequencies based oni) the required weighing accuracy of the application, andii) the impact (e.g. for business, consumer or environment), in case that the weighing instrument should not

function properly.iii) the detectability of a malfunction.

The recommended frequencies for the test of all properties extend from daily for risky applications (user or auto-matic tests), over weekly, monthly, quarterly, twice a year to yearly (e.g. calibration by authorised personnel).It is assumed that the more stringent the accuracy requirements of a weighing are, the higher the probability becomes that the weighing result does not meet the accuracy requirements. In this case, the test frequency is increased. Similarly, if the severity of the impact increases, the tests should be performed more frequently. That way, a higher impact is offset by more frequent tests, thereby lowering the likelihood of occurrence of the impact, and hence, offsetting the increase of risk that otherwise would occur.

If the malfunction of the weighing instrument is easily detectable, the test frequency is decreased.

Test Fr

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Low Medium High

10%

1%

0.1%

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Severity of Impact

Weighing Accuracy

Fig. 3: Test frequencies increase as a function of more stringent weighing accuracy and increasing severity of impact in case of a incorrect weighing (qualitative chart).

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3.4 TestLimits–ControlandWarningLimit

Routine tests are based on the required weighing accuracy for an application. Simply speaking, the weighing accuracy must be better than or equal to the accuracy required. The required accuracy is referred to as control limit CL, meaning that if this limit is exceeded, immediate action must be taken. In its simplest fashion, the test limit is equal to the control limit, and thus equal to the required weighing accuracy Areq of the application.

It was previously recommended to introduce a warning limit WL, the value of which is smaller than the control limit by a suitable factor, namely the safety factor SF introduced previously 16). The warning limit is obtained by dividing the control limit by the safety factor WL = CL/SF . This allows to test for the warning limit. If the warning limit is violated, there is still a safety margin before a process must be halted. This gives “room” for corrective actions.

Test results of each individual property are therefore to be compared to warning limits, which in turn depend on thecontrollimitsviathesafetyfactor.However,thesedeviations(sensitivity,repeatability,eccentricityandnon-linearity 17)mayoccursimultaneously;thesumoftheirdeviationsmaythusbelargerthanthewarninglimit.Asimple way to deal with this is to allocate only a part of the warning limit allowance to each individual property. This is achieved by dividing the warning limit by the uncertainty combination factor UC 18) to obtain the test limit against which the individual test results are compared, accounting for the accumulation. The warning limits for all properties (with the exception of repeatability 19) are thus obtained as follows ∆WL = mT·Areq/(SF·UC) = ½(mT·Areq/SF) (limit value for sensitivity offset, nonlinearity and eccentricity), sRP|WL = mS,min (Areq/k)/(SF) (limit standard deviation for repeatability),where Areq is the required relative accuracy, SF the safety factor, mT the mass of the test weight, mS,min the mass of the smallest sample to be weighed and k the expansion factor.

3.5 Test Weights

“ Which weight should I use to test my balance? “For the user tests, two test weights are recommended: i) A large weight preferably of a mass equal to the capacity of the weighing instrument. GWP® recommends the

next available single weight denomination according to the OIML20) classification which is smaller than or equal to the nominal capacity of the weighing instrument.

ii) A small weight preferably of a mass equal to a few percent of the capacity of the weighing instrument. GWP® recommends the next available single weight denomination according to the OIML20) classification which is smaller than or equal to 5% of the nominal capacity of the weighing instrument.

16) GWP®recommendsatleastafactorof2;ifalargeoperationalmarginisrequired,thisfactorshouldbecho-sed correspondingly higher.

17) nonlinearity is not tested by the user18) UC=2;see'uncertaintycombinationfactor'inglossary19) Repeatability dominates uncertainty in region 1 (fig. 2, yellowish). In a laboratory environment, by far the most

number of weighings of sample masses will occur in this region. The allowance of repeatability need therefore not be reduced and can thus be directly compared to the warning limit. Moreover, the standard deviation of repeatability is already expanded by k, the coverage or expansion factor.

20) or ASTM

Fig. 4GWP® recommends two test weights. The large weight has mass close to the nominal capacity of the weighing instrument, while the small weight amounts to a few percent of the nominal capacity. The large weight is used to test sensitivity and eccentricity, the small for repeatability (if required, together with an additional tare mass).


