Measuring - SFERA

Measuring SFERA school 2013 Emmanuel Guillot CNRS-­‐PROMES Odeillo, France

CNRS-PROMES E. Guillot — SFERA Summer School 2013 2

CNRS-PROMES E. Guillot — SFERA Summer School 2013 3Plan• Measuring?• Part I: Instrumentation• Part II: Uncertainties• [Part III: Quality]• Measurement techniques

CNRS-PROMES E. Guillot — SFERA Summer School 2013 4Special slideSome tools should be shortlydefined and usable here

CNRS-PROMES E. Guillot — SFERA Summer School 2013 5Introduction• What is measuring?– Determine a numeric value of a physicalparameter in a given set of conditions• => instrumentation– With an evaluated trust of the numeric value• => uncertainties– With an evaluated trust of the procedure• => quality

CNRS-PROMES E. Guillot — SFERA Summer School 2013 6It is a science!• Instrumentation + Uncertainties = MetrologyMetrology is defined by the International Bureau ofWeights and Measures (BIPM) as"the science of measurement,embracing both experimental and theoreticaldeterminationsat any level of uncertaintyin any field of science and technology.”

Part I InstrumentaCon Emmanuel Guillot CNRS-­‐PROMES Odeillo, France

CNRS-PROMES E. Guillot — SFERA Summer School 2013 8InstrumentationMEASURINGISCOMPARING

CNRS-PROMES E. Guillot — SFERA Summer School 2013 9Instrumentation• Measuring: determine a numericevaluation of a physical parameter of aprocess– Primary characteristics: time, length, mass…– Derived characteristics: speed, surface, massflow, viscosity, specific heat, hardness……

CNRS-PROMES E. Guillot — SFERA Summer School 2013 10Instrumentation• Measuring: determine a numeric evaluation of aphysical quantity of a process…• …With comparison to a reference quantity=> Number + UnitWhat is the length of the car? 4,3 mWhat is the temperature of the oil? 235 °CHow strong is the DNI of the sun? 954 W/m2

CNRS-PROMES E. Guillot — SFERA Summer School 2013 11InstrumentationMEASURINGISCOMPARING

CNRS-PROMES E. Guillot — SFERA Summer School 2013 12The SI system of units• 7 units to define it all:– Temperature => kelvin– Time => second– Length => meter– Mass => kilogram– Luminous intensity => candela– Quantity of matter => mole– Electric current => ampere

CNRS-PROMES E. Guillot — SFERA Summer School 2013 13The SI system of units

CNRS-PROMES E. Guillot — SFERA Summer School 2013 14The SI system of units• Definitions of the units? Universal!– It should be stable in time– With a repeatable procedure⇒ Second = number of pulsations of transition state of Cesium⇒ Meter = distance travelled by light in vacuum in 1 second⇒ Mole = as many as many atoms in 12 mg of Carbon 12⇒ …⇒ Kilogram = mass of the International Prototype Kilogram

CNRS-PROMES E. Guillot — SFERA Summer School 2013 15The SI system of units• SI = Système International d'unités• French Revolution: Universal for Mankind=> including the measurement system=> still many things in French by French organisations

CNRS-PROMES E. Guillot — SFERA Summer School 2013 16TraceabilityMEASURINGISCOMPARING

CNRS-PROMES E. Guillot — SFERA Summer School 2013 17TraceabilityInternational ReferencesNational ReferencesRegional / Private ReferencesUser Measurements

CNRS-PROMES E. Guillot — SFERA Summer School 2013 18Comparison:Process of MeasurementQuantityto be determinedXComparisonProcessReference[X]Measurement result{X}

CNRS-PROMES E. Guillot — SFERA Summer School 2013 19Process of measurementDirect quantityWidth of a rectanglewidth

CNRS-PROMES E. Guillot — SFERA Summer School 2013 20Process of measurementheightExample of indirect quantitySurface of a rectangleS = h x wwidth

CNRS-PROMES E. Guillot — SFERA Summer School 2013 21Process of measurementWidth WComparisonProcessReference[meter]Measurement result{W}Formulaf(W,H) = W x HHeight HComparisonProcessReference[meter]Measurement result{H}

CNRS-PROMES E. Guillot — SFERA Summer School 2013 22One observation of a measurement• At the end, a numeric evaluation with a unitThe width of the rectangle is13,45 cmThe surface of the rectangle is127 cm 2

