A Guide On Measurement Uncertainty In Chemical .
ACCREDITATION SCHEME FOR LABORATORIESTechnical Guide 2A Guide on Measurement Uncertainty inChemical & Microbiological AnalysisTechnical Guide 2, Second Edition, 29 March 2019The SAC Accreditation Programme is managed by Enterprise Singapore All rights reserved
Technical Guide 2A Guide on Measurement Uncertaintyin Chemical & Microbiological AnalysisSecond Edition All rights reserved2 Fusionopolis Way,#15-01, Innovis,Singapore 138634
AcknowledgementThe Singapore Accreditation Council (SAC) would like to thank members of the Task Forceon Measurement Uncertainty for Chemical & Microbiological Analysis and their respectiveorganization for their effort & contributions in establishing this technical guide.The members of the Task Force are:NameOrganisationChairman:Dr Li SihaiTÜV SÜD PSB Pte LtdMembers:Dr Charles TangDr Ng Kok ChinMr Yeoh Guan HuahSingapore General HospitalSingapore PolytechnicALS Technichem (S) Pte LtdSecretary:Ms Lee Ham EngMs Angela WibawaSingapore Accreditation CouncilSingapore Accreditation CouncilSAC would also like to thank the following laboratories for contributing additional workedexamples to the second edition of the Technical Guide 2:ALS Technichem (S) Pte LtdAVA – Veterinary Public Health LaboratoriesMarine Fisheries Research DepartmentSGS Testing & Control Services Pte LtdSingapore General HospitalSingapore Test Services Pte LtdTÜV SÜD PSB Pte LtdWe are grateful to EURACHEM/CITAC measurement uncertainty working group forpermission to utilize sections from the EURACHEM/CITAC Guide on Quantifying Uncertaintyin Analytical Measurement (available from http://www.vtt.fi/ket/eurachem).Note: Use of the material does not imply equivalence with the EURACHEM/CITAC guide.Technical Guide 2, 29 March 20192
Contents1.IntroductionPage12.What is Uncertainty of Measurement23.Reasons for Estimating Uncertainty24.Sources of Uncertainty in Chemical Measurement35.Evaluation Methods46.Structure of Analytical Procedure67.Process for Estimating Uncertainty78.Reporting Uncertainty179.General Remarks1810.Measurement Uncertainty for Quantitative Microbiological Testing18Appendix AGlossary of Statistical Terms26Appendix BDistribution Functions35Appendix CFlow Diagram of the Overview on Different Approaches to MeasurementUncertainty Estimation36Appendix DISO/TS 21748 Approach38Appendix EGeneric Worked ExamplesE.1 WeighingE.2 Volume PreparationE.3 Calculating the Molecular Weight of a SoluteE.4 Calibration CurveE.5 Application of GC-MSE.6 Estimation of Bias Based on the Recovery Data40414345474953Appendix FWorked ExamplesF.1 Acid/Base Titration: Determination of Concentration of HCl solutionF.2 Determination of Linoleic Acid of Milk Fat Extracted from Milk Powderby GC-FIDF.3 Determination of Acid Value in Palm OilF.4 Kinematic Viscosity of Fuel OilF.5 Determination of Crude Fibre in Animal Feeding StuffF.6 Moisture Determination in ScallopF.7 Benzoic Acid in Food ProductsF.8 Fluoride Content in Water by SPADNS MethodF.9 Stack VelocityF.10 Vanadium in Fuel OilF.11 Total Coliform Count of Reservoir WaterAppendix G5766717476788184878997BibliographyTechnical Guide 2, 29 March 20191043
1.0Introduction1.1The International Standard ISO/IEC 17025:2005 on "General Requirements for theCompetence of Testing and Calibration Laboratories" [1] has included a series ofclauses on the estimation of measurement uncertainty for calibration and testinglaboratories. It requests the assessment of uncertainty of test results during methodvalidation and requires testing laboratories to have and apply procedures forestimating uncertainties of measurement in all test methods except when the testmethods preclude such rigorous estimations.1.2The SAC-SINGLAS 002 document on "General Requirements for the Competenceof Calibration and Testing Laboratories" [2] also states that a laboratory shall useappropriate methods and procedures, including an estimation of uncertainty in allmeasurements, and indicate the quantitative results accompanying with a statementof the estimated uncertainty.1.3The SAC-SINGLAS Technical Guide 1 on "Guidelines on the Evaluation andExpression of the Measurement Uncertainty" [3] was first produced in July 1995 withan aim to harmonize the procedure for expressing measurement uncertainty. Thedocument has been well written and widely accepted. However, it only coversguided examples in the field of calibration and physical measurements. Whilst thecorrections are small and experimental error may be negligible in physics(metrology), the estimation of uncertainty of