peer reviewed measurement uncertainty

8/12/2019 Peer Reviewed Measurement Uncertainty

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Measurement Uncertaintyncertainty in the broad sense is

no new concept in chemistry;

analysts have always sought to

quantify and control the accuracy of their

results. Few analysts would dispute that a

result is of little value without some

knowledge of the associated uncertainty;

clearly, without such information, inter

pretation is impossible.

Correct interpretation depends on a

good assessment of accuracy. When esti

mates of accuracy are optimistic, results

may appear irreconcilable and may be

overinterpreted; with unduly pessimistic

assessments, methods may appear unfitfor a particular purpose and may be opti

mized when it's not necessary.

In general, different methods of estimating uncertainty will lead to different values.

Most estimates of accuracy have been

based on the standard deviation of a series

of experiments or interlaboratory compari

sons,often in association with estimates of

bias in the form of recovery estimates.

When individual effects are being consid

ered, the contribution from random vari

ability can be estimated from repeatability

reproducibility or other precision mea

sures.In addition separate contributions

from several systematic or random effects

can be combined linearly or by the root

sum ofsquares.Finally, the way uncer

tainty is expressed can vary substantially.

Confidence intervals, absolute limits, stan

dard deviations, and coefficients of variance

are all in common use. Clearly, with so

many possibilities for estimating and ex

pressing such a critical parameter, a con

sensus is essential for comparability.

The most recent recommendation is

that accuracy be expressed in terms of a

quantitative estimate of uncertainty as de

scribed in the International Standards Or

ganization's (ISO)Guide to the ExpressionofUncertaintyin Measurement t1) and other

measurement authorities (2,3).The guide

is published under the auspices of several

organizations, includingISO,the Interna

tional Bureau of Weights and Measures

(BIPM) the Organization for International

and Legal Metrology (OIML) and the In

ternational Union of Pure and Applied

Chemistry (IUPAC)

The document lays out a standard ap

proach to estimating and expressing un-

Correctinterpreta

tion ofaccuracyen

sures thatresultsare

judged neitheroverly

optimistically norun

duly pessimistically.

Steve EllisonLaboratory of the Government Chemist

(U.K.)

Wolfhard WegscheiderUniversity of Leoben (Austria)

Alex WilliamsEURACHEM Working Group on

Measurement Uncertainty (U.K.)

S0003-2700(97)09035-5 CCC: $14.001997 American Chemical Society

Analytical Chemistry News & Features, October1, 1997 607 A


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certainty across manyfieldsof measure

mentand,in view ofitspedigree, is widely

accepted by accreditation and certification

agencies worldwide. This Report deals

primarily with the provisions and interpre

tation ofthisdocument, though itisrecog

nized that different approaches are used

in otherISOdocuments.

Defin i t ions

The definitionofmeasurement uncertainty

is"aparameter associated with the resultof

a measurementthatcharacterizesthedis

persion ofthe valuesthatcouldreasonably

be attributedtothe measurand"(1,4).

Thus, measurement uncertainty describes

a range or distribution ofpossiblevalues.

For example,82 5describes s rangeeo

values. Measurement uncertainty, there

fore,differs from "error", whichisdefined

as asingle valuethe difference between a

resultandthe true value.The stated range must also include the

values the measurand could reasonably

take,on the basis of the result. That

makes it quite different from measuresof

precision, which give only the range

within which the mean ofaseries of ex-

perimentswilllie. Precision makes no

allowance forbias;measurement uncer

tainty includes random components and

systematic components. Note that known

systematic errors, or bias, should be cor

rected for as fully as possible; failure to

make such a correction is simply to report

a result known to be wrong. But an uncertainty associated with each correction fac

tor remains and must be considered. This

consideration of systematic effects makes

measurement uncertainty more realistic

than measures such as standard error.

