Handbook of Weighting Applications

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Preliminary Considerations

In many areas of applications, the balance,scale or weight value is only a means to anend. The quantity that is actually of interest isderived from the weight value or mass. Forthis reason, each booklet of the Handbook of Weighing Applications thoroughly treats aspecific topic. For every subject, the individual

booklets include an explanation of the gener-al and theoretical principles of the applica-tion concerned – this is not always possiblewithout discussing equations according tothe laws of physics or mathematical formulas.Part 3, which is now available, discusses thesubject of “Balances and Scales Used as TestEquipment in a Quality System.”

An important part of all quality systems is thearea covering inspection, measuring and testequipment and its monitoring for accuracy.The quality element “control of inspection,measuring and test equipment” requires thatthe supplier of a product or service developand maintain Standard Operating Procedures

(SOPs) for inspecting, calibrating andservicing test and measuring equipment. Thepurpose of these SOPs is to ensure that thesupplier´s products conform to defined qualitystandards. When referring to the control of inspection, measuring and test equipment, wemean an orderly sequence that ensures thatthe equipment is inspected in a timely fashionand, if necessary, appropriate measures aretaken so that the equipment corresponds tothe given requirements.

Using the laboratory balance as an example,this chapter explains how one can establishan acceptable level of confidence in the testand measuring equipment being used. Suit-ability of the equipment is the initial require-ment for obtaining reliable results.

Marketing, Mechatronics DivisionApril 2001

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Contents

4 Motivation4 Quality

5 Quality Systems Overview5 Universal Quality Systems5 ISO 9000 Series5 EN 45000 Series

5 Legally Regulated Quality Systems5 GLP (Good Laboratory Practice)5 GMP (Good Manufacturing Practice)

6 Selection of Suitable Test andMeasuring Equipment

6 Equipment Qualification6 Design Qualification (DQ)6 Installation Qualification (IQ)6 Operational Qualification (OQ)6 Performance Qualification (PQ)6 Device Qualification / Final Report

6 Test Methods

7 Determination of the Uncertaintyof Measurement

7 Weighing Range7 Repeatabil ity7 Standard Deviation8 Linearity Error

9 Influence Quantities9 Sensitivity9 Temperature Coefficient9 Zero Point Drift9 Off-Center Load Error

10 Operator

10 Weighing Location10 Leveling10 Gravitational Acceleration11 Mechanical Disturbances11 Humidity11 Barometric Pressure11 Air Buoyancy12 Electromagnetic Disturbances

13 The Sample13 Static Electricity13 Magnetic or Magnetizable Samples14 Hygroscopic Samples14 Sample Temperature

15 Traceability of a Measurement

15 Calibration and Adjustment15 Calibration15 Adjustment15 External Calibration and Adjustment15 Internal Calibration and Adjustment

17 Mass and Weights

3

19 Documentation19 Description and Identification of the

Test and Measuring Equipment19 Calibration Equipment and Results19 Defined Maximum Permissible Errors19 Ambient Conditions and Corresponding

Adjustments

20 Maintenance Procedures20 Modification of the Weighing

Instrument(s)20 Appointment and Identification of

Personnel Responsible for MonitoringTest Equipment

20 Restrictions on the Suitability of Testand Measuring Equipment

20 Defining the Interval of Confirmation20 If Non-Conforming Test and Measuring

Equipment Causes Consequential Damage21 Manufacturer’s Recommendation21 Tendency Toward Component Wear

and Drift21 Environmental Influences21 Demands of Customers, Standards or

Laws21 Experience with Similar Test and

Measuring Equipment

21 Summary

22 Error Calculation22 Systematic Errors22 Random Errors24 Deriving the Uncertainty of

Measurement from theStandard Deviation

25 Appendixi Example of a Standard Operating

Procedure (SOP)v Example of a Logbook



Motivation

In the meantime, extreme ranges of resolutionhave been attained in the field of analyticalweighing technology. Reaching these newlimits, however, has opened up discussionabout the competence of individual laborato-ries. For this reason, most laboratories keepcertificates, accreditation documents and

written attestations on file. These credientalsprovide objective evidence of the laboratory´sperformance and assure those using thelaboratory’s services that analytical questionswill be answered by an expert.

In addition, the flood of analytical data hasconfronted laboratory employees with aproblem. Namely, they must test and validatemany measured values for plausibility andaccuracy. Here again, quality assurancemeasures are essential for correct, comparableand verifiable results, and are fundamental tolong-term success.

Regulations and standards of the most promi-nent quality systems that relate to the controlof inspection, measuring and test equipmentare:• GLP (Good Laboratory Practice)• GMP (Good Manufacturing Practice)• ISO 9000 series• EN 45000 series

They have been generalized to cover a largenumber of devices and procedures and,therefore, must be interpreted accordingly.

ISO 10012 provides a more extensive andconcrete explanation of the requirements fortest and measuring equipment. Accordingly,a series of measures for using the test andmeasuring equipment can be summarized asa few general, basic requirements.

The objective of each quality system is toprovide a product or service with the appro-priate quality. But what is quality? The term“quality” is defined in the EN ISO 8402standard as follows:

“Totality of characteristics of an entity thatbear on its ability to satisfy stated andimplied needs”

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QualityDefinitionResponsibilities

Ensured byquality systems

GLP/GMP

“Quality elements”: apparatus, test equipment

ISO 9000 EN45000/DIN17025

TraceabilityTolerancerequirements

Uncertainty of measurement

Documen-tation

Confirmationsystem

Mathematicalmethods

Technicalspecifications

Influence factorsDisturbances



Quality Systems Overview

The following descriptions of the qualitymanagement systems intend to highlight thekey features and application areas. One thingthat all quality systems have in common is intheir requirements placed on test equipment.These common requirements describe howequipment qualification is carried out for all

test equipment before initial operation andhow this equipment that is used daily is testedand calibrated on a regular basis.

Quality management systems are subdividedinto various categories. We distinguishbetween universal and industry-specificquality systems.

Universal Quality Systems

ISO 9000 SeriesThe ISO 9000 series is a set of widely usedinternational standards applicable to produc-tion and the service industry. Considering itsgeneral applicability, ISO 9000 does notcontain requirements specifically related tolaboratories, but is a suitable approach forassuring quality in laboratories. The ISO 9000series covers voluntary requirements for allareas of production and service. A manage-ment representative for quality oversees theintegrated quality management and assur-ance entities. Internal audits are carried outcontinually, and recertification is done everythree years.

The focal points of this quality system lie onthe following:

• Internal and external interfaces• Purchaser-supplier relations• Corrective action

EN 45000 SeriesThis quality system involves European-widerecognition of testing laboratories. A testinglaboratory accredited for compliance withEuropean Standards obtains the status of an“institution qualified for specific tasks.” Thislaboratory is accredited for a defined scope of

validity and is re-accredited every five years.A typical example of a laboratory accreditedfor compliance with the EN 45000 standardsis a testing laboratory commissioned to per-form analyses relating to environmental pro-tection. The particular focal points of a quali-ty system based on European Standards arethe following:

• Employee qualification• Qualification of the processes used• Accuracy of the results• Device testing• Calibration and validation of the method

used

Legally Regulated Quality Systems

GLP (Good Laboratory Practice)GLP is a system of standards applied world-wide and is legally regulated for data used toassess products for safety approval in orderto protect people and the environment fromhazards. The requirements imposed by GLPrefer to the organization and to personnel. Anaudit for compliance with GLP requirementsis performed every four years. A typical exam-ple of a GLP-compliant unit is a toxicologicalor analytical laboratory in a chemicals

company that conducts research, or a testinglaboratory that is commissioned to performtests. The focal points of GLP are the following:

• Organizational rules and formal require-ments

• Documentation• Independence of the quality assurance unit

GMP (Good Manufacturing Practice)This system is prescribed for the pharmaceuti-cal industry and medical device manufactur-ers. The scope of application for GMP lies inthe manufacture and analysis of pharma-ceuticals. The focal points of GMP are thefollowing:

• Defined and validated manufacturingprocesses

• Release of each product lot• Self-audits

The most important prerequisites for imple-menting GLP and GMP are listed as follows:

• Organizational structure of the testingfacility

• Qualification of personnel• Quality assurance program• Testing facilities• Equipment, materials and reagents• Test and reference materials• Standard operating procedures (SOPs)• Study plans, raw data and test reports• Filing and preservation of records and

materials

If we compare all quality systems with oneanother, we discover that many areas overlap.These systems differ from one another in theirfocal points because each system has differ-ent objectives. For instance, GLP is a system of documentation that contributes towardsimproving quality. By contrast, accreditationaccording to the EN 45000 series entails less

work for documentation. For the latter quali-ty system, the focus is on the competence of personnel and the quality of results.