Part II UncertainCes Emmanuel Guillot CNRS-­‐PROMES Odeillo, France

CNRS-PROMES E. Guillot — SFERA Summer School 2013 24ReferenceCopyrightsUncertainty inMeasurementEven if the electronic version of this document isavailable free of charge on the BIPM’s website(www.bipm.org), copyright of this document isDroits d’auteurshared jointly by the JCGM member organizations,and all respective logos and emblems are vested inthem and are internationally protected. Third partiescannot rewrite or re-brand this document, issue orsell copies to the public, broadcast or use it on-line.For all commercial use, reproduction or translation ofthis document and/or of the logos, emblems,publications or other creations contained therein, theGuide to the expressionprior written permission of the Director of the BIPMofmust be obtained.Même si une version électronique de cepeut être téléchargée gratuitement sur le sdu BIPM (www.bipm.org), les droits d’auà ce document sont la propriété conorganisations membres du JCGM et l’enleurs logos et emblèmes respectifs leurnent et font l’objet d’une protection inteLes tiers ne peuvent le réécrire ou le mdistribuer ou vendre des copies au publicou le mettre en ligne. Tout usage creproduction ou traduction de ce documenlogos, emblèmes et/ou publications qu’ildoit recevoir l’autorisation écrite prédirecteur du BIPM.© JCGM 2009 – All righ

CNRS-PROMES E. Guillot — SFERA Summer School 2013 25MEASURINGISCOMPARINGBut how good is thecomparison?How trustworthy is it?

CNRS-PROMES E. Guillot — SFERA Summer School 2013 26Process of measurementParasite influencesParasite influencesCharacteristicto be determinedXComparisonProcessReference[X]Parasite influencesMeasurement result{X}Parasite influences

CNRS-PROMES E. Guillot — SFERA Summer School 2013 27UncertaintiesProvide a reasonable evaluationof how much doubt we haveabout the numeric evaluation of themeasurementThe Truth Is Out There

CNRS-PROMES E. Guillot — SFERA Summer School 2013 28UncertaintyMeasurement = number + unit + uncertaintythe length of the truck is12,5 m ± 0,1 m with 95 % confidence

CNRS-PROMES E. Guillot — SFERA Summer School 2013 29Significance of differencesSignificance of DifferencesSignificantX aX bU 95Not SignificantX aX bFrom WMO — Instruments And Observing Methods Report No. 86

CNRS-PROMES E. Guillot — SFERA Summer School 2013 30Conformity tests

CNRS-PROMES E. Guillot — SFERA Summer School 2013 31Modelisation of a measurement{One observed value}=(True value)+(systematic error)+(random error)

CNRS-PROMES E. Guillot — SFERA Summer School 2013 32Modelisation of a measurementSystematic errorRandom errorMean ofan infinite set ofMeasurementsTrueValueResults of theMeasurement

CNRS-PROMES E. Guillot — SFERA Summer School 2013 33Systematic errorIf a systematic error arises from a recognizedeffect of an influence quantity on a measurementresult,the effect can be quantified and, if it is significant insize relative to the required accuracy of themeasurement,a correction or a correction factor can be appliedto compensate for the effect.It is assumed that, after correction, the expectationor expected value of the error arising from asystematic effect is zero.

CNRS-PROMES E. Guillot — SFERA Summer School 2013 34Systematic error• Examples:– While measuring a resistance, the connectionwires => R observerd = R unknown + R wires– The thermal expansion of a ruler=> L = L 0 + α • ∆T– A systematic bias observed during calibrationof the sensor

CNRS-PROMES E. Guillot — SFERA Summer School 2013 35Random errorRandom error presumably arises from unpredictableor stochastic temporal and spatial variations ofinfluence quantities.The effects of such variations give rise to variations inrepeated observations of the measurand.Although it is not possible to compensate for therandom error of a measurement result, it can usuallybe reduced by increasing the number ofobservations; its expectation or expected value is zero.

CNRS-PROMES E. Guillot — SFERA Summer School 2013 36Uncertainty evaluation• Systematic errors can be reduced with acorrection=> but we only have an estimate of thecorrection• Random error can be reduced with a largenumber of observations=> effect of the size of the set on theestimate knowledge??