Finally, measurement uncertainty is an

estimate. Obviously, all statistical calcula

tions onfinitesamples provide estimates

of population parameters, but the estimate

goes deeper thanthis.Devising experi

ments that can accurately characterize

uncertainties in method bias and other

systematic effects is extremely difficult.For example, most derivatizations are pre

sumed to proceed to completion. How

certain can the analyst be ofthis?Unfortu

nately, statistics help little; in practice the

chemistisoften forced to make an edu

cated estimate from prior experience

However itiscrucialtorealize that the

attempt must be made the correction for

bias and the uncertainty ofthiscorrection

factor cannot simply be ignored if compa-

rability is to be established

Error and uncertainty. In common parlance, the terms error and uncer

tainty are frequently used interchange

ably. However, several significant differ

ences in the concepts are implied by the

terms defined byISO(4).Errorisdefined

as the difference between an individual

result and the true value of the measur

and. Error, therefore, has a single value

for each result. In principle, an error could

be corrected ifallthe sources of error

wereknown,though the random partof

an errorisvariable from one determina

tion to the next.Uncertainty, on the other hand, takes

the form ofarange and, if estimated for

an analytical procedure and a defined

sample type, may applytoall determina

tions so described.Nopart of uncertainty

can be corrected for. In addition, estima

tion of uncertainty does not require refer

ence to a true value, onlyto aresult and

the factors that affect theresult.This shift

in philosophy marks a concept rooted in

observable, rather than theoretical, quan-

Box 1. Calcu lati ng uncert aint y using ISO rules

Rule1:Alllontributions are eombined in the formoofsandard deviationn sSDs).

Combining as SDs allows calculating a rigorous combined SD using standard

forms. It does not imply that the underlying distribution is or needs to benormalevery distribution has an SD. It is not perfectly rigorous to deduce

a confidence interval from a combinedSD,but in most cases, especially when

three or more comparable contributions are involved, the approximation is at

least as good as most contributing estimates.

Rule2:Uncertainties are combined according to

in in whichu(y)is the uncertainty ofa valuey,lFu2,- the uncertainties ofthe independent parametersxh x2,... on which it depends, anddy/dXjis the

partial differential ofywith respectto *,-.When variables are not independent,

the relationship is extended to include a correlation term (1).

Rule2establishes the principle of combination of root sum squares. One

corollaryisthat small components are quickly swampedbylarger contributions,

making it particularly important to obtain good values for large uncertainties

and unnecessary to spend time on small components. In pictures, this looks

like a simple Pythagorean triangle. For the uncertaintiesuxandu2,the

combinationuccan be visualized.

Rule3:TheSDobtained ffom Eq. . 1neds to ob multiplied dbycoverage factor

kto obtain a range called the expanded uncertainty, which includes a large

fraction of the distribution. For most purposes,k=2 is sufficient (2)and will

give a range corresponding to an approximately95%confidence interval.

Similarly,k=3 is recommended for more demanding cases.

608 A AnalyticalChemistryyews &&eatures, October1, 1991


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titles. To further illustrate the difference,

the result ofananalysis after correction

mayby chancebe very close to the

value of the measurand, and hence have a

negligible error. The uncertainty may

nonetheless still be very large, simply be

cause the analystisunsure ofthesize of

the error.Uncertainty and quality assur-

ance.ISOexplicitly excludesgrosserrors

of procedurefrom considerationwithinan

uncertaintyassessment.Uncertainty esti

mates can realistically apply onlytowell-

established measurement processesinsta

tisticalcontrol, and thus they areastate

ment of the uncertainty expected when

proper quality control (QC) measures are

inplace. Itisthus implicit thatQCand qual

ityassurance (QA) processesbe inplace

and within specification if an uncertainty

statementis tobeat allmeaningful.

Repeatability andreproducibility

The most generally applied estimates of

uncertainty at present are those obtained

from interlaboratory comparisons, particu

larly those using the collaborative trial

protocols ofISO5725 (5) and the Associa

tion of Official Analytical Chemists

(AOAC)(6).

For legislative purposes, the collabora

tive trial reproducibility figure is the closest approach to uncertainty that attempts

to estimate the full dispersion of results

obtained by a particular metiiod, and it

has the considerable advantages of sim

plicity and generality, though at high cost.