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Selection of Suitable Test and Measuring Equipment Test Methods

Equipment QualificationThe use of inspection, measuring and testequipment in a quality management systemrequires a detailed description and documen-tation of the results of measurements and of confirmation. Processes and standard proce-dures must be traceably documented and

these documents filed.

Many leading quality systems, such asGLP/GMP and the ISO9000 and the EN 45000series, explain how to comply with thestandards.

Equipment qualification provides document-ed evidence that an instrument is appropriatefor its intended use to ensure that it willoperate on demand, under specified serviceconditions, to meet system performance andaccuracy requirements.

Equipment Qualification is subdivided into4 sections:

1. Design Qualification (DQ)2. Installation Qualification (IQ)3. Operational Qualification (OQ)4. Performance Qualification (PQ)

Design Qualification (DQ)In design qualification, the user defines hisor her requirements on the test or measuringequipment. Parameters, such as accuracy,method of measurement, and requirementson the supplier that relate to design valida-tion or services, must be defined and docu-

mented before purchasing (procurement). Thepurpose of design qualification is to ensurethat the measuring equipment – in this case,the balance, scale or weighing system – issuitable for the particular application.

The data generated using the test equipmentare merely observed values of a quality char-acteristic, for example, the weight valuesgenerated in a laboratory. Systematic andrandom errors that occur during the weighingprocess and result from the weighing equip-ment itself affect the accuracy of these values.Therefore, the result determined by theweighing instrument has a degree of uncer-

tainty, which is called “uncertainty of mea-surement” and must be indicated as a matterof principle for each weighing process. Thefactors that play a role in this uncertainty of measurement are explained in the following.

The selection of a suitable measuring instru-ment must be based on answering the ques-tion of how great the uncertainty of mea-surement may be to allow reliable compliancewith the required tolerances. A good approachto answering this question is to apply the“golden rule of metrology“ that says that themeasurement uncertainty of a measuringdevice may only be 1/10 of the tolerance of

the measured values.

For example, let’s suppose that a 10-mgsample is to be weighed to an accuracy of 1 percent, which corresponds to 0.1 mg.

According to the “golden rule,“ the totaluncertainty of the balance may not exceed0.01 mg.

Especially if a cost-intensive process is used, itis important that this criterion be met undereconomically feasible conditions. Under cer-

tain circumstances, a ratio of 1/3 is accept-able if these tolerances are met throughsuitable measures, such as the frequency of testing to ensure that the test equipment isappropriate.

The basis for the selection of a measuringinstrument or test equipment is provided bythe manufacturer’s technical specifications,such as repeatability, linearity or temperaturecoefficient. Besides these instrument parame-ters, additional factors that may affect theresults of a measurement must be considered.These include the ambient conditions at theplace of measurement, qualification of theoperator, test object and test procedure.

Installation Qualification (IQ)Installation qualification describes startupand the detailed sequence of setting up themeasuring equipment. Special attention mustbe paid to the completeness and correctinstallation of the equipment supplied. Tooperate high-resolution analytical andmicrobalances, you should essentially consid-er using specially designed anti-vibrationbalance tables. In addition, the climate condi-tions (particularly the temperature) should bekept as constant as possible.

Operational Qualification (OQ)Operational qualification describes themetrological testing of a weighing instrumentat the place of installation. Adequatelytrained personnel must test weighing instru-ments using the corresponding auxiliaryequipment and weights that have the appro-priate accuracy. In addition, the test resultsmust be documented in a calibration certifi-cate or test report of the weighing instru-ment. This testing must be performed atestablished intervals (known as “ intervals of confirmation“).

Performance Qualification (PQ)All manufacturers´ specifications refer tonearly ideal measurement conditions as re-commended in the installation and operatinginstructions. In practice, however, operatorsfrequently operate weighing instrumentsunder conditions that differ from these.Therefore, performance qualification requiresverification that the measuring equipmentfunctions as intended in its normal operatingenvironment (e.g., weighing a sample under alaboratory fume hood).

Device Qualification/Final ReportOnce all qualification procedures described

above have been successfully performed andthe adequate performance of the measuringequipment has been verified, equipmentqualification along with a final report iscompleted.

All manufacturer specifications are based on“idealized“ weighing conditions. Otherwise,comparisons could not be made between dif-ferent instruments. But the methods actuallyused in the field often differ from those usedby the manufacturer. Variations in the meth-ods used should be documented appropriately

in the SOP, and allowances should be madefor deviations in the weighing accuracy thatmay result. For example, if a hanger forbelow-balance weighing is used to weigh amagnetic sample, the manufacturer specifica-tions, which were determined under the bestweighing conditions, cannot be maintained.In this case, preliminary tests must be runusing reference samples to verify the attain-able degree of accuracy.

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Determination of the Uncertainty of Measurement

Manufacturer specifications, which are thebasis for selecting test and measuring equip-ment, are explained and interpreted in thefollowing sections.

The limits of a weight measurement, i.e.,the range within which the defined certainty

of measurement is maintained, is called“weighing range.”

Repeatability describes the ability to displaycorresponding results under constant testingconditions when the same load is repeatedlyplaced on the weighing pan in the same man-ner. Repeatability is essentially independentof the load on the balance or scale. It can bedesignated as the most important metrologi-cal feature because its influence on theuncertainty of measurement – especially withlighter loads – becomes the dominant factor.

Either the standard deviation or the diffe-rence between the highest and the lowestresult for a defined number of measurementsis used to specify this quantity.

Example of a Weighing Series:

Weight No. Weighing Series

1 9.997g

2 10.002g

3 9.998g

4 10.002g

5 10.001g

6 10.002g

7 10.001g

8 10.000g

9 9.998g

10 10.002g

11 9.997g

For evaluating the quality of a weighinginstrument on the basis of its technical speci-fications, both values (lowest and highestresult) are approximately comparable witheach other if the minimum/maximum specifi-cation is compared with three times the stan-dard deviation. Within the standard deviationtimes three, you will find 99.7% of allrepresentative values of a weighing series.

The standard deviation corresponds to thespread of the bell curve on either side from itspoint of inflection. Sixty-eight point threepercent (68.3%) of the individual values willbe located within this area or, to put it differ-ently, the individual values will fall within therange of

__χ ± s with a confidence interval of

68.3%. In practice, the use of the standarddeviation times two has become the norm.This interval has a probability of 95.5%.This means that 95.5% or 99.7% of all values

will be distributed with respect to the meanvalue within the range defined by thestandard deviation times two or three.

7

The mean value is calculated from the sum of the individual values W1 to Wn, divided by thenumber “n” of individual values; hence

_χ = 1 . s

nχ

i__n

i =1

Using our example, this means:

_χ = 9.997+ 10.002 + 9.998 +10.002 +10.001+10.002+10.001+ 10.000 + 9.998 + 10.002 + 9.997

11_χ = 10.000 g

The difference between the highest and lowest result in the weighing series iscalculated as follows:

10.002 g – 9.997 g = 0.005 g

The standard deviation is computed using the following equation:

s = √ ____________________

_

The standard deviation of our example is:

s = √

____________________________________________________________________________________

1. [(9.997- 10.000)2 + (9.997- 10.000)2] 0.0020976 g ≈ 2mg

_______

11-1

1 n____ · s (χ

i- χ )2n-1

i=1

χi= individual value measured in the

weighing series

n = total number of weight measurements– mean value of the individual resultsmeasured



The following Figures show a weighing serieslisted in a chart and plotted as a graph; theeleven individual weights are marked aspoints.

Frequently, the relative standard deviationis also given in percent

[ ].In our example, the standard deviation is:

The values of our weighing series given as anexample yield the following results:

Weighing Series

Number of individual valuesmeasured "n" 11

Sum of the individual valuesmeasured 110.000 g

Mean value 10.000 g

Standard deviation 0.002 g

Approximate (relative)

standard deviation 0.00167 g

Repeatability acc. to OIML R76 0.005 g

0.002 g= ____________ · 100 %= 0.02%

10.000 g

8

9.990 g 9.995 g 10.000 g 10.005 g 10.010 g

N u

m b e r o f i n d i v i d u a l v a l u e s “ n ”

0

1

2

3

4Standard deviations = 0.0020976 g

•

•

•

s__

· 100 %__χ

The linearity error (usually referred to aslinearity) indicates how much a balance ora scale deviates from the theoretically linearslope of the characteristic calibration curve.In the case of an ideal characteristic curve,the mass on the weighing pan will alwaysequal the weight displayed on the balance

or scale. If the zero point is correct and theweighing instrument has been correctly cali-brated and adjusted at maximum capacity,the linearity can be determined by the posi-tive or negative deviation of the valuedisplayed from the actual load on the pan.Linearity is caused by the specific inherentproperties of a weighing instrument and istherefore unavoidable. Two of the mostfrequent curves are slopes of the 2nd order(convex or concave curve) and of the 3rdorder (S-shaped curve).