CNRS-PROMES E. Guillot — SFERA Summer School 2013 37Uncertainty evaluation• Method:1. Describe the measurement: list all theinfluence quantities2. Determine each quantity3. Determine the uncertainty for each quantity4. Calculate the combined uncertainty5. Calculate the expanded uncertainty

Annex F.CNRS-PROMES E. Guillot — SFERA Summer School 2013 38Uncertainty evaluation4.1 Modelling the measurement1. Describe4.1.1 Inthemostmeasurementcases, a measurand Y iY X 1is , determined X 2 , ..., X N through from N quantities a functional Xi relation( )Y = f X1, X2,..., XNComparisonReferenceWidth WProcess[meter]NOTE 1 For economy of notation, in this Gfor the random variable (see 4.2.1) that repreMeasurement result{W}FormulaF(W,H) = W x Hstated that XComparisonReferenceHeight Hi has a particular probability distribProcess[meter]quantity itself can be characterized by an esseMeasurement result{H}

CNRS-PROMES E. Guillot — SFERA Summer School 2013 395Ms — Ishikawa — FishboneManMachineUncertainty of theMeasurementProcess Environment Material

CNRS-PROMES E. Guillot — SFERA Summer School 2013 405M — Ishikawa — Fishbone

CNRS-PROMES E. Guillot — SFERA Summer School 2013 41Uncertainty evaluation• Method:1. Describe the measurement: list all theinfluence quantities2. Determine each quantity3. Determine the uncertainty for each quantity4. Calculate the combined uncertainty5. Calculate the expanded uncertainty

CNRS-PROMES E. Guillot — SFERA Summer School 2013 42Uncertainty evaluation3. Determine the uncertainty for each quantity=> 2 cases:- Repeated observations => TYPE A- Other evaluation => TYPE B

uncertainty varies components randomly are [a founded random on variabl frequenpriori distributions. obtained under It must the be same recognized conditions that inrepresent (C.2.19) the state of of the our n knowledge. observations:CNRS-PROMES E. Guillot — SFERA Summer School 2013 43Uncertainty Type A1 n qknk = 14.2 Type A qevaluation = of standard uncer4.2.1 In most cases, the best available estimatvaries randomly [a random variable (C.2.2)],If we have n repeated observations:obtainedThus,underfortheansameinputconditionsquantity Xof i measureestimat(C.2.19) of X ithe obtained n observations: from Equation (3) is usedresult y; that is, xi= Xi. Those input eother methods, such as those indicate⇒ The best estimate of the quantity is the meand measurement under statistical control, a com1 n q = qkimental standard deviationnk = 1 s p ) that characterize4.2.2 The individual observations q kThus, for or an random input quantity effects X(see 3.2.2). The exσ 2 i estimated from n inX i obtained of from the Equation probability (3) distribution used as the of q, inpisresult y; that is, xi= Xi. Those input estimates nonother with methods, 2 such as those 1s ( q ) ( ) 2k = qj− qn −1indicated in the sec4.2.2 The individual observations j=1 q k differ in vaor random effects (see 3.2.2). The experimentalσ 2 of the This probability estimate distribution of variance of q, is and given its by pothe value of a measurand q is determined from⇒ The best estimate of the uncertainty ise arithmetic mean q of the observations is estimtainty is u = s n. (See also the Note to H.3.6.)pf an input quantity X i is obtained from a cu

CNRS-PROMES E. Guillot — SFERA Summer School 2013 44Uncertainty Type BIf the quantity is not determined from repeatedobservations, the uncertainty is evaluated byscientific judgement based on all of theavailable information on the possible variability.Examples: • manufacturer's specifications• data provided in calibration and other certificates• uncertainties assigned to reference data taken fromhandbooks

CNRS-PROMES E. Guillot — SFERA Summer School 2013 45Uncertainty Type B⇒ Use the existing knowledge⇒ Assume a distribution law of the variations⇒ Calculate the uncertainty

CNRS-PROMES E. Guillot — SFERA Summer School 2013 46Uncertainty Type B- For a numeric display ±a- For a hysteresis ±aate of t is its expectation µ t = (a + + a )/2 = 1this estimate is u( µ ) = a 3 ≈ 2,3° C, whictJCGM 100:2008ure 2 b), it is assumed that the available infory a symmetric, triangular a priori probability disound a + = 104 °C, and thus the same half-wid

CNRS-PROMES E. Guillot — SFERA Summer School 2013 47Uncertainty evaluation• Method:1. Describe the measurement: list all theinfluence quantities2. Determine each quantity3. Determine the uncertainty for each quantity4. Calculate the combined uncertainty5. Calculate the expanded uncertainty