Another substantial advantage is its objec

tivity, because itisbased entirely on ex

perimental observations inarepresenta

tive range of laboratories. Though it

serveswellin cases in which the chief

issue is comparability among particular

laboratories with a common aim several

factors leave this approach wantingReproducibility is inevitably a measure

ofprecision;although it covers a range of

laboratorybias,it cannot cover bias inher

entinthe methoditself,nor, in general,

sample matrix effects. Arguably, these

effects are not relevant for a standard

method, which may simply define a proce

dure that generatesaresult for trade or

legislative purposes. Many methods, in

deed fall into this class; even when a

metiiod purports to determine a specific

molecular species, there is no guarantee

that it determines all thatispresent or,

indeed, any particular species at all.

An example is the semiquantitative

AOACmethod for detecting cholesterol.

Though standardized and properlyac

cepted for certain trade and regulatory

purposes on the basis of collaborative trial

data showing sufficient agreement be

tween laboratories (7), subsequent work

using internal calibration (8)has shown

that method recovery is poorer than the

reproducibility figure suggests. It follows

that long-term studies of cholesterol levels

in food could be expected to misinterpretchanges in apparent level particularly

nations using different cholesterol

determination methods Reproducibility

figures will in treneral suffer from the

absence ofbiasinformation

These arguments suggest that repro

ducibilitywillgenerally underestimate

uncertaintybut not necessarily.Asingle

laboratory can have much smaller uncer

tainties for a determination than the repro

ducibility figure would indicate, which

tends to includearange of pooras wellas

good results. This issue can be put morebluntly: What does the spread of results

found byahandful of laboratories on a

specific set of samples at some time in the

past have todowith the results ofanindi

vidual laboratorytoday?Indeed, this is the

very question that mustbeanswered

quantitatively before any laboratory can

make use of collaborative trial information

inaformal uncertainty estimate. It follows

that reproducibility, although a powerful

tool, is notapanacea.

The ISO approachThe approach recommended in the ISO

guide, outlined below, is based on com

bining the uncertainties in contributory

parameterstoprovide an overall estimate

of uncertainty (Figure 1).

To begin, write down a clear statement

ofwhat isbeing measured, including the

relationship between the measurand and

the parameters (measured quantities, con

stants, calibration standards, and other

influences) on which it depends. When

Figure 1 . Uncertainty estimation process.

Analytical Chemistry News & Features, October1, 1997 609 A


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Figure 2. Dioxin analysis.

possible, include corrections for known

systematic effects. Though the basic spec

ification information is normally given in

the relevant standard operating procedure

or other method description, itisoften

necessarytoadd explicit terms for factors

such as operating temperatures and ex

traction time or temperature, which will

not normally be included in the basic cal

culation given in a method description.

Then, for each parameterinthis rela

tionship, listthepossible sources of uncer

tainty, including chemical assumptions.

Measure or estimate the size of the uncer

tainty associated with each possible source

of uncertainty(orforacombinationof

sources). Combine the quantified uncer

tainty components, expressed as standard

deviations, accordingtothe appropriate

rules (seeBox onp.608 A)),ogive ecom

bined standard uncertainty, and apply theappropriate coverage factorto givean ex

panded combined uncertainty

The most important features are that

all contributing uncertainty components

are quantified as standard deviations in

the first instance, whether they arise from

random variability or systematic effects;

also, that estimates of uncertainty from

experiment, prior knowledge, and profes

sionaljudgment are treated in the same

way and given the same weight.

Quantifyingallcontributing uncertainty

componentsasstandard deviationspro

videsaparticularly simple and consistent

methodof calculationbased on standard

expressions for combining variances.It is

justified in principle because, although an

errorin aparticular casemay besystem

atic, lackof knowledgeaboutthesizeof the

errorleadstoaprobability distribution for

theerror.This distribution canbetreated

inthesame way asthat ofarandom vari

able. Treating estimatesofuncertainty fron

experiment prior knowledge and profes

sional judgmentthe same wayand giving

them the same weight ensures thatall

known factors contributingtouncertainty

are accounted forevenwhen experimental

determinationisnot possible

In principle, this approach overcomes

many ofthedeficiencies in currently used

approaches. It is much quicker and lesscostly to apply than a collaborative trial,