The maximum deviation between the actualcharacteristic curve and the linear slope of the two interdependent values – the zeropoint and the maximum capacity – is definedas linearity. The maximum linearity is givenin the data sheets of balances and scales. Insome cases (such as an analytical balance),

a limited range is specified, for instance,200 g = ± 50 µg within 2 g = ± 10 µg.

Value displayed

Characteristic curve of the 2nd order

Ideal characteristiccurve

Characteristic curve of the 3rd order

Mass on theweighing pan100 g

100 g

Linearityerror



Influence Quantities

The measured result, or weight, can be affect-ed by so-called influence quantities, such astemperature, barometric pressure and humi-dity. In general, a distinction is made betweenthe temperature coefficient of the zero pointand of the sensitivity. Each of these parame-ters shows a more or less considerable impact

on the measured result, affecting both theelectronic components and weighing systemto an equal extent.

The sensitivity is the change in a displayedvalue divided by the change in the load signalgenerated by the mass on the pan. If abalance or scale with a digital display hasbeen correctly adjusted, the sensitivity mustalways be exactly 1.

The equation for the sensitivity is as follows:

∆ DS=

∆ m

where ∆ D is the number of scale intervalsthat correspond to the change in load ∆m.

A sensitivity error ∆S is caused by usinginappropriate calibration weights to adjust abalance or scale. The sensitivity error is alwaysindicated as a relative number, e.g., 20 ppmper K (1ppm = one part per million = 10-6).

If the value of the zero point or of thesensitivity changes because the temperaturefluctuates, the temperature coefficient isused to characterize this change. If a weightis divided by the change in temperature, thiswill yield the value of the temperaturecoefficient.

Example:Temperature coefficient : 2 · 10-6 K-1

Initial sample weight : 10 gChange in temperature : 5 K

Systematic error due to the temperaturecoefficient:

2 · 10-6 K-1 · 10 g · 5 K = 0.1 mg

The value of the temperature coefficient isthe major criterion for judging whether ornot the weight readout has stabilized when abalance or scale is exposed to fluctuations inthe ambient temperature.

If a light load is left on the balance or scale,over time you will see a drift in the zeropoint ∆ ZP on the display. Zero point drift is

only important for long-term measurementsinvolving a constant load, as in thermogravi-metric and sorption measurements.

The off-center load error, also called“corner load error,“ means the change inreadout when the same load is placed invarious positions on the weighing pan or loadplate.

The off-center load error is officially called“eccentric loading error.“ To verify the error,a weight is placed exactly in the middle of theweighing pan and the balance or scale istared. Then the weight is placed in 3 to 4 dif-ferent locations on the edges of the weighing

pan; if the pan is rectangular, the weight isplaced in the corners. The off-center loaderror can then be directly read off the display.This value can be negative or positive andusually ranges from 1 to 10 digits or scaleintervals. Therefore, especially when you usebalances with high resolution, the sample tobe weighed should always be placed exactlyin the middle of the weighing pan. In addi-tion, other factors that can substantiallyinfluence the weighing results must be takeninto account: operator, weighing location,sample and weighing procedure. For thisreason, it is recommended that the effectsof these factors be minimized whenever

possible.

In the following, these factors will be dealtwith in more detail.

9

Measured value displayed

Characteristic curve of the 2nd order

Ideal characteristiccurve

Mass on theweighing pan100 g

100 g

~ ∆S



Operator Weighing Location

Today, leading manufacturers offer balanceswith a readability of up to 0.1 µg and a reso-lution of up to 21 million digits. It almostgoes without saying that the operator mustreceive proper training in order to capitalizeon the accuracy and precision of these instru-ments.

For instance, the operator must be aware of and strictly comply with basic rules, such as:• Placing the sample in the middle of the

weighing pan (to avoid off-center loaderrors);

• Attempting to work as consistently aspossible (to maintain the specifiedrepeatability);

• Making sure that the balance is set up ona level surface (to prevent a systematicsensitivity error)

A scale or balance is adjusted in a manufac-turing process so that the force transmittedto the weigh or load cell when the scale isloaded is parallel to the direction of the grav-itational acceleration and perpendicular tothe cell. A level indicator (small spirit level)attached to the scale enables the operator to

pinpoint this position exactly, allowing it tobe reproduced at all times. This step is calledleveling.

The importance of leveling a balance or scalewill be explained using the following exam-ple. Suppose a laboratory bench with an edgelength of 1,000 mm is raised at one end by 5mm. Then the following applies to the angleof inclination: a= arctan 5/1,000 = 0.2865°

Moreover, the following applies to the forcegenerated by a load in the direction of theweighing axis:A = W · cos α = W · 0.9999875,i.e., the weight measured by the tilted balanceis 2.5 mg too low for a sample with a mass of 200 g.

Because of the earth´s rotation and geo-graphical features, the gravitationalacceleration varies depending on wherethe balance or scale is set up. We thereforerecommend that the weighing instrumentbe adjusted each time it is set up in a newlocation and before initial startup. During

this procedure,a known mass is loaded on the weighinginstrument and the adjustment factor isdetermined from the weight value displayed.Another effect that often goes unnoticed isa change in altitude and how it can influencethe gravitational acceleration when, forexample, the balance is moved to a higherlocation. Moving the balance will affect theaccuracy of the weight displayed!

The following is obtained in the relationshown below for a difference in altitude of only 4m:

10

Leveling foot

Level indicator

g = Gravitational acclerationRe = Earth's radiush = Difference in height (altitude)

R E

h

α

A = W · cos α

RE hg · (R

Ε+h)≈ g

K· (________ ) ≈ g

K· 1 - 2 · (____)R

E+ h RE g · ( R

Ε+4 m)≈ g · 1-2 · ______________ ) =g · 0.9999987(

6370000m

4 m



This means that a semi-microbalance, whichmeasures a mass accurately to 200.00000 g,will only measure 199.99974 g for the samemass when set up 4m higher. This underscoresthe necessity of calibrating and adjusting abalance or scale each time it is moved to adifferent location.

As a result of the moment of inertia,mechanical disturbances register on thebalance or scale as periodic or stochastic“weight changes“ depending on their attrib-utes. A digital filtering feature on the weigh-ing instrument, which can be activated byselecting a suitable integration time, canreduce these disturbances.

Low-frequency interference, however, is lesslikely to be filtered out because the filter canno longer differentiate between mechanicalinterference and a slowly changing weightreadout (for example, during filling). Wegenerally recommend that specially designedweighing tables be used for balances thathave extremely high resolution. If vibrationsin the building cause the disturbances, werecommend that the balance be set up on alower floor. If this is not possible, the balanceshould be used with a specially designed wallconsole.

Mechanical disturbances can be caused bypumps, laboratory shakers, turbulence underlaboratory fume hoods, and so forth.

Under normal circumstances, humidity as an

ambient quantity affecting the weighingprocedure can be neglected. However, forbalances of older designs and scales with astrain-gauge load cell, the change in humiditymust be kept as low as possible as damagecaused by corrosion of the connections canoccur at high humidity. The humidity alsoaffects the long-term stability of such loadcells.

For standard weighing procedures, barometricpressure is a negligible source of error.

However, for precision weight measurements(urel =< 5 · 10 -4), the air buoyancy must betaken into account as it is of considerableimportance for assessing the accuracy of thevalue measured by the balance or scale.

If an object is in a medium, this lifting forceopposes the weight of this object. Buoyancyreduces the weight of the mass to be meas-ured by the amount that equals the weight of the displaced medium.

If you consider two materials of the sameweight but of a different volume, such as an

aluminum cylinder with a density of 2.7 g/cm3 and a weight standard with adensity of 8.000 g/cm3, both of these are inequilibrium when weighed under vacuum.

mSTD = Mass of the weight standardm

S= Mass of the sample

g = Gravitational acceleration

If you consider the same setup weighed in air,both samples are no longer in equilibrium.

ρA

= Density of the air V STD = Volume of the weight standard V S = Volume of the sample

This is caused by the different buoyanciesresulting from the different material densitiesand volumes.

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Weighing under vacuum:

mSTD · g m

S · g

Standard Sample

Weighing in air:

mSTD · g mS · g

ρA · VSTDρA · VS



Because air has mass (density under standardatmospheric conditions: ρ

A= 1.2 mg/cm3),

the weight W of a sample depends on thedensity of its materials and thus on thevolume it takes up.

Let ∆m be the difference measured between

two masses mSTD and mS. You will obtain theactual difference ∆′m using the followinggeneral equation:

where V STD and V S are the volumes of theobjects of the masses mSTD and mS , and ρ

A

is the density of the air according to theconditions prevailing during the weighingprocedure.