CNRS-PROMES E. Guillot — SFERA Summer School 2013 484.4.5 For the case illustrated in Figure 2 a), it is assumed that little in5.1.2 The combined standard uncertainty uquantity t and that all one can c (y) is the positive square root of the combinedo is suppose that t is described by a symwhich is given byCombineddistribution of loweruncertaintybound a = 96 °C, upper bound a + = 104 °C, and(see 4.3.7). 24.1.1 The probability In most density cases, function a of t measurand is then Y isN2 ∂f 2uc( y) = uX ( xi4.2.4 ) For a well-characterized measurement under sxi=1∂ip1 , X 2 , ..., X() 2 N through a functional relationsht = 1variance( 2 a), s ap− (or ut ua apooled + experimental standard deviatiavailable. In such cases, when the value of a measuranwhere f is the function given() = 0,in YEquation = fthe experimentalotherwise. ((1). X Each u(x i ) is a standard uncertainty evaluated a(Type A evaluation) or as in 4.3 (Type B evaluation).1, Xvariance 2,..., XThe combined of Nthe )arithmetic standard mean uncertainty q of u cthstandard deviation and characterizes s 2 (q k )/n the and dispersion the standard of the uncertainty values that is could u = sreasonably p n. (SeebAs indicated in 4.3.7, the best estimate of t is its expectation µ t = (aNOTE 1 For economy of notation, in this Guid +C.3.1. The standard 4.2.5 Often uncertainty an estimate of this estimate x i of an is input u( µ t) quantity = a 3 ≈X i 2,Equation (10) and its counterpart for the experimental for random correlated data variable input by quantities, the (see method Equation 4.2.1) of least (13), that both squares. represe of whic• We have the law p t4.1 Modelling the measurement• We measurand have the Y (see 2.2.3). X i and their uncertaintiesEquation (7)].5.1.2first-order TaylorTheseriesstated combinedapproximationuncertainties thatofXY =of standardf (Xthe 1 , Xfitted 2 , ..., Xparameters N ), expressuncertaintywhatcharacterizingis termed inuthethipropagation of uncertainty (see E.3.1 and i has a particular probability distribuE.3.2).cquantity itself can be characterized by an essentiwhich is given by=> The combined uncertainty is (uncorrelated quantities)4.4.6 For the calculated case illustrated by well-known in Figure statistical 2 b), it is procedures assumed that (see the H.3 avaalimited and that t can be described by a symmetric, triangular a priori proNOTE When the nonlinearity of f is significant, higher-order terms in the Taylor series expansionthe expression for bound a = 964.2.6 °C, the The same degrees upper of bound freedom a + = (C.2.31) 104 °C, and v i of thus u(x i ) the (see sam Gin 4.4.5 u 2c ( y ),(see Equation 4.3.9). (10). and u( The When xi) = probability the distribution s( X )N2 idensity of each calculated function X i is normal, the most imphighest order to be added NOTE to the terms 2 of Equation In a (10) series are of observations, from of n t is independent then the kth oboof a given resistor, when the Type kth A evaluations observed of value uncertainty of the component resista2N N 2 ∂f(2)() 2u ( )c y = 2p t = ( t −31 f ∂ ∂f ∂ fa−) 2a , 2 a− ut u( a+ + a−) 2+u ( x )2 i u4.2.7 If the ( xrandom u)2 j∂x x1 1 i∂x j ∂x i= j=i ∂xi∂xjvariations i in the observations of a NOTE() the3mean ∂x2p t =i( a1t) ai, andTheexperimentalestimate ofstandardXdeviation of the me+ − ( a+ + a− ) 2ut u a i (strictly speaking,+2See H.1 for an example of a situation estimators where the (C.2.25) contribution of of the higher-order desired statistics terms to u c ( (C.2.23). y ) needs to Inbp()t = 0, statistical methods otherwise. specially designed to treat a series of5.1.3 The partial derivatives f/x i are equal to f/X i evaluated at X i = x i (see Notederivatives, often called sensitivity NOTE coefficients, Such specialized describe how methods the output are used estimate to treat y varies meas wwhere f is the function given in Equation (1). Eavalues of the input As indicated estimates that in x 1 4.3.9, , xas 2 , ..., one the x N . expectation goes In particular, from short-term of the t is change µ t = measurements (a +in + y aproduced )/2 = 100 to by long-te °C, a sm winput estimate x i is given by (∆y) assumption i = (f/xof i )(∆x uncorrelated i ). If this change random is variations generated may by the no standard longer b

CNRS-PROMES E. Guillot — SFERA Summer School 2013 49Combined uncertainties• Example:additive measurement of 2 quantities with equiprobabledistributionsJCGM 104:2009--Y = X 1 + X 2- @@Figure 3 — An additive measurement function with two input quantities X 1 and X 2 characterized byrectangular probability distributions4.11 Often an interval containing Y with a specified probability is required. Such an interval, a coverage