but it can use collaborative trial data ad

vantageously if available. The approach

covers all the effects onaresult, system

atic or random, and it takes into account

all available knowledge. In addition, it

mandates a particular form of expression,

leadingtoimproved comparability in un

certainty estimates

However, disadvantages exist. The

ISO approach, because it requires appro

priatejudgment, cannot be entirely objec

tive;to some extent it relies on the experi

ence of the analyst.Asignificant costin

time and effort isafactor; estimating un

certainties on the basis oflocalconditions

without using published data involves

more effort than simply quoting a pub

lished reproducibility figure.The lack of objectivity can be compen

sated for by third-party review, such as

quality system assessment, interlabora-

tory comparisons, in-house QC sample

results, and certified reference material

checks. Finally, it should be clear that a

decision to excludeaparticular contribu

tion entirely rather than makesomejudg

ment ofitssize represents a de facto deci

sion to allocate the contribution a size of

zero hardly an improvement.

Cost,too,may berecouped in direct or

indirect benefits. Uncertainty estimation

improves knowledge ofanalyticaltech

niques and principles, formingapowerful

adjuncttotraining.Knowing themain con

tributionstouncertainty determines the

directionof methodimprovement most

effectively. Efficiency can be improvedwith

minimal impactonmethod performance.

Finally, normalQAprocedures,such as

checking the method for use, maintaining

recordsofcalibration and statisticalQC

procedures, should provideallthe required

data;additional costshouldbe no morethan

thatofcombining the dataappropriately

Sources of uncertainty

Many factors affect analytical results, and

every one is a potential source of uncer

tainty. In sampling, effects such as ran

dom variations between different samples

and any potential for bias in the sampling

procedure are components of uncertainty

affecting thefinalresult. Recovery ofan

analyte from a complex matrix, or an in

strument response, may be affected by

other constituents ofthematrix. Analytespeciation may further compound this

effect. When a spike is used to estimate

recovery the recovery of the analyte from

the sampleiricivdiffer" from the recoverv

ofthespike Stability effects are also im-

portant but frequently are not well-known

Cross-contamination between samples

and contamination from the

laboratoryemnrrtnment are pupr nrpcpnt risk s

Though ISO does not include accidental

gross cross-contamination in its definition

610 A Analytical Chemistry News & Features, October1, 1997


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of uncertainty, as it represents loss of con

trol ofthemeasurement process, the pos

sibility of background contamination

should nonetheless be considered and

evaluated when appropriate.

Although instruments are regularly

checked and calibrated, the limits of accu

racy on the calibration constitute uncertainties. Calibration used may not accu

rately reflect the samples presented; for

example, analytical balances are com

monly calibrated using nickel check

weights, although samples are rarelyof

such high density. Though not large in

most circumstances, buoyancy effects

differ between calibration weight and sam

ple. Other factors include carry-over and

systematic truncation effects.

The molarity ofavolumetric solution is

not exactly known, even iftheparent ma

terial has been assayed, because some

uncertainty relating to the assay proce

dure exists.A widerange of ambient con

ditions, notably temperature, affects ana

lytical results. Reference materials are

also subjecttouncertainty; fortunately,

most providers of reference materials now

state the uncertainty in the manner rec

ommended in the guide.

The uncritical use of computer soft

ware can also introduce errors. Selecting

the appropriate calibration model is im

portant, and software may not permit the

best choice. Early truncation and round

ing offcanalso lead to inaccuracies in the

final result.

Operator effectsmaybe significant;

they can be evaluated either by predicting

them or by conducting experiments in

volving many operators. The latterap

proachwillnot normally detect an overall

operator bias (for example, a particular

scale reading may be taken in the same

manner byagroup of operators similarly

trained), but the scope of variation can be

estimated. "Operator effect" could reasonably be considered a proxy for a range of

poorly controlled input parameters such

as scale-reading accuracy time and dura

tion of agitation during extraction and so

on It follows thataformal mathematical

model oftheexperimental process would

not normally include "operator" as an in-

niit factor but only the specific factors un

de r ooerator

Random effects contribute to uncer

tainty in all determinations, and this en

try is usually included in the list as a

matter of course. Conceptualizing every

component of uncertainty as arising

from both systematic and random effects

is also frequently useful; this step avoids

the most common trap for the unwary

overlooking systematic effects in the

effort to obtain good precision measures.Both need to be taken into account,

though the ISO approach requires only

the overall value.