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As further guidelines, GWP® uses the following rules:1. Weights for the test of the sensitivity of weighing instruments need to be calibrated and must be traceable

(reference weight). Their maximum permissible error (mpe) must not be larger than 1/3 of the warning limit, so that its influence compared to the warning limit may be neglected entirely 21). The lowest weight class which fulfills this condition is selected. Since the warning limit depends on the control limit, and thus on the required weighing accuracy, so does the mpe of the test weight.

2. All other tests (i.e. tests of repeatability or eccentricity) may be performed with any weight, provided it does not change its mass during the test. Of course, it is always possible to use a calibrated test weight for these tests as well, but this is not required.

3. According to figure 2, testing for sensitivity with a test weight which is too small (compared to the capacity of the weighing instrument) runs the risk of the test measurement becoming “contaminated” by the influence of repeatability 22).

Testweightsforsensitivityaretypicallyofhigheraccuracyclass(OIMLForE).However,eventhoughinsomecases an OIML class M weight would suffice for a test, GWP® substitutes that class for an OIML class F2 weight. The reason is that the surface of class M weights is allowed to remain rough 23). This increases the chances for potential contamination, a feature which is not tolerated in laboratories.

Test weights for sensitivity must be (re-)calibrated themselves in regular intervals to provide traceability.

3.6 UserTests

The following tests are recommended: a) Sensitivity preferably with the large weight. At the user’s discretion, the test can be performed with the small

weight, or at an arbitrary “operating point” 24).b) Repeatability preferably with the small weight. It is recommendable to involve in the repeatability measure-

ment tare weights or containers that will be used later. 25)

c) Eccentricity preferably with the large weight.

21) with this condition, the contribution of variance of the test weight is limited to less than 10% of the variance of the warning limit

22) depending on the test limit which depends on the required weighing accuracy23) see OIML R 111-124) There is a potential loss of test selectivity when using a small weight, i.e., the sensitiv-

ity test becomes contaminated by repeatability deviations (see fig. 2, region 1). This may especially apply to test weights smaller than the second weight recommended by GWP®.

25) Tare weights, or even more so, vessels may degrade repeatability.

Balance Model Capacity Readability Large Weight Small Weight

XP6U 6.1 g 0.1 µg 5 g 200 mgXP26 22 g 1 µg 20 g 1 gXP205 220 g 10 µg 200 g 10 gXP204 220 g 0.1 mg 200 g 10 gXP1203S 1.21 kg 1 mg 1 kg 50 gXP4002S 4.1 kg 10 mg 2 kg 200 gXP10001S 10.1 kg 0.1 g 10 kg 500 gXP64000L 64.1 kg 1 g 50 kg 2 kg

Table 1: Examples of balance models and recommended test weights.

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Revisiting the example introduced earlier, featuring the requirement of a relative weighing accuracy of Areq = 1%, with a smallest sample mass of mS,min = 20 mg, a safety factor of SF = 2, and an expansion factor of k = 2, a balance with a nominal capacity of 200 g was chosen. According to the rules for test weights, a large weight of mT = 200 g, and a small weight of 10 g (5%) should be used for the user tests. The warning limits for the test of sensitivity and eccentricity is ∆WL = ½(mT·Areq/SF) = ½(200 g·1%/2) = 0.5 g, while the warning limit for the test of repeatability is sRP|WL = mS,min (Areq/k)/SF = 20 mg(1%/2)/2 = 0.05 mg (standard deviation).

Why is 5% enough to test repeatability?

As pointed out above, the majority of weighings take place with small samples. This is the case in a labora-tory when weighing small amounts of substance in a vessel, for example. It is therefore reasonable to test the repeatability with a test weight in the order of a few percent of the capacity of the weighing instrument, rounded to the next weight denomination. While repeatability generally tends to increase with increasing gross load, thisincreaseisusuallyfeeble,afactorof2fromzeroloadtonominalcapacity26),forexample.Nevertheless,repeatability may be regarded as essentially constant for small sample weights, i.e., weighings where the tare and gross loads are close to each other and therefore both readings exhibit essentially the same repeatability. This fact is depicted in figure 5. It can be seen that the uncertainty, and therefore the repeatability, as all other contributions are negligible, remains essentially constant for small sample weights (compared to the capacity of the balances) 27).

If repeatability is a critical issue, it is recommendable to put the tare object (container, vessel, flask, etc.) on the weighing platform and to test repeatability with the test weight at this “working point”. 28)

Why can the minimum weight be determined with a test weight larger than the minimum weight?