CNRS-PROMES E. Guillot — SFERA Summer School 2013 50Combined 5.1.2 The combined uncertainties standard uncertaintywhich is given byN22 ∂f 2c = ∂xi=1i ( ) ( )u y u xwhere f is the function given in Equation (1)(Type A evaluation) or as in 4.3 (Type B evSensitivity coefficientsstandard deviation and characterizes the dmeasurand Y (see 2.2.3).Equation (10) and its counterpart for correliAbsolute uncertaintyNOT relative values

CNRS-PROMES E. Guillot — SFERA Summer School 2013 51Uncertainty evaluation• Method:1. Describe the measurement: list all theinfluence quantities2. Determine each quantity3. Determine the uncertainty for each quantity4. Calculate the combined uncertainty5. Calculate the expanded uncertainty

of RecommendatCNRS-PROMES E. Guillot — SFERA Summer School 2013 52The result of a mExpanded uncertainty• u(Xi) describes the uncertainty• But we would like to say: the length is 12,5 m± 0,1 m with 95 % confidence6.2 Expanded6.2.1 The addiindicated in 6.1.obtained by multi=> Expanded uncertainty U=> Coverage factor kU = ku ( ) c y

of Recommendation INC-1 (1980). It iCNRS-PROMES E. Guillot — SFERA Summer School 2013 53Expanded uncertainty6.2 Expanded uncertainty• Assuming a few things (normal distributions…)6.2.1 The additional measure of un=> For 95% confidence k = 2indicated in 6.1.2 is termed expand=> For 99% confidence k = 3obtained by multiplying the combinedU = ku ( ) c yThe result of a measurement is then

CNRS-PROMES E. Guillot — SFERA Summer School 2013 54Assumptions• Normal distributions• Large number of observations• No correlations between quantities

Measurement techniques Emmanuel Guillot CNRS-­‐PROMES Odeillo, France

CNRS-PROMES E. Guillot — SFERA Summer School 2013 56Instrument properties• Measurement range• Linearity — accuracy of response within range• Stability — short and long term drift• Response time• Accuracy• Precision• Hysteresis• Quantization — signal and sampling rate• Cost — money, time, complexity• …

CNRS-PROMES E. Guillot — SFERA Summer School 2013 57Measurement range• How wide is the possible measurementrange?• Examples:– Size of a ruler– Starting and destruction speed of ananemometer– Freezing and boiling points of a thermometer

CNRS-PROMES E. Guillot — SFERA Summer School 2013 58Linearity• How many corrections to apply along themeasuring range?

CNRS-PROMES E. Guillot — SFERA Summer School 2013 59Stability• How much drift of the measurementevaluation:– short term– long term– Example for a temperature measurement bythermocouple:• Short term drift: thermal sensitivity of the ADC• Long term drift: chemical alteration of the TC

CNRS-PROMES E. Guillot — SFERA Summer School 2013 60Repeatibility and ReproducibilityRepeatabilityVariability on an occasionWith-in run precisionReproducibilityVariability on different occasionsBetween-run precision

CNRS-PROMES E. Guillot — SFERA Summer School 2013 61Response time• How fast the output signal changes?Thermocouples: Speed vs Diameter

CNRS-PROMES E. Guillot — SFERA Summer School 2013 62Accuracy and PrecisionAccuracy (Justesse)The closeness of the experimental mean valueto the true value.High accuracy = Small systematic error.Precision (Fidélité)The degree of scatter in the results.High precision = Small random error.