Determinands are not always com

pletely defined. For example, volumes

may or may not be defined with refer

ence to a particular set of ambient con

ditions. Similarly, the determinand may

be defined in terms ofarange of condi

tions.For example, material extracted

from an acidified aqueous solution at pH

below 3.0 allows substantial latitude.

Such incomplete definitions result in thedeterminand itself having a range of val

ues,irrespective of good analytical tech

nique, and that range constitutes an

uncertainty.

Many common analytes, such as fat,

moisture, ash, and protein, are defined not

in terms ofaparticular molecular or

atomic species but against some essen

tially arbitrary process. In effect, the re

sult is simply a response to a stated proce

dure,expressed in the most convenient

units. Such measurements are not gener

ally compared with results from other

methods; in effect, bias is neglected by

convention. However, the procedure itself

may lack full definition or permitarange

of conditions, giving rise to uncertainties.

Of course if comparison with other meth

ods is desired additional sources of un

certainty including method bias must be

taken into

Increasing confidence

The ISO guide suggests multiplying the

standard uncertainty by a coverage fac

torkto express uncertainties when a

high degree of confidence is desired.

This representation exactly mirrors the

situation in conventional statistics, in

which a confidence interval is obtainedby multiplying a standard deviation for a

parameter by a factor derived from the

Student ^-distribution for the appropriate

number of degrees of freedom.

The formal approach in the guide re

quires estimation ofasimilar parameter,

the "effective degrees of freedom", and

uses this value in the same way. Though

the details are beyond the scope of this

article, some important points can be

made.

This parameter is almost invariably

dominated by the number of degrees of

freedom in the dominant contribution to

the overall uncertainty. When the domi

nant contribution arises from sound and

well-researched information, effective de

grees of freedom remain high, normally

leadingtok= 2for near95%confidencce

Only where large uncertainty contribu

tions are based on meager datawillthe

choice ofkbecome significant.Aprag

matic approach, therefore, is simply to

adoptk = 2for routtne work ,ndk k=

when a particularly high confidence is

required(2)

The question of possible distributions

mustalsobe consideredat thepointofde

ciding coverage factors. Although the guide

usesacombination of standard deviations

based on established error propagation

theory, the step from standard deviation to

confidence involves some assumptions.

The guide takes theviewthat,in mostcir-

Table 1. Contributions to uncertainty in dioxin analysis.

Parameter u(RSD) Main contributio n3

Oss 0.02

V 0.02

Ak an d -4SS 0.09

RRFn 0.08

"lspk 0.12

Combine d uncertainty 0.17

Syringe specification; certified reference solution

uncertainty

Density (volume determined by weight)

Permitted abundance ratio range

Range permitted by method

Permined range of spike recovery

[(0.02) +(0. 02) +(0. 09) + (0.08)2 +(0.12)2]1/2

(a) Contributions are listed if they contribute more than 10% of the stated uncertainty.(b) Permitted ranges are treated as limits of rectangular distributions and adjusted to SDvalues (1)by dividing by the square root of 3.(c) Recovery of added material is not, in general, fully representative of recovery of analytematerials.

Analytical Chemistry News & Features, October 1, 1997 61 1 A


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cumstances, the centrallimittheoremwill

apply, and the appropriate distributionwill

be approximately normal. Certainlyit is

raretocalculate confidence intervals based

on other distributionsingeneral analytical

chemistry, ifonly because it isunusual to

have sufficient datatojustify other assump

tions. Nonetheless, when additional knowl

edge about underlying distributions exists,

it ismost sensible to basekonthe best

available information.

Dioxin example

The analysis ofdioxinsin the effluentof

paper and pulp mills by isotope dilution

MS (Figure2)isagood example (9). For

the sake ofdiscussion,we willconsider

only the analysis of 2,3,7,8-tetrachloro-

dibenzodioxin (2,3,7,8-TCDD) and will

ignore the normally important uncertain

ties caused by interference from other

TCDD isomers,GCintegration, and res

olution difficulties.Byway of illustration,

some minor contributions that would

not normally be included will also be

examined.