results in chemical analysis is morecomplicated. This is because chemical testing usually requires several steps in theanalytical process, very often with the use of a few analytical equipments, and, eachof these actually involves certain element of uncertainty.1.4It is the aim of this Guide to give general information of the application of uncertaintyto chemical analysis and microbiological analysis and its effects on compliance. ThisGuide outlines the current thinking of methodology, based on the methodsprescribed in the ISO Technical Advisory Group on Metrology (TAG4's) lengthydocument ISO guide 98 on "Guide to the Expression of Uncertainty inMeasurement", commonly known as GUM [4] in 1995, the EURACHEM documenton "Quantifying Uncertainty in Analytical Measurement" [5] and ISO/TS21748:2004(E) on “Guidance for the use of repeatability, reproducibility andtrueness estimates in measurement uncertainty estimation”. [10]. Simplifiedmethods adopted elsewhere are also considered. Guidance is also given on theexpression and reporting of uncertainty values.1.5However, it must be noted that although the concept of uncertainty itself is wellaccepted, there are different opinions among many learned establishments on howit should be estimated and, to a lesser extent, how it should be referred to. Hence, itis anticipated that this Guide will require constant reviewing and updating, in order tokeep up with the most current methodology.1.6The appendices accompanying this document are several detailed examples ofuncertainty evaluation processes taken from different areas of chemical analysis.These examples are intended to illustrate the application of the proceduresdescribed in this Guide.1.7A summary of definitions as stated in the ISO 5725-1 (1994) on "Accuracy(Trueness and Precision) of Measurement Methods and Results - Part 1: GeneralPrinciples and Definitions) [6], ISO TAG4 [4] and EURACHEM [5] is given inAppendix A.Technical Guide 2, Nov 071
2.0What is Uncertainty of Measurement?2.1The word "uncertainty" means doubt, and thus in its broadest sense "uncertainty ofmeasurement" means doubt about the validity of the result of a measurement.2.2Measurement uncertainty is defined as "parameter, associated with the result of ameasurement that characterizes the dispersion of the values that could reasonablybe attributed to the measurand" [5]. The word "measurand" is further defined inanalytical chemistry term as "particular quantity or concentration of a speciessubject to measurement" (such as copper content in water).2.3This definition is also consistent with other concepts of uncertainty of measurement,such as:a measure of the possible error in the estimated value of the measurand asprovided by the result of a measurement;an estimate characterizing the range of values within which the true value ofa measurand lies.2.4When uncertainty is evaluated and reported in a specified way, it indicates the levelof confidence that the value actually lies within the range defined by the uncertaintyinterval.3.0Reasons for Estimating Uncertainty3.1There is a growing awareness that analytical data for use in any decision processmust be technically sound and defensible. Limits of uncertainty are required whichneed to be supported by suitable documentary evidence in the form of statisticalcontrol as for some kind of ‘quality assurance’. When a measurement process isdemonstrated by such statistical control, the accuracy of the process can be impliedto characterize the accuracy of all data produced by it.3.2It is a recognized fact that any chemical analysis is subject to imperfections. Suchimperfection gives rise to an error in the final test result. Some of these are due torandom effects, typically due to unpredictable variations of influence quantities, suchas fluctuations in temperature, humidity or variability in the performance of theanalyst. Other imperfections are due to the practical limits to which correction canbe made for systematic effects, such as offset of a measuring instrument, drift in itscharacteristics between calibrations, personal bias in reading an analogue scale orthe uncertainty of the value of a reference standard.3.3Every time a measurement is taken under essentially the same conditions. Randomeffects give rise to random errors from various sources and this affects themeasured value. Repeated measurements will show variation and a scatter of testresults on both sides of the average value. Statisticians say that random errorsaffect the precision, or reproducibility. A number of sources may contribute