The mass of the sample is determined accord-ing to the density values available,

ρA1− _____

ρSTDms=

____________ρ

A1− ____ρ

s

where ρSTD is the density of the standard andρ

Sthe density of the sample.

The graph shows how the weight readoutof a mass is corrected for air buoyancy as

a function of the material density for a fewselected density values given in g/cm3.

Electromagnetic disturbances consist mainlyof electromagnetic radiation in the range of afew kHz up to several GHz, which is frequentlyused for wireless communication:

• Radio communications• Mobile or closed-circuit radio

communications• Transmission of weights• Telecommunications through remote

control• Radar transmissions or measurement of

noise in electric circuits

Every measuring instrument, in other words abalance or scale, must be able to functionproperly when exposed to the effects of theseelectromagnetic disturbances, generallyreferred to as radio frequency interference.Every balance or scale that is supplied with aDeclaration of Conformity (CE mark) haspassed the test prescribed by the EC CouncilDirective 89/336/EEC “Electromagnetic Com-patibility” (EMC). This means that the balanceor scale has a defined immunity to emissions

in residential, commercial and industrial areasincluding light industrial environments.Based on the results of the EMC test, electro-magnetic disturbances have no effect on theweighing results.

12

∆′m = mS− mSTD =∆m + ρ

A· ( V S− V STD) or

mSTD−ρ

A· V STD =mS

−ρA

· V S

1 2 3 4 5

0

2

4

6

0

0.8

1.4

2.0

8.0

∆m [mg]

Weight readout [mg]



The Sample

In the majority of cases, the properties of thesample itself are the cause of inadmissibleresults. The most important factors thatinfluence weighing accuracy are:

• Electrostatic charges• Magnetic or magnetizable materials

• Hygroscopic materials• Sample temperatures that deviate too

much from the ambient conditions in thelaboratory

Static electricity – or electrostatic charges,which are particularly noticeable when thehumidity is low – is characterized by a weightreadout that drifts considerably and by poorreadability. This phenomenon primarilyaffects substances that have a low electricalconductivity and can therefore pass oncharges (caused by friction with air, internalfriction or direct transfer) to their environ-ment only slowly. Examples of these sub-stances are plastics, glass and filter materialsas well as powders and liquids.

Depending on the polarity of the chargedparticles involved, this force either attracts orrepels, so a weighing result may deviate ineither direction. This effect is based on theinteraction of electrical charges that havebuilt up on the sample weighed and on thefixed parts of the balance that are not con-nected to the weighing pan.

This problem can be eliminated by:

• Shielding the sample (using a metalcontainer)

• Increasing the surface conductivity of the sample by raising the level of humidityinside the draft shield of an analytical bal-

ance• Directly neutralizing the surface charges

using so-called static eliminators

If a sample is magnetic or magnetizable, i.e.,contains a percentage of iron, nickel orcobalt, forces of a different origin are gener-ated, which also have a significant influenceon the weighing result. If the sample is mag-netized, as is the stirring bar of a magneticstirrer, the forces of attraction that this mag-net exerts on the magnetizable parts of thebalance will override the weight of the sam-ple. Vice versa, the influence that the residualmagnetic field of the electromagnetic-forcecompensating weighing system has on a sam-ple cannot be ruled out. Magnetic forcesmanifest themselves as a loss of repeatabilityof the weighing result because they dependon the orientation of the sample within thefield of interference. Unlike electrostaticinterference, magnetic interference is stableover time.

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Static electricity eliminator withintegrated high-voltage source

Microbalance for weighingfilters; with a metallic pan cover

Semi-microbalance with a staticelectricity eliminator integratedas a standard feature

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+

+

+

+

+

+

+Example of the pattern of fieldforces generated by a magneticor magnetizable sample

Interaction of electrostatic charges

that attract one another; the sampleappears to be lighter

Interaction of electric charges that

repel one another; the sample appearsto be heavier



To eliminate problems with magnetic forces,one of the following approaches can betaken:

• Increase the distance between the sampleand the weighing pan

• Use a hanger for below-balance weighing

(under-scale weigh kit)• Use a shield made of a soft magnetic

material• Use a special anti-magnetic weighing pan

Hygroscopic samples cannot be preciselyanalyzed because they absorb moisture,which causes a constant increase in weight.If appropriate steps cannot be taken to keepthe humidity to a minimum at the weighinglocation, we recommend that the sample beweighed in an enclosed container that is

suitable for its size.

The sample temperature is an influencequantity that is often underestimated.Especially during very precise weighingprocedures, it is imperative that the samplebe adapted to the ambient temperature.Otherwise, convection currents on the surfaceof the sample can lead to major errors inmeasurement. Research has shown that whenbeakers with a large surface area are usedduring weighing, temperature differencesof a few degrees [°C] can cause the readout todiffer in the gram [g] range.

14

Hanger for below-balance weighing

Special anti-magneticweighing pan



Mass on theweighing pan10.000 g

Weight readout

9.009 gActual value

10.000 g

Nominal value 0.991gDeviation

Traceability of a Measurement

Calibration and Adjustment

The previous sections covered a series of influence quantities that can adversely affectthe accuracy of test and measuring equipmentin a variety of ways. Therefore, it is hardlysurprising that the test and measuring

equipment standards used in all qualitysystems require that errors in measurementbe quantified. In addition, measures for elimi-nating such errors must be specified. This isdone through calibration and adjustment.

Calibration checks the deviation between theweight readout on the balance and a referenceweight (in the field of weighing technology,this is a weight whose value is indicated on anaccompanying certificate). Calibration is themost important source of information forchecking an balance’s or scale’s uncertaintyof measurement under actual installation andoperating conditions. Therefore, it playsa central role in controlling the accuracy of inspection, measuring and test equipment.

Adjustment always entails corrective inter-vention in the balance or scale to eliminatethe existing error as far as possible. Duringadjustment, the weight readout is comparedto the “correct“ value of the calibrationweight, and the resulting correction factor isstored in the balance’s or scale’s processoruntil the next adjustment. Weighing procedu-res performed after adjustment are correctedaccordingly.

How frequently a balance or scale needs tobe adjusted depends significantly on thefollowing parameters:

• The frequency of weighing procedures• The ambient conditions• The effects of an incorrect result

A variety of instruments and methods existfor performing both of these procedures. Ingeneral, a distinction is made between internaland external calibration and adjustment.

The external calibration and adjustmentprocedure is used mainly on older-modelbalances and scales or those with highcapacities. Comparison and correction areaccomplished using one or more weightswhose value and uncertainty must be knownand documented.

National testing laboratories, calibrationlaboratories and qualified manufacturersprovide appropriate certificates for thispurpose.

For internal calibration and adjustment,a reference weight that is built into thebalance or scale is used. The exact value of this weight was previously determined duringmanufacture and stored as a fixed value inthe electronically programmable read-onlymemory (EPROM) of the weighing instrument’sprocessor. On the simplest models, the userplaces a weight on the balance’s or scale’sweighing system with the help of a mechani-

cal device. The motorized calibration weightfeature, which is operated at the touch of abutton, has recently become the standard.The most advanced balances and scales areequipped with a fully automatic calibrationand adjustment device that initiates calibra-tion after a preprogrammed or user-definedamount of time has elapsed.

15

External calibration and adjustmentof a precision balance



In addition, an internal sensor continuouslymonitors the balance or scale temperature (asa parameter for determining accuracy) andtriggers automatic calibration once a certaintemperature difference has been exceeded.This ensures the continuous accuracy of thebalance or scale without requiring the user to

intervene.

The figure below shows the sequence of functions that take place during fully auto-matic calibration.

Besides the advantages offered by thisconvenience feature, internal calibration isgenerally considered preferable over externalcalibration.

The internal weights are better protectedfrom dirt and damage and are always at the

same temperature as the balance or scale,per se. Moreover, the motorized calibrationfeature ensures that the weight is placed onthe balance or scale in the most reproduciblemanner possible. The fully automatic modeultimately ensures that one of the mostimportant requirements of the test andmeasuring equipment is fulfilled.

The question is often asked about how thetraceability of a balance’s or scale’s built-incalibration weight can be ensured. This can beaccomplished by tracing the internal calibra-tion weight to an extremely precise referenceweight from the manufacturer. With regardto its materials and surface properties, the

internal weight must possess all of the featuresof a classified weight. As is the case with allexternal weights, internal weights must alsobe tested at certain intervals to ensure thatthey are within tolerance limits. This is usuallydone when the balance or scale is serviced.