CNRS-PROMES E. Guillot — SFERA Summer School 2013 63On On admet queAccuracyque les les variations de de l’erreur systématiqueand autourPrecisionde de la la correction effectuée sont sont aléatoires,On ce ce On qui admet qui admet permet que que de les de supposer les variations que que de l’erreur de l’erreur systématique suit autour suit une une de loi de la loi la de de correction probabilité effectuée bien bien définie. sont sont aléatoires,ce ce qui qui permet de de supposer que que l’erreur systématique suit suit une une loi loi de de probabilité bien bien définie.On On peut peut illustrer ces ces notions d’erreurs systématique et et aléatoire par par le le tir tir dans dans une une cible cible : :On On peut peut illustrer ces ces notions d’erreurs systématique et et aléatoire par par le le tir tir dans dans une une cible cible : :• •• •• •• • • •• •• •• •• •• •• •juste, juste, mais mais pas pas fidèle(valeurs juste, centrées juste, ACCURATEmais mais pas mais pas dispersées) fidèlefidèle(valeurs erreurs centrées aléatoires mais mais dispersées)erreurs aléatoires• •• •• • • •• ••• •• • • •• • • •• •ni ni juste, whatever… juste, ni ni fidèle fidèleerreurs aléatoires ni ni juste, juste, ni et ni et fidèle systématiques fidèleerreurs aléatoires et et systématiques• ••• •••••• ••••fidèle, mais mais pas pas juste juste(valeurs fidèle, fidèle, décentrées mais PRECISE mais pas mais pas juste mais juste resserrées)(valeurs erreurs décentrées systématiquesmais mais resserrées)erreurs systématiques• ••• •••••••••••ACCURATE fidèle fidèle et and et juste juste PRECISEerreurs fidèle fidèle et faibles et justejusteerreurs faibles

CNRS-PROMES E. Guillot — SFERA Summer School 2013 64Hysteresis• Does the output depends on pastenvironment?Hysteresis & LinearityEx: Meniscus500400Linearity3002001000Hysteresis100 200 300 400 500

CNRS-PROMES E. Guillot — SFERA Summer School 2013 65Quantization• Quantity of steps between the analogsignal and the numeric value:– Signal output– Sampling rateEg: 16 bits = 65536 valuesfor the Full Scale of theconverterEg: 1 ksps = 1000 values per seconds

CNRS-PROMES E. Guillot — SFERA Summer School 2013 66Instrument properties• Measurementrange• Linearity• Hysteresis• Stability• Response time• Quantization• Accuracy• Precision• Repeatability• ReproductibilityOn admet que les variations de l’erreur systématique autour de la correction effectuée sce qui permet de supposer que l’erreur systématique suit une loi de probabilité bien d• Cost €€€-timeOn peut illustrer ces notions d’erreurs systématique et aléatoire par le tir dans une c••••• …••juste, mais pas fidèle(valeurs centrées mais dispersées)erreurs aléatoiresHysteresis & Linearity• • • •••fidèle, mais pas juste(valeurs décentrées mais resserrées)erreurs systématiques•500400• ••300200100•0•100 200 300 400 500ni juste, ni fidèleHysteresisLinearity•• •• ••fidèle et juste

CNRS-PROMES E. Guillot — SFERA Summer School 2013 67Choice of the instrumentwidthWidth of a rectangle

CNRS-PROMES E. Guillot — SFERA Summer School 2013 68Instrument propertiesThere are no perfect sensor which has the perfectproperties for all the measurements needs.⇒ Need to adapt the technology and setup of thesensor to the actual requirement of measurementperformance: “the size of the uncertainty”⇒ In order to save time and €€€⇒ In order to be realistic with the environment

CNRS-PROMES E. Guillot — SFERA Summer School 2013 69Instrument propertiesThere are no perfect sensor which has theperfect properties for all the measurementsneeds.⇒ A wished performance may beunreachable with the provided resourcesand the current state of the art of theMetrology⇒ Eg: measuring the irradiated surface temperature of a tower solarreceiver at ±1 K @ 95% uncertainty: next to impossible in realfield, at least for now… no ?

Summary Emmanuel Guillot CNRS-­‐PROMES Odeillo, France

CNRS-PROMES E. Guillot — SFERA Summer School 2013 71MeasuringisComparing

CNRS-PROMES E. Guillot — SFERA Summer School 2013 72The TruthisOut there

CNRS-PROMES E. Guillot — SFERA Summer School 2013 73Reference books aboutmeasurement techniques• Béla G. LiptakCRC Press4 th edition: 2005ISBN13: 978-084-931-0812• Georges AschÉditions DUNOD7 th edition: 2010ISBN13: 978-210-054-9955

CNRS-PROMES E. Guillot — SFERA Summer School 2013 74THE reference guide for uncertainties, termsBureau Internationaldes Poids et Mesureshttp://www.bipm.orgJCGM 104:2009Evaluation of measurementdata — An introduction to the“Guide to the expression ofuncertainty in measurement”and related documentsÉvaluation des données de mesure — Uneintroduction au “Guide pour l’expression del’incertitude de mesure” et aux documentsqui le concernenthttp://www.bipm.org/en/publications/guides/gum.htmlhttp://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdfFirst edition July 2009© http://www.bipm.org/utils/common/documents/jcgm/JCGM_104_2009_E.pdf