The basic equation for determining the

concentrationCxof TCDD is

Cx=AkQss/AaJiRFnVR%pk

in whichAk isthe peak area oftheana-

lyte,Qssis the amount of spike,i4ssis the

peak area ofthestandard,RRFnis the

relevant response factor for the relevant

ion13C-12, Fis the original sample vol

ume,andi?spkisthe (nominal) recoveryof

the analyte relative to added material.

Rakmerits explanation, because it is

not used in the standard. Because the13

C-12 calibration spike is added to the

slurry and is not naturally part ofthesam

ple, differential behavior is possible. If

measurable, this behavior would appear

as imperfect recovery of analyte.Acom

plete mathematical model of the system

therefore requires some representation of

the effect. Because no existing parameter

in the equation is directly influenced by

recovery the recovery term has been

added in the form ofanominal correction

factor The resultis abasic equation en

compassing all the main effects on the

result

Identification oftheremaining contri

butions to the overall uncertaintyisbest

achieved by considering the parameters

in the equation, any intermediate mea

surements from which they are derived,

and any effects that arise from particular

operations within the method (such as the

possibility of"spikepartitioning"). Table 1

lists parameters, calculated uncertainties

(as relative standard deviations), and

some contributory factors.

Informationin Table 1 showsthat uncer

tainties associated with the physical measurements of volume and mass contribute

essentially nothingtothe combined uncer

tainty and thatanyfurther study should be

directed primarilyat theremainingcompo

nents. The largest contributionarisesfrom

the extraction recovery step,in linewith

most analysts' experience.

The method studied hereisunusualin

specifying directcontrol of allthe major

factors affecting uncertainty, which makes

itrelativelyeasy toestimate uncertainty as

longasthe method isoperating withincon

trol.For most methods currentlyinuse,

however, such controllimitsarenot closely

specified.Typically,one ortwocriticalpa

rameters are given single target values, and

precision controllimitsare setIt thenfalls

to the laboratorytoestimate the contribu

tion ofits ownlevel ofcontrol tothe uncertainty, ratherthan simplydemonstrating

compliancewithan established set of fig

ures and an associated, carefully studied,

uncertainty estimate.

Legislation and compliance

Two issues are importantwhenuncer

taintyisconsidered in the context of legis

lation and enforcement. The first con

cerns the simpler problem of whether a

result constitutes evidence ofnoncompli

ance with some limit, particularly when

the limitiswithin the uncertainty quoted.The second issue is the use of uncertainty

information in setting limits.

Two instances in compliance are

clear-cut: Either the result is above the

upper limit, including its uncertainty,

which means that the result is in non

compliance (Figure 3a); or the result,

including its uncertainty, is between the

upper and lowerlimits,and is therefore

in compliance (Figure 3d). For any other

case, some interpretation is necessary

and can be made only in the light of the

and with the knowledge and

understanding of the end of the

information

For example, Figure 3b represents

probable noncompliance with the limit,

but noncompliance is not demonstrated

beyond reasonable doubt. In the case of

legislation, the precise wording needs to

be consulted; some legislation requires

that, for example, process operators dem

onstrate that they are complyingwitha

limit. In such acase,Figure 3b represents

noncompliance with the legislation; compliance has not been demonstrated be

yond doubt.

Similarly, if legislation requires clear

evidence of noncompliance withalimit

that triggers enforcement, although there

is no clear demonstration of compliance,

there is insufficient evidence of noncom

pliance to support action, as in Figure 3c.

In these situations, end-users and legisla

tors must spell out how the situation

should be handled.

Upperlimit

Lowerlimit

(a)Result above

limit plusuncertainty

(b)Result abovelimit, but limit

withinuncertainty

(c)Result belowlimit, but limit

withinuncertainty

(d)Result belowlimit minusuncertainty

Figure 3. Uncertainty and compliance limits.

612 A AnalyticalChemistry News &&eatures, October1, 1991


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A recent editorial (10)pointed out the

need to avoid setting limits that cannot be

enforced without disproportionate effort.