to thisvariability, and their influence may be changing continually. They cannot becompletely eliminated but can be reduced by increasing the number of replicatedanalysis.3.4Systematic errors emanate from systematic effects. They cause all the results to bein error in the same sense, i.e. either producing consistently higher or lower resultsthan the true value. They remain unchanged when a test is repeated under thesame conditions. These effects also cannot be eliminated but may be reduced orcorrected with a correction factor if a systematic effect is recognized. In fact,systematic errors must be first dealt with before estimating any uncertainty in achemical analysis.Technical Guide 2, 29 March 20192
3.5Hence, measurement uncertainty is a quantitative indication of the quality of the testresult produced. It reflects how well the result represents the value of the quantitybeing measured. It allows the data users to assess the reliability of the result andhave confidence in the comparability of results generated elsewhere on the samesample or same population of the samples. Such confidence is important in theattempt to remove barriers to trade internationally.3.6An understanding of the measurement uncertainty helps also in the validation of anew test method or a modified test method. One can suggest additionalexperiments to fine tune the test method if the uncertainty of the results is found tobe large. One can also optimize the critical steps in a chemical analytical procedurein order to reduce uncertainty.3.7By quoting measurement uncertainty, the laboratory operator reflects well on thetechnical competence of his laboratory staff performing the analysis and helps tocommunicate the limitations of test results to his customer.4.0Sources of Uncertainty in Chemical Measurement4.1There are many possible sources of uncertainty of measurement in testing,including but not limiting to:a) Non-representative samplingthe sample analyzed may not berepresentative of the defined population, particularly when the it is nothomogeneous in nature;b) Non-homogeneity nature of the sample, leading to uncertainty in testing asub-sample from the sample;c) Incomplete definition of the measurand (e.g. failing to specify the exact formof the analyte being determined, such as Cr3 and Cr6 );d) Imperfect realization of the definition of the test method. Even when the testconditions are defined clearly, it may not be possible to produce theseconditions in a laboratory;e) Incomplete extraction and pre-concentration of the test solution beforeanalysis;f)Contamination during sample and sample preparation;g) Inadequate knowledge of the effects of environmental conditions on themeasurement or imperfect measurement of environmental conditions;h) Matrix effects and interference;i)Personal bias in reading measurements (e.g. colour readings);j)Uncertainty of weights and volumetric equipmentk) Uncertainty in the values assigned to measurement standards and referencematerials;l)Instrument resolution, or discrimination threshold, or errors in the graduationof the scale;Technical Guide 2, 29 March 20193
m) Approximations and assumptions incorporated in the measurement methodand procedure;n) Values of constants and other parameters obtained from external sourcesand used in the data reduction algorithm;o) Random variation in repeated observations of the measurand underapparently identical conditions. Such random effects may be caused byshort term environmental fluctuations (e.g. temperature, humidity, etc.) orvariability between analysts.It is to be noted these sources are not necessarily independent and, in addition,unrecognized systematic effects may exist that are not taken into accounts butwhich contributed to an error. However, such errors may be reduced, for example,from examination of the results of an inter-laboratory proficiency programme.5.0Evaluation Methods5.1The ISO Guide 98, ISO/TS 21748:2004 and the EURACHEM document have alladopted the approach of grouping uncertainty components into two categoriesbased on their method of evaluation, i.e. Type A and Type B evaluation methods.5.2This categorization, based on the method of evaluation rather than on thecomponents themselves, applies to uncertainty and is not substitutes for the words"random" and "systematic". It avoids certain ambiguities - a random component ofuncertainty in one measurement may become a systematic component in anothermeasurement that has, as its input, the result of the first measurement. Forexample, the overall uncertainty quoted on a certificate of