16

99.991 g 100.000 g

100 g 100 g

isoCAL

+

-

Motorized calibration weights of amicrobalance that are sphericallyshaped to improve the area-to-volume ratio

Built-in calibration weights



Mass and Weights

To enable comparison of results obtained withvarious balances and scales, we must be ableto trace these results to a definedstandard. A balance’s weighing results aretraced and monitored by comparing them toa standard that represents the value of themeasurand (quantity subject to measurement)

that is required to be correct. This standard isalso traced to the international prototypethrough an uninterrupted chain of suchstandards for comparison.

Relation to the Base Unit

1ng = 10-12 kg

1µg = 10-9 kg

1mg = 10-6 kg

1g = 10-3 kg

Base unit

1t = 103 k

The necessity of tracing other units to thekilogram by mass comparison has given riseto the hierarchical structure of mass stan-dards. In this hierarchy, the uncertainty of measurement at a certain level depends onthe number of previous mass comparisons.

17

Germany’s national kilogram prototype

Mass standards Mass comparison

At the BIPMwhen necessary

At the BIPMwhen necessary,e.g., every 5 years

At the BIPM whennecessary, e.g.,every 12 years

At the placeof use, < 1 year

At the placeof use, <10 years

At the placeof use, < 5 years

Secondary standardsof companies

Material:steel (brass)

Secondary standardsof the Verification

Board. Material:steel (brass)

Working standards

Secondary standardsof the PTB

Material:steel (brass)

Control standards

International kilogram prototypeMaterial: Pt-lr Density:21.5 g/cm3

Primary standards of the PTBMaterial: steel or brassDensity: 8.0g/cm3 8.4g/cm3

National kilogram prototype; in this caseno. 52 in the Federal Republic of GermanyMaterial: Pt-Ir

Primary standards of the BIPMMaterial: Pt-Ir



Weights of various accuracy classes areavailable to the user. The minimum valuesand corresponding uncertainties of theseweights are specified in R111 of the OIML(Organisation Internationale de MétrologieLégale.)

The maximum permissible errors according tothe OIML Recommendation R111 are shownin the chart on the right:

In the meantime, certain manufacturers alsohave been providing comprehensive informa-tion about which accuracy classes are suitablefor the particular application and resolutionof the balance or scale being used.

The test weight should weigh more than 80%

of the maximum capacity of the balance orscale being used. In the following table,individual weights or weight combinationscan be selected.

Example:A balance has a capacity of 2,200g andreadability of 0.01g. This translates to220,000 display digits, which corresponds toa class E2 test weight. In this case, 2,000g isselected as the weight.

Calibration weights must be clearly identifiedas such so that they cannot be confusedwith other weights. The manner in which

they are handled (manufactured, stored,tested, or transported) must be regulatedand documented.

18

+ / - in mg

Nominal value E1 E2 F1 F2 M1 M2 M3

1 mg 0.002 0.006 0.020 0.06 0.20

2 mg 0.002 0.006 0.020 0.06 0.20

5 mg 0.002 0.006 0.020 0.06 0.20

10 mg 0.002 0.008 0.025 0.08 0.25

20 mg 0.002 0.010 0.03 0.10 0,3

50 mg 0.004 0.012 0.04 0.12 0.4

100 mg 0.005 0.015 0.05 0.15 0.5 1.5

200 mg 0.006 0.020 0.06 0.20 0.6 2.0

500 mg 0.008 0.025 0.08 0.25 0.8 2.5

1 g 0.010 0.030 0.10 0.3 1.0 3 10

2 g 0.012 0.040 0.12 0.4 1.2 4 12

5 g 0.015 0.050 0.15 0.5 1.5 5 15

10 g 0.020 0.060 0.20 0.6 2 6 20

20 g 0.025 0.080 0.25 0.8 2.5 8 25

50 g 0.030 0.10 0.30 1.0 3.0 10 30

100 g 0.05 0.15 0.5 1.5 5 15 50

200 g 0.10 0.3 1.0 3 10 30 100

500 g 0.25 0.75 2.5 7.5 25 75 250

1 kg 0.5 1.5 5 15 50 150 500

2 kg 1.0 3,0 10 30 100 300 1000

5 kg 2.5 7.5 25 75 250 750 2500

10 kg 5 15 50 150 500 1500 5000

20 kg 10 30 100 300 1000 3000 10000

50 kg 25 75 250 750 2500 7500 25000

M1 E2F1F2

5,000

10,000

50,000

100,000

500,000

Digits

ClassE1*

1,000,000

n=max: d n = resolution of the weighing instrument (digits)max = max. weighing capacity of the weighing instrumentd = readability of the weighing instrument

* or E2, DKD calibrated



Documentation

A characteristic element of all quantity sys-tems is the requirement of documentation.Requirements as to the extent and depth of the documentation vary significantly depend-ing on the system being used. In any case, it ishelpful to use the rule of five W’s as a guidewhen developing a set of instructions that

must be followed. This rule states that proce-dures must be documented in such a way asto answer the question:

“Who Did What, with What, When andWhy?”In the area of management of test and mea-suring equipment, experience has shown thatthis requirement is best met by introducingand maintaining an SOP and a logbook forthe weighing instrument. While all aspects of operation are laid out in the SOP, the logbookcontains entries about the maintenance, serviceand repair procedures for the particular bal-ance or scale.

Practical examples of an SOP and a logbookare given in the Appendix of this Handbook.

In particular, the following must be recorded:

• Description and identification of the testand measuring equipment

• Calibration equipment and results• Defined maximum permissible errors• Ambient conditions and corresponding

adjustments• Maintenance procedures• Modification of the weighing instrument(s)

• Identification of the personnel responsible• Restrictions on the suitability of test andmeasuring equipment

These items are discussed in more detail in thefollowing sections.

Description and Identification of the Testand Measuring Equipment: This includesgeneral information about the type of weigh-ing instrument (e.g., analytical balance with amotorized draft shield); the most importantmanufacturer specifications; and the model,serial number or inventory number at theweighing location.

Calibration Equipment and Results: Thesetwo factors are decisive for maintaining thedesired degree of weighing accuracy.Depending on the resolution of the balanceor scale and its construction features (motor-ized placement of the weight on the weighingpan, fully automatic calibration function),determinations must be made about thenominal value, the maximum permissibleerrors and how the weights are to be used.The weights or sets of weights employed arealso considered test and measuring equip-ment and must be labeled and identifiedaccordingly. Intervals for recalibration of the

weights must also be defined. Especially whenthere are large deviations in the calibrationresults, control limits must be defined, and aprocedure must be developed for reportingsuch deviations.

For defined maximum permissible errors,the overall uncertainty of measurement,which was determined using the test andmeasuring equipment described above, mustbe traceable. On the basis of this value, theuser can determine whether a balance orscale is suitable for the tolerance indicated

in the SOP (e.g., the analysis.

Ambient Conditions and CorrespondingAdjustmentsThe specifications that characterize thebalance or scale are determined by themanufacturer under well-defined standardconditions. In reality, however, certain usuallyunfavorable conditions often cannot beavoided. For example, if the balance or scale islocated under a fume hood in the laboratoryor in a place where there are great fluctuationsin temperature, the analysis can be adverselyaffected. Modern balances and scales can beadapted to the ambient conditions at theweighing location by varying the set of parameters in the operating system so thatthe balance or scale may be used in thatlocation. However, this usually results in theaccuracy being reduced.

19

YSL 01E

Sartorius StandardOperating Procedure (SOP)

for Working with an Electronic Balance/ScaleDocumentation for Quality Assurance

SartoriusAG,WeighingTechnology R e g . N o . 1 94 4 0

- 0 3

M A N A G E M E N T S Y

S T E M

C ERT I F

I E D

isoCAL

--------------------24.09.2000 09:48

SARTORIUSMod. LP420Ser.no. 60806248Vers. 1.1007.12.1BVers. 01-30-03ID--------------------Internal CalibrationStart: isoCAL/tempDiff. + 0.01 gInternal adjustmentcompletedDiff. + 0.00 g--------------------16.09.1996 09:48Name:

--------------------

Date and time

Serial no.

Difference betweennominal/actual

User identification

Version no. of thebalance/scale software

Model name of weighing instrument

Difference afterisoCAL

Space for signature

Date and time

Practical example of the “rule of 5 W’s“applied to the isoCAL printout:

WHAT

WHO

WHY

WITH WHAT

WHEN



Example:For example, if the “stability range“ parameteris increased, the balance or scale can deliveraccurate results even when it is subjected to afield of interference of a great amplitude. Theattainable repeatability however, is sacrificedin the process. In this case, the change in the

parameters of the balance or scale operatingsystem and the influence on the uncertaintyof measurement must be documented.

Maintenance ProceduresDeterminations must be made about• when the balance or scale should be

cleaned,• who should service it and at what intervals,• and how to proceed if a repair is necessary.

The results of regularly performed maintenanceprocedures can also be useful for analyzingthe trend of certain deviations. This facilitiesappropriate definition of the interval of confirmation.