By definition, minimum weight is the lowest amount of sample mass that can be weighed, complying with a given required weighing accuracy. The most obvious method to test for minimum weight is to use a test weight with a mass of the (expected) minimum weight and determine the repeatability of the weighing instrument with this test weight. If the resulting weighing uncertainty is smaller than the required uncertainty, the test passes, if it is greater, the test fails.

This method has several disadvantages.

First, if the test passes, there is no guarantee that there might not be still a smaller mass satisfying the accuracy requirements. To find out about this, the test need to be repeated with a smaller test weight.

Second, if the test fails, the test need to be repeated, too, but this time with a larger test weight. In both cases, the test may require an iterative approach, demanding more effort than just for one test. This is a waste of resources.

26) gross27)seealsoUSP<1251>"WeighingonanAnalyticalBalance",draftrevisionPF35(2)

[March-April2009],Table1:"SuggestedPerformanceQualificationTests"28) It should be mentioned here that not only the mass of a tare load, but also its dimen-

sions may influence the repeatability of the weighing. On an XP205 semimicro bal-ance, for example, repeatability increases about 5 times when weighing a sample into a volumetric flask of 250 ml, compared to weighing the sample together with a com-pact tare of the same mass as the flask (around 90 g). See also [1].


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aper Third, using OIML test weights, as is very convenient, come only in denominations of 1-2-5. This means that a

minimum weight of 3.5 g, for example, could not be confirmed, unless the test is carried out with a weight com-binationofthreeweightpieces,namely2g,1gand0.5g.Needlesstosaythatdeterminingtherepeatabilitywith a test load composed of three test weights is a tedious and error prone task.

Fourth,minimumweightofanalyticalandmicrobalancesareintheorderofafewmilligrams.Handlingsuchasmall weight is difficult, and the faintest draft may blow the weight away.

Absolute Weighing Uncertainty

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XP6UXP26XP205XP204XP1203SXP4002SXP10001SXP64000L

1E-05 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000

Fig. 5: Weighing uncertainties of various balances, from an ultra-microbalance with a readability of 0.1 µg to a pre-cision balance with 1 g. Shown is the (absolute) uncertainty U (in g) versus sample mass mS(ing).Uncertaintiesare estimated from typical specifications of the balances, and are expanded with a factor k=2, with the assumption ofzerotareload(i.e.,grossload=samplemass).

Fig. 6: Sensitivity of a weighing instrument: Shown is the displayed weighing value W versus the load m on the platform. To test for sensitivity, it is recommended to use a test weight close to nominal capacity (1). Usingasmallertestweight(a<1)resultsinasmallermeasurablesensitivity offset, which is partially disturbed by repeatability (red band).Usingaverysmalltestweight(b<<1)resultsinameasur-able sensitivity offset which is buried entirely in the dispersion band of repeatability.

(Remark: This diagram, and particularly the test masses of (a) and (b) weights, are not shown to scale.)

W

m0 1ab

0

1

[nom. capacity]

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There is a more efficient method to test minimum weight. It bases on the fact that with all balances, repeatability is no function of sample mass, i.e., remains constant, as long as the sample mass amounts to no more than a few percent of the weighing capacity 29). With this knowledge, it becomes clear that the repeatability needs not be determined with a test weight of the very minimum mass, but can be chosen larger, as long as the condition stated is met. The repeatability obtained from this test can then be used to calculate the minimum weight (see footnote 1, page 2). The advantages of this method are manifold: • onlyonetestmustbeperformed;• themassofthetestweightcanbechosensothatthetestcanbeconvenientlycarriedout;• intermediate,i.e.,non1-2-5valuesfortheminimumweightarepossible.

Why should a test weight close to capacity be chosen for the test of sensitivity?

Referring to figure 2, region 1, where the sample mass is smaller than the lower rollover limit mass, 10 g in this example 30), it was said that repeatability dominates the uncertainty, i.e., all other properties (sensitivity, eccen-tricity and nonlinearity) contribute negligible amounts to uncertainty, compared to repeatability. A test result in this region is contaminated by deviations caused by repeatability, the more so, the smaller the test weight becomes. Simply speaking, sensitivity is buried in repeatability (see also figure 6). Therefore, a test weight close to capacity should be chosen.