calibration of aninstrument will include the component due to random effects, but, when this overallvalue is subsequently used as the contribution in the evaluation of the uncertainty ina test using that instrument, the contribution would be regarded as systematic.5.3Type A evaluation of uncertainty is based on any valid statistical method in analysisof a series of repeated observations. The statistical estimated standard uncertaintyis called, for convenience, a Type A standard uncertainty.5.4Component of Type A evaluation of standard uncertainty arises from random effect.The Gaussian or Normal Law of Error forms the basis of the analytical study ofrandom effects. (See Appendix B)5.5It is a fact that the mean of a sample of measurement provides us with an estimateof the true value, µ of the quantity we are trying to measure. Since, however, theindividual measurements are distributed about the true value with a spread whichdepends on the precision; it is most unlikely that the mean of the sample is exactlyequal to the true value of the population.5.6For this reason, it is more useful to give a range of values within which we arealmost certain the true value lies. The width of the range depends on two factors.The first is the precision of the individual measurements, which in turn depends onthe variance of the population. The second is the number of replicates made in thesample. The very fact that we repeat measurements implies that we have moreconfidence in the mean of several values than in a single one. Most people will feelthat the more measurements we make, the more reliable our estimate of µ, the truevalue.Technical Guide 2, 29 March 20194
5.7In most cases, the best available estimate of the expected value of a measurandquantity x that varies randomly, is the arithmetic mean x for n number of replicates:x xi / n5.8 (1)The experimental standard deviation s is used to estimate the distribution of x as:s [ (xi - x )2/(n-1)] (2)Alternatively, it can be simplified to the following form:s 5.9[( (xi)2 / (n-1) ) - ( (xi)2 / n (n-1) )] (3)The experimental standard deviation of mean, or standard error of the mean(s.e.m.), x, or a distribution of sample means has an exact mathematicalrelationship between it and the standard deviation, , of the distribution of theindividual measurements, which is independent of the way in which they aredistributed. If N is the sample size, this relationship is:s.e.m. x 5.10 / (4)NFrom the equation (4) above, it is noted that the larger N is, the smaller the spreadof the sample means about µ. This universally used term, the standard error of themean, might mislead us into thinking thatand µ. This is not so. The / /N gives the difference between xN gives a measure of uncertainty or confidenceinvolved in the estimating µ from x .5.11On the other hand, Type B evaluation is by means other than used for Type A suchas:- from data provided in calibration certificates and other reports;- from previous measurement data;- from experience with, or general knowledge of the behaviour of theinstruments;- from manufacturers' specifications;- from all other relevant information.Components evaluated using Type B methods are also characterized by estimatedstandard uncertainty.5.12When we are considering Type B uncertainty, we have to convert the quoteduncertainty to a standard uncertainty expressed as standard deviation. We canconvert a quoted uncertainty that is a stated multiple of an estimate standarddeviation to a standard uncertainty by dividing the quoted uncertainty by themultiplier.Example:A calibration report for reference weights states that the measurement uncertainty ofa 1-gm weight is 0.1 mg at 2 standard deviations. The standard uncertainty istherefore 0.1 mg divided by 2 which gives 0.05 mg.Technical Guide 2, 29 March 20195
5.13The quoted uncertainty can also be converted to a standard uncertainty from theknowledge of the probability distribution of the uncertainty. These probabilitydistributions can be in the standard form of rectangular, triangular, trapezoidal andnormal or Gaussian. See Appendix B. Divide the quoted uncertainty by a factorwhich depends on the probability distribution.5.14It may be stressed that those uncertainty components quantified by means otherthan repeated analysis are also expressed as standard deviations, although theymay not always be characterised by the normal distribution. For example, it may bepossible only to estimate that the value of a quantity lies within bounds (upper orlower limits) such that there is an equal probability of it lying anywhere