Modification of the Weighing Instrument(s)A variety of technical applications requirethat a standard-equipped balance or scale bemodified. For example, a hanger for below-balance weighing might be used if either thesize of the sample or special ambient condi-tions (such as magnetic fields, temperature,humidity and so forth) dictate the manner inwhich the analysis should be conducted.Weighing pans of modified shapes and sizesand analytical balances with specially designeddraft shields are also often used. Today,

leading manufacturers are in a positionto offer their customers application-specificsolutions with respect to digital filtersor other weighing parameters. Dynamicweighing procedures constitute one of themain application areas for which this typeof modification is necessary.

Appointment and identificationof Personnel Responsible for MonitoringTest EquipmentThe laboratory manager appoints a personto oversee the test and measuring equipment.This person is responsible for the appropriateuse of the balances and scales.

Restrictions on the Suitability of Test and Measuring EquipmentIf a confirmation or calibration proceduredetermines that the test and measuringequipment can no longer operate within thedefined maximum permissible errors, even if corrective intervention is taken, the balanceor scale should no longer be used for theintended purpose. Of course, it is possible touse the balance or scale for analyses that donot require such a high level of accuracy. Inthis case, the limited application range mustbe clearly denoted on the instrument andindicated in the SOP.

Defining the Interval of ConfirmationWe use the term confirmation to summarizeall activities that ensure that the predefinedproperties of the test and measuring equip-ment are maintained. Therefore, the intervalof confirmation corresponds to the timeinterval or number of analyses performedwith the test and measuring equipmentbetween two successive inspections. Froman economic standpoint, testing should beoptimized so that it is performed beforea balance or scale exceeds the maximumpermissible errors. This is also closely connected

to the previously mentioned rule, whichstates that the uncertainty of measurementof the test and measuring equipment shouldbe much lower than that required by aparticular weight measurement application.The following should be taken into accountwhen first defining the interval of confirmation:

• The extent of possible adverse effects onthe analysis due to non-conforming testand measuring equipment

• Manufacturer s recommendation• Tendency toward component wear and

drift

• Environmental influences• Demands of customers, standards or laws• Experiences with similar test and

measuring equipment

The following questions should be taken intoaccount if non-conforming test andmeasuring equipment causes consequentialdamage:

1. When should data obtained witha nonconforming instrument be rejected?

2. What additional expenses can result fromoverfilling expensive substances?

3. Can the customer assert product liabilityclaims in such case?

20



Summary

Manufacturer´s RecommendationLaboratory balance manufacturers – if theyprovide service and maintenance for theirproducts – have an extensive amount of dataat their disposal with respect to all importantfeatures of the balance. This is especially truegiven various areas of use and ranges of

application of lab balances.

Tendency Toward Component Wear andDrift: On advanced laboratory balances andscales, this tendency can be neglectedbecause these weighing instruments aredesigned and constructed to keep componentwear to a minimum when they are operatedaccording to the manufacturer´s instructions.The readout might drift in individual casesand after prolonged use of the balance orscale due to the electronic components.

Environmental Influences:The range of uses for balances and scales arespecified according to temperature andhumidity classes. If a weighing instrument ismainly or constantly subjected to tempera-tures or levels of humidity that border on theallowable limits of these classes, the specifi-cations will likely be affected and must betaken into account accordingly.

Demands of Customers, Standards or LawsIf the equipment is to be used in sensitiveareas with very high security standards (e.g.,in the aerospace industry, for medical tech-nology, for pharmaceutical production and soforth), the customer will place high demands

on the supplier´s quality system. Thesedemands can go far beyond the standardrequirements and, therefore, can have aninfluence on the control of inspection, testand measuring equipment.

Experience with Similar Test andMeasuring EquipmentBecause of the multitude of factors that mustbe considered when defining the interval of confirmation, a general recommendation onhow to do so cannot be made. It makes moresense to follow your technical “intuition“ andconsider the relevant factors to determine asuitable interval. Statistical data from the

current inspection can be used to checkcalibration and optimize the interval that isinitially selected. For example, the interval of confirmation can be gradually adjusted bycutting the test interval in half, if themaximum permissible errors are exceeded,or doubling it if the requirements are metsatisfactorily. From an economical standpointand to ensure the traceability of test results,it may be useful to combine extensive inspec-tions at longer intervals with additionalshort-term tests or calibration proceduresusing suitable working standards.

The control of inspection, measuring and testequipment is an element of functional qualitymanagement. It is a prerequisite forobjectively demonstrating the performanceof a laboratory as well as for introducing andmaintaining processes that can be controlled.

This starts with the selection of a suitable testor measuring device based on the tolerancesto be tested, which, for instance, are indicatedin the laboratory’s SOPs. Measuringequipment suitable for this purpose has anoverall uncertainty of measurement that ismuch lower than the sample with respect tothe specifications of the equipment and allfactors that have an influence on the

measurement.

Suitable SOPs should be indicated in writingto ensure that the test requirements arealways met, and all related data should bedocumented.

21

Protect people and

the environment

International

relationsbetween suppliers

Ensure marketabilityand competitiveness

Optimize costsBoost productivity

In-house cooperationand motivation

Intensify supplier/

customer relations

Protection against

disputes and claimsfor damages

QUALITY



Error Calculation

A deviation in the displayed value from thetrue value is commonly known as an “error“or “deviation“; the standardized term is “errorof measurement.“ In the following, we willuse the simpler form “error.“ We distinguishbetween two types of error: systematic andrandom errors.

Systematic ErrorsThe cause of the error is known, perhaps eventhe value of this error, or at least an upperlimit of error.

Examples:

1. A scale of lengths is not exactly accurate inlength; all measurements are made withthe same scale of lengths.

2. The same holds true for a weighing instru-ment; e.g., a balance with an incorrectlyadjusted sensitivity.

3. A measuring instrument is adjusted to20°C, but the measurement is carried outat 25°C (this is important, e.g., in the caseof a volumeter.)

Random ErrorsThe cause of a deviation is either unknown,or this deviation is caused by varying influencefactors.

Examples:

1. Friction in a measuring instrument thathas mobile components

2. Random fluctuations in the zero point of a weighing instrument

3. Statistical influence of the operator(e.g., parallax errors when the operatorreads off the measuring instrument displaythat has a pointer; or a change on the massof the object being weighed when theoperator touches it with his or her hands)

Note:There is no hard-set difference betweensystematic and random errors. By means of additional measurements or information,many random errors can be transformed intocorrectable systematic errors.

22



The standard deviation “s“ is given as the quantity for repeatability:

s =

√

___________________

n = total number of measurementsχi = individual results measured__χ = mean value of the individual results measured

_χ =

Gaussian distribution (“normal distribution“)__χ = average weight; s = standard deviation68.3% of the weighing results lie within the range of

_χ ± s

95.5% of the weighing results lie within the range of _χ ± 2s

99.7% of the weighing results lie within the range of _χ ± 3s

ESum

= √

_______________

F1, F2 = individual errors

Example:The gross weight mG of 210.213 gAnd the tare weight mT of 205.171 g

Yield the mass mNet

of 5.042 g

The individual errors of mG and mT, respectively, are each 1 mgHence, the absolute error of m

Netis :

ENet

= √

_______________________

and the relative error is:

EResult______ = √

_______________________

Result

Example: Density determination in accordance with the equation:

m = mass = 150.27 g ± 0.01 g V = volume = 173.4 cm3 ± 0.1 cm3

ρ = density

150.27 g gρ = _____________= 0.866609 ____173.4 cm3 cm3

Eρ___ = √

_________________

ρ

Eρ___ = √

__________________________

5.80 · 10-4ρ

g gEρ =ρ · 5.8 · 10-4 = 0.8666 ___ · 5.8 · 10-4 = 0.5 · 10 -3 ___cm3 cm3

gFinal result: ρ = (0.8666 ± 0.0005) ___cm3 23

There are mathematical rules for randomerrors:

Rule 1:If a measurement is repeated a sufficientnumber of times and the frequencydistribution of the individual values

measured are plotted, you will obtain acharacteristic curve, the so-calledGaussian curve.

Rule 2:Law of error propagation for sums anddifferences:In sums or differences, the squares of theabsolute individual errors (E) are addedand the square root of this sum is taken:

Rule 3:Law of error propagation for products andquotients:In products or quotients, the square of therelative individual errors are added andthe square root of this sum is taken:

1 n____ · s (χi -

__χ)2

n-1 i=1

1 n____ · s χ

in i=1

(E1)2 + (E

2)2

(1 mg)2 + (1 mg)2= 1.4 mg

ENet

1.4 mg___ = _______ = 0.028% = 2.8 · 10-4

mNet

5.042 g

E12 E2

2

(_______) + (________) Value1

Value2

mρ = _____ V

Fm2 Fv

2

(____)+ (___ )m v

0.01 g 2 0.1 cm3 2

(__________) + (__________ __)150.27 173.4 cm3=



Deriving the Uncertainty of Measurementfrom the Standard DeviationOnly approximately 68% of the measuredresults lie within the range of ± s from themean value. Therefore, for practical purposes,the (maximum) uncertainty of measurement“u“ is frequently defined as ± 2 s (95% of the

measured results lie within the range of ± 2 s from the mean value).

