BS ISO 11843-6-2013 Capability of detection Methodology for the determination of the critical value and the minimum detectable value in Poisson distributed measurements by normal a.pdf

1、BSI Standards PublicationBS ISO 11843-6:2013Capability of detectionPart 6: Methodology for the determinationof the critical value and the minimumdetectable value in Poisson distributedmeasurements by normal approximationsIncorporating corrigendum October 2015BS ISO 11843-6:2013 BRITISH STANDARDNatio

2、nal forewordThis British Standard is the UK implementation of ISO 11843-6:2013.The UK participation in its preparation was entrusted to TechnicalCommittee SS/6, Precision of test methods.A list of organizations represented on this committee can beobtained on request to its secretary.This publication

3、 does not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplication. The British Standards Institution 2015. Published by BSI StandardsLimited 2015ISBN 978 0 580 91712 7ICS 03.120.30; 17.020Compliance with a British Standard cannot confer immunity

4、 fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 March 2013.Amendments/corrigenda issued since publicationDate Text affected31 October 2015 Implementation of ISO corrected text 1 August2014: Figure 1 updated ISO 2013Ca

5、pability of detection Part 6: Methodology for the determination of the critical value and the minimum detectable value in Poisson distributed measurements by normal approximationsCapacit de dtection Partie 6: Mthodologie pour la dtermination de la valeur critique et de la valeur minimale dtectable p

6、our les mesures distribues selon la loi de Poisson approxime par la loi NormaleINTERNATIONAL STANDARDISO11843-6First edition2013-03-15Reference numberISO 11843-6:2013(E)Corrected version2014-08-01ISO 11843-6:2013(E)ii ISO 2013 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2013All rights reserv

7、ed. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO

8、at the address below or ISOs member body in the country of the requester.ISO copyright officeCase postale 56 CH-1211 Geneva 20Tel. + 41 22 749 01 11Fax + 41 22 749 09 47E-mail copyrightiso.orgWeb www.iso.orgPublished in SwitzerlandBS ISO 11843-6:2013ISO 11843-6:2013(E) ISO 2013 All rights reserved i

9、iiContents PageForeword ivIntroduction v1 Scope . 12 Normative references 13 Terms and definitions . 14 Measurement system and data handling 15 Computation by approximation 25.1 The critical value based on the normal distribution 25.2 Determination of the critical value of the response variable 45.3

10、 Sufficient capability of the detection criterion 45.4 Confirmation of the sufficient capability of detection criterion . 56 Reporting the results from an assessment of the capability of detection . 67 Reporting the results from an application of the method . 6Annex A (informative) Symbols used in I

11、SO 11843-6 . 7Annex B (informative) Estimating the mean value and variance when the Poisson distribution is approximated by the normal distribution . 9Annex C (informative) An accuracy of approximations .10Annex D (informative) Selecting the number of channels for the detector 14Annex E (informative

12、) Examples of calculations .15Bibliography .20BS ISO 11843-6:2013ISO 11843-6:2013(E)ForewordISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out throu

13、gh ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collabora

14、tes closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.The main task of technical committees is to prepare International Standards

15、. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.Attention is drawn to the possibility that some of the elements of this

16、document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights.ISO 11843-6 was prepared by Technical Committee ISO/TC 69, Application of statistical methods, Subcommittee SC 6, Measurement methods and results.ISO 11843 consists of the fo

17、llowing parts, under the general title Capability of detection: Part 1: Terms and definitions Part 2: Methodology in the linear calibration case Part 3: Methodology for determination of the critical value for the response variable when no calibration data are used Part 4: Methodology for comparing t

18、he minimum detectable value with a given value Part 5: Methodology in the linear and non-linear calibration cases Part 6: Methodology for the determination of the critical value and the minimum detectable value in Poisson distributed measurements by normal approximations Part 7: Methodology based on

19、 stochastic properties of instrumental noiseThis corrected version of ISO 11843-6:2013 incorporates the following correction: in the key of Figure 1, the meanings of X and Y have been transposed.iv ISO 2013 All rights reservedBS ISO 11843-6:2013ISO 11843-6:2013(E)IntroductionMany types of instrument

20、s use the pulse-counting method for detecting signals. X-ray, electron and ion-spectroscopy detectors, such as X-ray diffractometers (XRD), X-ray fluorescence spectrometers (XRF), X-ray photoelectron spectrometers (XPS), Auger electron spectrometers (AES), secondary ion mass spectrometers (SIMS) and

21、 gas chromatograph mass spectrometers (GCMS) are of this type. These signals consist of a series of pulses produced at random and irregular intervals. They can be understood statistically using a Poisson distribution and the methodology for determining the minimum detectable value can be deduced fro

22、m statistical principles.Determining the minimum detectable value of signals is sometimes important in practical work. The value provides a criterion for deciding when “the signal is certainly not detected”, or when “the signal is significantly different from the background noise level”1-8. For exam

23、ple, it is valuable when measuring the presence of hazardous substances or surface contamination of semi-conductor materials. RoHS (Restrictions on Hazardous Substances) sets limits on the use of six hazardous materials (hexavalent chromium, lead, mercury, cadmium and the flame retardant agents, per

24、bromobiphenyl, PBB, and perbromodiphenyl ether, PBDE) in the manufacturing of electronic components and related goods sold in the EU. For that application, XRF and GCMS are the testing instruments used. XRD is used to measure the level of hazardous asbestos and crystalline silica present in the envi

25、ronment or in building materials.The methods used to set the minimum detectable value have for some time been in widespread use in the field of chemical analysis, although not where pulse-counting measurements are concerned. The need to establish a methodology for determining the minimum detectable

