Raad voor Accreditatie (Dutch Accreditation Council RvA) Explanation on ISO/IEC "Calibration Certificates"

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Geoffrey Mervin Wright
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1 Raad voor Accreditatie (Dutch Accreditation Council RvA) Explanation on ISO/IEC "Calibration Certificates" Document code:

2 A RvA-information document gives information about the policy and/or the procedures of the RvA concerning a specific field of accreditation. A current version of the information document is available through the website of the RvA. (

3 Contents 1 Introduction 2 2 Explanation on EA-4/ Decimal sign 4 4 Expressing (display)- readouts on certificates 5 5 Literature 5 6 Modification compared to previous revision 5 page 1 of 5

4 1 Introduction Previous issues of this document only considered the application of EA-4/02 on calibration certificates and the use of the decimal sign. For practical reasons it was decided to have this document encompass all aspects concerning describing measurement results on calibration-certificates and explicitly link these explanations to the clauses according to ISO/IEC paragraph Explanation on EA-4/ Introduction Document EA-4/02 (previously EAL-R2 and translated in Dutch in RvA-TK 2.8) sets out the criteria for the calculation of measurement uncertainty for calibrations and general rules for the statement of uncertainty on calibration certificates. I.e. implementation of clause of ISO/IEC Paragraph 6.1 and 6.2 expression regarding statement on measurement uncertainty Paragraphs 6.1 and 6.2 give two expressions concerning the expression of uncertainty on calibration certificates. The Dutch translation is: (see left column) 6.1: " The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k = 2, which for a normal distribution corresponds to a coverage probability of approximately 95%. The standard uncertainty of measurement has been determined in accordance with Publication EA-4/02." 6.2: " The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k = XX, which for a t-distribution with v eff = YY effective degrees of freedom corresponds to a coverage probability of approximately 95%. The standard uncertainty of measurement has been determined in accordance with Publication EA-4/02." According to EA-4/02 one of these statements shall be used on calibration certificates. After consulting EA committee 2 it has been decided to allow the following less complicated statement: "The reported uncertainty is based on a standard uncertainty multiplied by a coverage factor of k = 2, which provides a confidence level of approximately 95 %. The standard uncertainty has been determined in accordance with EA-4/02." page 2 of 5

5 2.3 Paragraph Rounding of figures Common rules for rounding of figures a) <5 : Rounded downwards b) >5 : Rounded upwards c) =5 : "In case the last figure 5 (or a 5 followed by exclusively zero's) to the next higher position has to be rounded, one should choose the closest figure with an even last figure" (NEN 1047 Page 2.1, 3.3b). d) =5 : Contrary to c), a 5 is generally rounded upwards. Most computer programs are in compliance with this rule. Although c) is preferred, d) is also accepted. Examples: a): 2, ! 2,845 b): 2, ! 2,846 c): 43,134500! 43,134 82,427500! 82,428 d): 43,134500! 43, Rounding of measurement values For rounding of measurement results, the commonly used rules are applied. Concerning the number of figures to be rounded to, EA-4/02 par. 6.3 sates: " The numerical value of the measurement result should in the final statement normally be rounded to the least significant figure in the value of the expanded uncertainty assigned to the measurement result." In other words: The numerical value of the measurement result should in the final statement be rounded to the figure equal to the decimal place of the last figure of the uncertainty. This is in line with GUM, Rounding of measurement uncertainty Regarding the number of figures that shall be rounded to, EA-4/02 states in 6.3: "The numerical value of the uncertainty of measurement should be given to at most two significant figures " Therefore the final result may be given in 1 or 2 significant figures. In "Expression of Uncertainty", the following is stated: page 3 of 5

6 "... In reporting final results, it may sometimes be appropriate to round uncertainties up rather than to the nearest digit. For example u c (y) = 10,47 mω might be rounded up to 11 mω. However common sense should prevail and u(x i ) = 28,05 khz should be rounded down to 28 khz...." Further discussion has led to additional statement in EA-4/02, 6.3: "The numerical value of the measurement result should in the final statement normally be rounded to the least significant figure in the value of the expanded uncertainty assigned to the measurement result. For the process of rounding, the usual rules for rounding of numbers have to be used (for further details on rounding see ISO 31-0:1992, Annex B). However, if the rounding brings the numerical value of the uncertainty of measurement down by more than 5%, the rounded up value should be used. Examples for rounding of measurement uncertainty: 0,2644! 0,26 0,2556! 0,26 0,2550! 0,26 0,2650! 0,26 10,47! 10 (0,47 < 5%) 9,48! 10 (0,48 > 5%) 1,051! 1 (0,051 < 5%) 1,053! 2 (0,053 > 5%) 20,1007! 21 (0,1007 > 5%) 41,2002! 41 (0,2002 < 5%) Finally it should be considered that the uncertainty of the determination of measurement intervals, usually does not exceed 20 to 30%. Therefore it is recommended to limit the measurement uncertainty to one significant figure when this figure is larger than 4. Examples: 0,1053! 0,11 of 0,2 (0,0053 > 5%) 0,3157! 0,32 of 0,3 (0,0157 < 5%) 0,421! 0,4 (0,021 < 5%) 0,422! 0,5 (0,022 > 5%) 3 Decimal sign RvA basically uses SI. Within ISO, SI has been described in ISO 31. ISO 31-0 (1992) states: "3.3.2 Decimal sign. The decimal sign is the comma on the line. If the magnitude of the number is less than unity, the decimal sign should be preceded by a zero. page 4 of 5

7 NOTE 17 - In documentation in the English language, a dot is often used instead of a comma. If a dot is used, it should be on the line. ISO Council decision, the decimal sign is a comma in ISO documents". This implies that the comma shall be applied in non-english documents, while in English document can be tolerated. 4 Expressing (display)- readouts on certificates Although paragraph claims that values given on certificates shall be rounded, an exception should be made for stating readouts: Under the condition that the stated value is taken directly (not a result of calculations) from the indicator, the total number of figures should be stated. 5 Literature EA-4/02 Expression of the Uncertainty of measurement in Calibrations EA/GA(99)21 "Implementation of EA-4/02 (previously EAL-R2), Expression of the Uncertainty of Measurement in Calibration, in Calibration laboratories."(1999) GUM Guide to the Expression of Uncertainty in Measurements; BIPM, IEC, IFCC, ISO, IUPAC, UPAP and OIML (1993) NEN 1047 Page 2.1, 3.3(b) ISO 31-0: 1992 General principles concerning quantities, units and symbols. 6 Modification compared to previous revision Compared to the previous revision of this document the following modifications are included: - New format; - NKO replaced by RvA. page 5 of 5

European cooperation for EAL-G23 THE EXPRESSION OF UNCERTAINTY IN QUANTITATIVE TESTING. The Expression of Uncertainty in Quantitative Testing

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