We will use: u = 2 s

Example for Calculating the Uncertainty of Measurement for Samples of Approx. 10 g:

Small amounts (approx. 10g) are to beweighed on a GENIUS ME2545 semi-microbalance with a resolution of 0.1 mg.Ambient conditions are good (no tilting;temperature difference of 5°C max.; none of the containers or objects is electrostaticallycharged, nor is there any electromagneticinterference.)

• The containers are small and must be cor-rectly centered, as directed in the standardoperating instructions. Therefore, the off-center load error can be neglected for 10 g.

• The repeatability/standard deviation is:< ± 0.07 mg

• The temperature coefficient for the sensiti-vity is 1ppm/K => < ± 1·10-6 /°C, as statedin the technical specifications.Hence, the error for 10 g and ∆ T = 5°C is< ± 10 g · 1 · 10-6 /°C · 5°C =< ± 0.05 mg

• The max. linearity error is as stated in thetechnical specifications:< ± 0.15 mg

• The balance has been calibrated andadjusted with a standard E2 class weightof 200 g (maximum error of 0.3 mg).In relation to a 10-g load, the error is:< ± 0.015 mg

The sample´s density is 2.0g/cm3, with anuncertainty of ±20%; the difference betweenair buoyancy of the samples and that of thestandard weights used to adjust the balanceis thus 2.25 mg with an uncertainty of ±20%± 0.45 g.

The uncertainty of this air buoyancy correc-tion value due to fluctuations in the airdensity of ±10% is considerably less thanthat of density fluctuations.

Deriving the Uncertainty of Measurementfrom the Standard DeviationWith the exception of the repeatability/standard deviation, all values are maximumerrors. If the equation of u=2s is used toexpress the maximum uncertainty of therepeatability and if the air buoyancy has beencorrected, the uncertainty of measurementwill be as follows:

However, if no correction is made for airbuoyancy, a systematic error of 2.25 mg isadded to the uncertainty of measurement “u“so that the total deviation can be as much as2.75 mg.

The uncertainty of measurement of a weigh-

ing instrument can be exactly determinedover its entire weighing range by calibrationin a DKD*-accredited laboratory, whichSartorius has.

*DKD = German Calibration Service officiallyrecognized throughout Europe

24

u= √ (2 · 0.07 mg)2 + (0.05 mg)2 + (0.15 mg)2 + (0.015 mg)2 + (0.45 mg)2

u= 0.50 g



Appendix

Balances and Scales Used as Measuring andTest Equipment in a Quality System

Example of a Standard OperatingProcedure (SOP) i

Example of a Logbook v

i



YSL 01E

Sartorius StandardOperating Procedure (SOP)

for Working with an Electronic Balance/ScaleDocumentation for Quality Assurance

Sartorius AG, Weighing Technology R e g . N o

.1 94 4

0 - 0 3

M A N A G E M E N T S Y

S T E M

C E

R TI F I E

D

Record the particular designationsor information in the spaces provided.

Connected accessories:

Installation and Operating Instructions/User’s Manuals are located at:

Operation began on:

Operation ended on:

Tested and released by:

(QA)

(Written by:)

(Head of the Test Facility)

3

Name of the test facility:

Sartorius balance/scale model:

Serial number of the balance/scale:

Inventory number:

Your in-house number for the Standard Operating Procedure:

4

ii



Introduction

This manual provides proof that thebalance/scale entered on the form(s)operates properly as required andhas the specified accuracy. Themanual includes the classification ofthe measuring and test instrument,i.e., the balance/scale and generaloperating instructions.

Supplementary text for explanation,printouts, records and reports can befiled in the Appendix of this manual.

Contents

Classification of the Measuring and Test Instrument ________________________________ 6

Operating Instructions __________________________________________________________________ 7

Getting Started______________________________________________________________________________ 7

Calibration/Adjustment __________________________________________________________________ 8

Simple Weighing Procedure ____________________________________________________________ 9

Cleaning ____________________________________________________________________________________ 9

Operating Errors and Error Codes ______________________________________________________ 10

Maintenance and Repair ________________________________________________________________ 10

5

Classificationof the Measuring andTest Instrument

Enter the specifications pertainingto the classification of your particularbalance/scale in the spacesprovided below.

Technical Specifications Given by the Manufacturer

Standard balance/scale:

Capacity/weighing range levels:

Readability:

Reproducibility1)/standard deviation:

Linearity:

Sensitivity drift:

Allowable temperature range:

Power requirements/frequency:

Balances/scales verified for use in legal metrology** :

Accuracy class:

Max. capacity:

Min. capacity:

Scale interval “d”:

Verification scale interval “e”:

Range for approved use as a legal measuring instrument:

Range for approved use in accordance with the EC Prepackage Directive:

Permissible ambient temperature range:

Power requirements/frequency:

Remarks:

1) standard deviation in accordance with DIN 8120** currently in the European Economic Area and Signatories

6

Operating Instructions

Title: Working with an Electronic Balance/Scale

These general operating instructions can be used for all Sartorius electronicbalances/scales. Fill in the blanks and check the appropriate boxes accordingto your in-house operating procedures. In the right-hand column you will findcomments and help for filling in the blanks.

1. Getting Started

1.1. Checking the Level Indicator/Leveling the Balance/Scale(depends on model)

1.2.Turning On the Balance/Scale Using the ON/OFF I/E Key

$Warm-up time for the balance/scale after connecting it to AC power:_______________ hours

$ In the “standby mode,” the balance/scale will beimmediately ready to operate again as soon as it is turned back on

Information for Supplementing/Writingthe Operating Instructions

Concerning “1.1. Checking theLevel Indicator”

At the place of installation, level thebalance/scale using the leveling feetso that the air bubble is centeredwithin the circle of the level indicator.

Concerning “1.2. Warmup Time”

Analytical and precisionbalances/scales:$ at least 30 minutes

Semi-microbalances:$ at least 2 hours

Microbalances:$ at least 6 hours

7

2. Calibration/Adjustment

The balance/scale must be adjusted after it has been set upin a different area:

Refer to the “Installation and Operating Instructions” correspondingto your balance/scale for a detailed description of the adjustment procedureor error codes.

Please do not forget to record and document the procedure (obligatory).

2.1 Calibration

If the difference of the test weight value exceeds the permissible readoutdeviation of _________, the balance/scale must be adjusted.

If you obtain unusual variations, make sure to notify the head of the test facility

2.1.1 Calibration with (an) internal weight(s):

(for balances/scales with built-in, motorized weight(s); depending on model series)

$ Test criterion:

2.1.2 Calibration with (an) external test weight(s):

$with test weight(s)

$ Permissible uncertainty of measurememt$ Test criteri(on) a

Adjust the balance/scale as follows:

2.2 Internal Adjustment:(for balances/scales with built-in, motorized weight(s)

2.2.1After pressing a key:

$ Adjustment criteri(on)a:

2.2.2 The balance/scale self-adjusts fully automatically(depends on the model):

2.3 External Adjustment: 1)

$with adjustment weight g

$ Permissible uncertainty of measurement

$ Adjustment criteri(on)a:

1) After verification for use in legal metrology in the EEA,an “External Adjustment” procedure is not allowed.

no yes

no yes

no yes

no yes

no yes

no yes

no yes

Concerning“2. Calibration/Adjustment”The balance/scale must bereadgusted after it has been setup in a different area.

Calibration/Adjustment CriteriaThe calibration/adjustment criteriadepend on your particular accuracyrequirements and the ambientconditions as well as the designof your balance/scale.

Weighing Instruments with Special Accuracy (analytical, microbalances andbalances/scales of accuracy classk verifiable or verified for use in legalmetrology must be adjusted as follows:

$ at least once daily (internal or external)$ if the temperature changes

by +/– 2.5°C$ to meet high measuring

accuracy requirements beforeeach weighing series

$if the barometric pressure changes:$ by more than 20 mbar for

a number of scale verificationintervals (ne) ≤ 150,000$ by more than 15 mbar for

a number of scale verificationintervals (ne) from 150,000up to 200,000

$ by more than 10 mbar fora number of scale verificationintervals (ne) ≥ 150,000

Weighing Instruments with High Accuracy These weighing instruments must beadjusted as follows:$ for balances/scales with an internal

adjustment weight: weekly adjust-ment; otherwise, every 3 months

$ for verifiable precision balances/scales of accuracy classK: with aninternal adjustment weight: at leastonce a day for balances/scaleswithout an internal adjustmentweight: check daily

Concerning “2.1 Calibration”Daily calibration is the standardprocedure for checking analyticalbalances and scales as well asmicrobalances; for verified balances/scales of accuracy classesk andK

, this is mandatory in general.Depending on the particular resolutionand accuracy requirements, daily tomonthly calibration is advisable.The span must be calibrated especiallyif the balance/scale is exposedto strong fluctuations in temperatureor barometric pressure.8

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3. Simple Weighing Procedure

$ Check the level indicator

$ Turn on the balance/scale using the ON/OFF I/E key(for warm-up period following connection to AC power, see step 1.2.)