3.7 Instruments with Automatic Test and Adjustment Features

“ What is the importance of the adjustment with built-in weights versus an adjustment with an external weight? “ Adjustment mechanisms built into weighing instruments consist of one or more reference weights, and a loading mechanism that is actuated either manually or automatically. Such a mechanism allows to conveniently test or adjust the sensitivity of the weighing instrument. Because the built-in weight cannot be lost, cannot be touched and is kept in a sheltered place inside the instrument, this concept has advantages over testing or adjusting with anexternalweight,whichisvulnerabletodamage,dirtandotheradverseeffects;besides,itallowstosubstan-tially reduce the frequency of such tests or adjustments with external reference weights.

However,becausethebuilt-intestweightisnotaccessible,itcannotbedeclaredasbeingtraceable,sincetrace-ability requires that the weight can be removed and compared periodically with another reference of a higher classwhichisnotpossible.Nevertheless,thebuilt-inweightcanbetestedagainstanexternalreferencebycom-paring the weighing result of the built-in weight with the weighing result of an external reference weight which is weighed immediately thereafter, the very weighing instrument being the comparator. With this comparison, the integrity of the built-in calibration mechanism can be tested.

If a weighing instrument features such an adjustment mechanism, GWP® recommends the (frequent) use of it, as it is a procedure that requires little to no effort, with the exception of a short interruption of use to the instru-ment. As a consequence, routine tests of sensitivity with external reference weights may then be performed less frequently. 31)

29) depending on the model of weighing instrument30) The lower rollover limit mass is a function of the model of weighing instrument and of the test limit. In the

example shown in the diagram, the test limit is the combination of the typical specification of sensitivity and eccentricity.

31) “For a scale with a built-in auto-calibrator, we recommend that external performance checks be performed on a periodic basis, but less frequently as compared to a scale without this feature.” AnswertoaquestiondirectedtotheUSFoodandDrugAdministrationaboutthe“autocalibrationfeature”. http://www.fda.gov/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/ucm124777.htm


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Estimating the Standard Deviation of a Stochastic Process

The determination of the repeatability of a weighing instrument from repeated weighings is an elusive operation. Primarily, this has less to do with weighing, than it has with statistics. Indeed, the results of weighings must be considered like a random variable, at least to some extent, since a weighing instrument may not always deliver the same results when the same load is repeatedly weighed. The higher the number of scale intervals of a weighing instrument, the more the result of a weighing tends to be disturbed by stochastic influences.

Fromasampleofreadings(“realizations”)ofastochasticprocess,itispossibletocalculatethestandarddevia-tion of the sample and use its value as an estimate for the true standard deviation of the process. One may ask for the confidence interval which contains 95% of the estimated standard deviations. These limits of the confi-denceintervalareafunctionofthesamplesize.Thelargerthesample(i.e.,thenumberofreadings),thecloserthese limits are to the true value, and vice versa. Figure 7 depicts the graph of these limits for a normally distrib-uted process.

Confidence Interval of Standard Deviation Estimator

0.1

1

10

1 10 100Sample Size n

95% Upper LimitTrue Std. Dev.95% Lower Limit

Estim

ated

to T

rue

Stan

dard

Dev

iatio

n Ra

tio s

/σ

Fig.7:Uncertaintyintervalofthestandarddeviationestimatedfromnormallydistributedsamples(readings),ver-sussamplesizen (number of readings), for a 95% confidence level. The uncertainty limits of the estimated stan-darddeviationarefarthestfromthetruevalueforthesmallestpossiblesamplesizeof2,andgetclosertothetruevaluewithincreasingsamplesize.Example:For10readings(n=10), the estimated standard deviation s lies within the interval of approximately 0.7 to 1.8 times of the true value s, with a confidence level of 95% for the standard deviation.

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accuracyThe closeness of agreement between a test result and the accepted reference value ([ISO 5725], 3.6). For repeated measurements, accuracy requires trueness (absence of systematic deviations) and precision. If no bias is present, or if bias is corrected for, the accuracy A of a result can be described by its uncertainty U.

adjustmentThe action of setting a measuring instrument or mass embodiment so that the measured value is correct, or deviates as little as possible from the correct value, or the deviation remains within limits of error.

applicationThe special use or purpose to which a weighing instrument is put, such as a weighing that must be performed for a specific task, with a specific method, in a specific sequence and in a specific environment.

control limitTolerance CL of a process relative to its target value. Violation of the tolerance is an infringement of the quality requirements, and therefore requires a correction of the process. warning limit

calibrationDetermination of the deviation between the measured value and the true value of the measurand under specified measurement conditions without making any changes ( adjustment).