within thosebounds. This is known as a rectangular distribution. There are simple mathematicalexpressions to evaluate the standard deviation for this and a number of otherdistributions encountered in measurement.5.15The components, evaluated by either Type A or Type B methods, are combined toproduce an overall value of uncertainty known as the combined standarduncertainty. An expanded uncertainty is usually required to meet the needs ofindustrial, commercial, health and safety, and other applications. It is obtained bymultiplying the combined standard uncertainty by a coverage factor, k. The k valuecan be 2 for a 95% confidence level and 3 for a 99.7% confidence level. Theexpanded uncertainty defines an interval about the result of a measurement thatmay be expected to encompass a large fraction of the distribution of values thatcould reasonably be attributed to the measurand.6.0Structure of Analytical Procedure6.1Before the discussion on the methods for estimating uncertainty, it is helpful to firstof all break down the analytical method into a set of generic steps in order to identifythe possible sources of uncertainty:a. Samplingb. Sample preparationc. Use of certified reference materials to the measuring systemd. Calibration of instrumente. Analysis for data acquisitionf.Data processingg. Presentation of resultsh. Interpretation of results6.2Each of these steps can be further broken down by contributions to the uncertaintyfor each. The following list, though not exhaustive, demonstrates the various factorsthat need to be considered when determining the sources of measurementuncertainty.6.2.1Sampling- The physical state of the population (
measurement" means doubt about the validity of the result of a measurement. 2.2 Measurement uncertainty is defined as "parameter, associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand" [5]. The word "measurand" is further defined in
1.1 Measurement Uncertainty 2 1.2 Test Uncertainty Ratio (TUR) 3 1.3 Test Uncertainty 4 1.4 Objective of this research 5 CHAPTER 2: MEASUREMENT UNCERTAINTY 7 2.1 Uncertainty Contributors 9 2.2 Definitions 13 2.3 Task Specific Uncertainty 19 CHAPTER 3: TERMS AND DEFINITIONS 21 3.1 Definition of terms 22 CHAPTER 4: CURRENT US AND ISO STANDARDS 33
73.2 cm if you are using a ruler that measures mm? 0.00007 Step 1 : Find Absolute Uncertainty ½ * 1mm 0.5 mm absolute uncertainty Step 2 convert uncertainty to same units as measurement (cm): x 0.05 cm Step 3: Calculate Relative Uncertainty Absolute Uncertainty Measurement Relative Uncertainty 1
fractional uncertainty or, when appropriate, the percent uncertainty. Example 2. In the example above the fractional uncertainty is 12 0.036 3.6% 330 Vml Vml (0.13) Reducing random uncertainty by repeated observation By taking a large number of individual measurements, we can use statistics to reduce the random uncertainty of a quantity.
Gauge R&R vs. Measurement Uncertainty to Assess Measurement Uncertainty Ways . CMM Measurement Uncertainty Specific to a particular measurand. Specific to a particular level of confidence. Sample Statement: “The uncertainty of the diameter of this nominal 10-mm . Size, Location & Orientation Controlled by Profile. Arc .
Measurement Uncertainty Approach 10 ISOGUM -ISO Guide to the Expression of Uncertainty Determine the uncertainty components based on the model: Isolate each component in the model that is anticipated to cause variation in the measured results. Calculate the sensitivity coefficients: Sensitivity coefficients are multipliers that are used to convert uncertainty
measurements 2. SI – the international system of units 2.1 System of units: from trade to science 2.2 Base and derived units 2.3 Measurement standards and traceability 3. Measurement uncertainty – part 1: Introduction 3.1 Terminology 3.2 Importance of the measurement uncertainty 4. Measurement uncertainty – part 2: Methods
Uncertainty in volume: DVm 001. 3 or 001 668 100 0 1497006 0 1 3 3. %. % .% m m ª Uncertainty in density is the sum of the uncertainty percentage of mass and volume, but the volume is one-tenth that of the mass, so we just keep the resultant uncertainty at 1%. r 186 1.%kgm-3 (for a percentage of uncertainty) Where 1% of the density is .
3. ISO 19036 - Components ISO 19036 (2019) general approach Combination between a global and a major component approach 4. ISO 19036 - Concepts not included in Measurement Uncertainty calculation 5. ISO 19036 - Practical approaches to estimate Measurement Uncertainty 6. ISO 19036 - Combined and Expanded Standard Uncertainty 7.