An important factor to consider is the actual

uncertainty involved in determining a level

of analyte; if legislation is to be effective, the

uncertainty must be small in relation to any

limiting range. In chemistry, measurementrequirements tend to follow a "best avail

able"presumption, even when this policy is

not actually written into legislation; an ex

ample is the Delaney Clause (11).

As the state of the art improves, new

measurements become possible and are

immediately applied, leading to a situa

tion in which the best available technol

ogy is the only acceptable technology. In

such a situation, uncertainties are, inevi

tably, hard to quantify well; they will of

ten be larger than required for the pur

pose. That legislation takes into account

the full uncertainty is particularly impor

tant; failure to include significant compo

nents may unreasonably restrict enforce

ment. In particular, the possibility of sys

tematic effects being considered is vital;

legislation based on measurement of

absolute amounts of substance, as in

most new European environmental legis

lation, must consider the full range of

methods and sample matrices that may

fall within that legislation.

Another important consideration is theinterpretation of results and their relevant

uncertainties against limits. Assumptions

about the handling of experimental uncer

tainty in interpretation for enforcement

purposes must be clearly stated in the

legislation. Specifically, do limits allow for

an experimental uncertainty or not? If so,

how large is the allowance?

A fundamental factor is how well leg

islators understand uncertainty. The

need to set limits in some contexts is

easily understood, such as how much of

a toxic compound is acceptable in anenvironmental matrix. However, judging

compliance is trickier, and a better un

derstanding of analytical uncertainly is

required. The current move toward spec

ifying method performance parameters,

such as repeatability, reproducibility,

and recovery rather than the method

itself, is a step in the right direction; but

these parameters do not necessarily

cover all of the significant components of

uncertainty. What is required is the addi

tional specification of the measurement

uncertainty to meet the needs of the

legislation.

Ellison's workwassupported under contractwith the Department of Trade and Industry as

part of the National Measurement SystemValidAnalytical Measurement Programme.

References

(1) Guide to the ExpressionofUncertaintyinMeasurement;ISO:Geneva,,193;ISBN92-67-10188-9.

(2) Quantifying Uncertainty ininalyticalMeasurement;Published do nehalf foEURACHEM by Laboratory of the Government Chemist: London,1995;ISBN0-948926-08-2.

(3) Taylor,B.N.; Kuyatt, C. E.Guidelines forEvaluating and ExpressingthtUncertaintyofNISTMeasurementResults;NIST Technical Note 1297, National Institute of Stan

dards and Technology: Gaithersburg,MD,1994.

(4) International VocabularyofBasicanaGeneral Standard Termsin Metrology,ISO:Geneva,1993;ISBN 92-67-10175-1.

(5) ISO 5725:1986,PrecisionofTestMethods:DeterminationofRepeatability anaReproducibility fora Standard Method byInter-laboratoryTests;ISO:Geneva, 1987.

(6) Youden,W.H.; Steiner, E. H.StatisticalManualofthe Associationof Official Analytical ChemiststAOAC:Washington, DC,1982.

(7) Thorpe, C.W.Assoc.Anal.Chem. 1969,52,778-81.

(8) Lognay, G. C; Pearse,J.;Pocklington, D.;Boenke, A.; Schurer,B.;Wagstaffe,P.J.

Analyst1995,1201831-35.(9) ReportEPSl/RM/19; Environment Can

ada: Ottawa, Ontario, 1992.(10) Thompson,M.Analyss1995,120,

117N-18N.(11) Delaney: Federal Food, Drug and Cos

meticAct;Food additives amendment,1958.

Steve Ellison is head of the analytical

quality and chemometrics section at the

Laboratory of the Government Chemist

(U.K.). His research interests include sta

tistics, validation and measurement un

certainty, and chemometrics in the con

texts of regulatory analysis and analyticalchemistry. Wolfhard Wegscheider is profes

sor of chemistry and dean of graduate

studies at the University ofLeoben (Aus

tria) and chair of EURACHEM Austria.

Alex Williams is chair of the EURACHEM

Working Group on Measurement Uncer

tainty Address correspondence about this

article to Wegscheider at Institute of Gen

eral and Analytical Chemistry University

ofLeoben A-8700 Leoben Austria

(wegschei@unileoben ac at)

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