DesignQualificationDefines the specifications of an instrument and documents the decision process that results in selection of the supplier and of the instrument.

eccentricityDeviation in the measurement value caused by eccentric loading, in other words, the asymmetrical placement of the center of gravity of the load relative to the load receiver. Eccentricity is expressed as the largest magnitude of any of the deviations between off-center and the center reading for a given test load (load dependent).

expansion factorFactor k that expands the standard (measurement) uncertainty u into the uncertainty interval U.

maximum permissible errorLargest allowed deviation from a specified value (nominal value).

mpe maximum permissible error

nonlinearityDeviationofthemeasurementvaluefromthestraightlinebetweenzeroloadandnominalload.Nonlinearityisexpressed as the largest magnitude of any linearity deviation within the test interval (load dependent).

OperationalQualificationDocuments that an instrument functions according to the defined specifications in the intended environment.


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Documents that an instrument conforms to the requirements and specifications in routine operation.

repeatabilityAbility of a weighing instrument to display identical measurement values for repeated weighings of the same or similar objects under the same conditions, such as the same measurement procedure, same operator, same measuring system, same operating conditions and same location over a short period of time. Repeatability is expressed as the standard deviation of multiple weighings (weakly gross load dependent, if at all).

reproducibilityAbility of a weighing instrument to display identical measurement values for repeated weighings of the same or similar objects under a set of conditions that includes different locations, operators or measuring systems. Repeatability is expressed as the standard deviation of multiple weighings.

safety factorThe safety factor SF is the quotient between control limit CL and warning limit WL SF = CL/WL .Asafetyfactor>1allowsfordifferencesbetweenrepeatabilityandreproducibility(standarddeviationofrepro-ducibility is larger) and adds safety to the process by accounting for any changes that could affect weighings during daily operation (e.g. environment, different handling by operators).

sensitivitySlopeofthestraightlinebetweenzeroloadandnominalload.Sensitivityisexpressedaseitheradimensionlessnumber (correct value: exactly 1) or as deviation from the correct value at nominal load.

sensitivity offsetMagnitudeofdeviationofthesensitivityfromthecorrectvalue(independentofload,ifexpressedasslope;loaddependent, if expressed as a deviation at nominal load).

traceabilityThe ability of a measurement result, or value of a standard, to be related to suitable other standards, usually international or national standards, through an unbroken chain of comparison measurements ([VIM] 6.10).

warning limitTolerance WL of a process relative to its target value. Violation of the tolerance is not in itself an infringement of the quality requirements, but indicates drift of the process and therefore requires more intensive monitoring of the process.—>controllimit

uncertaintyParameter,characterizingthedispersionofthequantityvaluesbeingattributedtoameasurand,basedontheinformation used. The parameter may be, for example, a standard deviation called standard measurement uncertainty [VIM].

uncertainty combination factorFactor UC = 2 that accounts for the fact that non-ideal properties, such as sensitivity offset, nonlinearity or eccentricity may occur simultaneously, and therefore not the entire warning limit allowance can be allocated to eachofthem.Instead,theallowanceisdividedbythestatisticalcombinationfactorof√(1+1+1)≈1.73,roundedup (for the sake of simplicity) to 2, yielding the warning limit applicable to each individual property.

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6 Literature References

[GUM]GuideToTheExpressionOfUncertaintyInMeasurement(GUM).InternationalOrganizationforStandardization,Geneva,Firstedition1995 [VIM]InternationalVocabularyofMetrology–BasicandGeneralConceptsandAssociatedTerms(VIM).ISO/IECGuide99:2007

[ISO 5725]Accuracy(TruenessandPrecision)ofMeasurementMethodsandResults; Part 1 – General Principles and Definitions.InternationalOrganizationforStandardization,Geneva,1994

[ISO 9001]Quality management systems — RequirementsInternationalOrganizationforStandardization,Geneva,2000

[1]Arthur Reichmuth: Weighing Small Samples on Laboratory Balances. 13thInternationalMetrologyCongress,Lille(F),June18-21,2007

Mettler-Toledo AG Laboratory&WeighingTechnologiesIm LangacherCH-8606Greifensee,SwitzerlandTel.+41449442211, Fax+41449443060

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