$ Place container on pan, if necessary

$ Tare with the T control (zero the weight display)

$ Place sample or object to be weighed on the pan

$ Do not read off the weight until the weight unit “g”or a different weight unit selected appears as the stability symbol

$ If necessary, print the weight by pressing the P print key

4. Cleaning

Clean the balance/scale whenever necessary. This dependson the particular application and environment in which it is used.Use a lint-free piece of cloth wet with a mild detergent(or a commercially available glass c leaning agent) for cleaning.Carefully remove residual traces of a weighingsample/powder using a brush or a hand-held vacuum cleaner.

Use blotting paper to soak up spills of liquid samples.Make sure that no liquid or particles enter the balance/scale housing.

Remarks:

Calibrating the span at the beginningof a work procedure (once the bal-ance/scale has warmed up or hasbeen in the standby mode overnight)is common; however, it makesmore sense to calibrate the spanimmediately before a measuringseries is performed.

The deviation of a readout duringspan calibration is constituted bydifferent error quantities, which in theworst case, equal absolute amounts(reproducibility, weight tolerances, etc.).

The value of an external test weightshould be at least half the maximumcapacity of a balance/scale.

Concerning“3. Simple Weighing Procedure”

Information on weighing magnetizedor electrostatically charged samples when using analytical balances/scales and/or microbalances.

When magnetized samples areweighed, the readouts constantlydeviate from the true mass, whereaselectrostatically charged samples arethe cause of unstable readouts (drift).In these cases, use a speciallydesigned, antistatic pan insteadof the standard weighing pan (seethe section on “Accessories” in thecorresponding “Installation andOperating Instructions.”)

9

5. Operating Errors and Error Codes

Problem Possible Causes Solution

No segments $ No line current is $ Check the ACappear on the available power supplydisplay $ The AC adapter/power supply $ Plug in the

is not plugged in unit/cable

The weight $ Unstable ambient $ Improve thereadout changes conditions ambient conditionsconstantly $ Residual traces of sample/ $ Remove the

foreign objects are t rapped residual traces/under th e wei gh in g pan f or eig n o bjec t

$ The closing plate of the $ Turn the platepor t f or the below-balance to c lo se itweighing hanger is open

$ The sample does not have astable weight (absorbs moisturesor evaporates)

$ Sample/object is electro- $ Decharge thestatically charged sample/object

using an ionizingblower or exchangethe standard weigh-ing pan for anantistatic pan (see“Accessories” in the“Installation and$peratingInstructions”

The readout of the $ The balance/scale $ Tare beforeweighing result is was not tared before weighingobv ious ly wrong weigh ing

$ The air bubble of the $ Level balance/scalelevel indicator is not using the levelc en te red w it hin t he c ir cl e i nd icat or

$ The balance/scale Adjust theis not adjusted balance/scale

$ Sample/object is $ Demagnetize themagnetized sample/object or

exchange the stan-

dard weighing panfor a special pan(see “Accessories” inthe “Installation and$peratingInstructions”

$ Exposure to strong $ Condition thet em pe ra tu re fl uc tu at io ns bal ance/s ca le

The weight dis- $ The load exceeds $ Unload theplay shows “H” the weighing capacity bal anc e/sc ale

The weight dis- $ The weighing pan $ Place the panplay shows is not in place on the balance/“L” or “Err 54” scale

$ Residual traces of sample $ Remove theare under the weighing pan residual traces/

foreign objects

The head of the testing facility must always be informed if an error cannot be eliminated.

Notes and Information for Supplementing/Writing theOperating Instructions:

10

6. Maintenance and Repair

The balance/scale must be maintained____________________a year

by service technician (specify name) _______________________________

Concerning“6. Maintenance and Repair”

Sartorius can offer you service con-tracts for regular maintenance of yourweighing equipment at intervals of1 month to 2 years (6 months are thenorm). Maintenance or repair work should be done by the Sartoriusservice organization. Our balances/scales are high-precision measuringinstruments which require trainedspecialists and the most advancedequipment to ensure proper main-tenance and repair.

11

Sartorius AGb37070 Goettingen, GermanypWeender Landstrasse 94–108,37075 Goettingen, Germanyt (551) 308-0,f (551) 308-289Internet: http://www.sar torius.com

Printed in Germany on paper that ha been bleached without any use of chlorine · W297-A00Publication No.: W-- 0041-e97101

iv



v



Adjustment 15Air buoyancy 11Ambient conditions 19Appointment and identification of 20personnel responsible for monitoringtest equipment

Balance/scale logbook vBarometric pressure 11

Calibration 15Calibration results 19Consequential damage 20

Defined maximum permissible errors 19Demands of customers 21Description of the test and measuring 19equipmentDesign qualification (DQ) 6Determination of the uncertainty 7of measurementDocumentation 19Drift in the zero point 9

EN 45000 series 5Environmental influences 21Equipment qualification 6, vError calculation 22Experience with similar test 21and measuring equipmentExternal calibration/adjustment 15

GLP (Good Laboratory Practice) 5GMP (Good Manufacturing Practice) 5Gravitational acceleration 10

Humidity 11Hygroscopic samples 14

Influence quantities 9Installation qualification (IQ) 6Internal calibration/adjustment 15Interval of confirmation 20ISO 9000 series 5

Legally regulated quality systems 5Leveling 10Linearity error, linearity 8

Magnetic and magnetizable samples 13Maintenance procedures 20

Manufacturer’s recommendation 21Mass and weights 17Mechanical disturbances 11Modification of the weighing instruments 20

Non-conforming test and 21measuring equipment

Off-center load error 9Operational qualification (OQ) 6Operator 10Overall uncertainty of measurement 19

Performance qualification (PQ) 6

Quality 4Quality systems 5

Random errors 22

Sample 13Selection of suitable test and 6measuring equipmentSensitivity 9Sensitivity error 9Standard deviation 7Standard operating procedure (SOP) ii

Static electricity 13Structure of mass standards 17Systematic errors 22

Temperature 14Temperature coefficient 9Tendency toward component wear 21Tendency towards drift 21Test methods 7Traceability of a measurement 15

Uncertainty of measurement, 24deriving from the standard deviationUncertainty of measurement, 24example for calculatingUniversal quality systems 5

Weighing location 10Weighing range 7

Index



References

(German titles have been translated intoEnglish in parentheses for convenience.)

• Christ, G.A., Harston, S.J.; Hembeck,H.-W.,Opfer,K.-H.1998. GLP-Handbuch fürPraktiker (GLP Handbook for ExperiencedProfessionals). Darmstadt, Germany:

Gt Verlag GmbH.

• Deutsches Institut für Normung e.V.(German Institute for Standardization).1995. Leitfaden zur Angabe der Unsicher-heit beim Messen (Guidelines for Indicatingthe Uncertainty during Measurement).Berlin, Germany.

• Deutsches Institut für Qualität e.V.(German Society for Quality). 1998.Prüfmittelmanagement (Managementof Inspection, Test, and MeasuringEquipment). Frankfurt, Germany.

• DIN ISO 10012. 1996. Forderungen an dieQualitätssicherung für Messmittel,Messunsicherheit und Fähigkeit, Qualitätund Zuverlässigkeit (Quality AssuranceRequirements for Measuring Equipment,Uncertainty of Measurement, andCapability, Quality and Reliability). Geneva,Switzerland: International Organizationfor Standardization.

• Verein deutscher Ingenieure (Associationof German Engineers). 1998. Prüfmittel-management und Prüfmittelüberwachung(Management and Control of Inspection,

Test, and Measuring Equipment).Düsseldorf, Germany.

• Weyhe, S. 1997. Wägetechnik im Labor(Weighing Technology in the Laboratory).Landsberg/Lech, Germany: Verlag ModerneIndustrie.



Sartorius AGWeender Landstrasse 94–10837075 Goettingen, Germany

Phone +49.551.308.0Fax +49.551.308.3289

www.sartorius.com

Specifications subject to change without notice.Printed in Germany on paper that has been

Handbook of Weighting Applications

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