26、value in that area is recognized.9In this part of ISO 11843 the Poisson distribution is approximated by the normal distribution, ensuring consistency with the IUPAC approach laid out in the ISO 11843 series. The conventional approximation is used to generate the variance, the critical value of the r

27、esponse variable, the capability of detection criteria and the minimum detectability level.10In this part of ISO 11843: is the probability of erroneously detecting that a system is not in the basic state, when really it is in that state; is the probability of erroneously not detecting that a system

28、is not in the basic state when the value of the state variable is equal to the minimum detectable value(xd).This part of ISO 11843 is fully compliant with ISO 11843-1, ISO 11843-3 and ISO 11843-4. ISO 2013 All rights reserved vBS ISO 11843-6:2013Capability of detection Part 6: Methodology for the de

29、termination of the critical value and the minimum detectable value in Poisson distributed measurements by normal approximations1 ScopeThis part of ISO 11843 presents methods for determining the critical value of the response variable and the minimum detectable value in Poisson distribution measureme

30、nts. It is applicable when variations in both the background noise and the signal are describable by the Poisson distribution. The conventional approximation is used to approximate the Poisson distribution by the normal distribution consistent with ISO 11843-3 and ISO 11843-4.The accuracy of the nor

31、mal approximation as compared to the exact Poisson distribution is discussed in Annex C.2 Normative referencesThe following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For

32、 undated references, the latest edition of the referenced document (including any amendments) applies.ISO Guide 30, Reference materials - Selected terms and definitionsISO 3534-1, Statistics Vocabulary and symbols Part 1: General statistical terms and terms used in probabilityISO 11843-1, Capability

33、 of detection Part 1: Terms and definitionsISO 11843-2, Capability of detection Part 2: Methodology in the linear calibration caseISO 11843-3, Capability of detection Part 3: Methodology for determination of the critical value for the response variable when no calibration data are usedISO 11843-4, C

34、apability of detection Part 4: Methodology for comparing the minimum detectable value with a given value3 Terms and definitionsFor the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 11843-1, ISO 11843-2, ISO 11843-3, ISO 11843-4, and ISO Guide 30 apply.4 Measurement sy

35、stem and data handlingThe conditions under which Poisson counts are made are usually specified by the experimental set-up. The number of pulses that are detected increases with both the time and with the width of the region over which the spectrum is observed. These two parameters should be noted an

36、d not changed during the course of the measurement.INTERNATIONAL STANDARD ISO 11843-6:2013(E) ISO 2013 All rights reserved 1BS ISO 11843-6:2013ISO 11843-6:2013(E)The following restrictions should be observed if the minimum detectable value is to be determined reliably:a) Both the signal and the back

37、ground noise should follow the Poisson distributions. The signal is the mean value of the gross count.b) The raw data should not receive any processing or treatment, such as smoothing.c) Time interval: Measurement over a long period of time is preferable to several shorter measurements. A single mea

38、surement taken for over one second is better than 10 measurements over 100 ms each. The approximation of the Poisson distribution by the normal distribution is more reliable with higher mean values.d) The number of measurements: Since only mean values are used in the approximations presented here, r

39、epeated measurements are needed to determine them. The power of test increases with the number of measurements.e) Number of channels used by the detector: There should be no overlap of neighbouring peaks. The number of channels that are used to measure the background noise and the sample spectra sho

40、uld be identical (Annex D, Figure D.1).f) Peak width: The full width at half maximum (FWHM) is the recommended coverage for monitoring a single peak. It is preferable to measurements based on the top and/or the bottom of a noisy peak. The appropriate FWHM should be assessed beforehand by measuring a

41、 standard sample. An identical value of the FWHM should be used for both the background noise and the sample measurements.Additional factors are: the instrument should work correctly; the detector should be operating within its linear counting range; both the ordinate and the abscissa axes should be

42、 calibrated; there should be no signal that cannot be clearly identified as not being noise; degradation of the specimen during measurement should be negligibly small; at least one signal or peak belonging to the element under consideration should be observable.5 Computation by approximation5.1 The

43、critical value based on the normal distributionThe decision on whether a measured signal is significant or not can be made by comparing the arithmetic mean ygof the actual measured values with a suitably chosen value yc. The value yc, which is referred to as the critical value, satisfies the require

44、mentPy yx()gc=0 (1)where the probability is computed under the condition that the system is in the basic state (x = 0) and is a pre-selected probability value.Formula (1) gives the probability that yygc under the condition that:yyzJKcb1b= +11(2)wherez1is the (1 )-quantile of the standard normal dist

45、ribution where 1 is the confidence level;bis the standard deviation under actual performance conditions for the response in the basic state;2 ISO 2013 All rights reservedBS ISO 11843-6:2013ISO 11843-6:2013(E)ybis the arithmetic mean of the actual measured response in the basic state;Jis the number o

46、f repeat measurements of the blank reference sample. This represents the value of the basic state variable;Kis the number of repeat measurements of the test sample. This gives the value of the actual state variable.The + sign is used in Formula (2) when the response variable increases as the state v

47、ariable increases. The sign is used when the opposite is true.The definition of the critical value follows ISO 11843-1 and ISO 11843-3. Its relationship to the measured values in the active and basic states is illustrated in Figure 1.0xcybycygxg, xXYKeyX state variableY response variable the probabi

48、lity that an error of the first kind has occurred the probability that an error of the second kind has occurredFigure 1 A conceptual diagram showing the relative position of the critical value and the measured values of the active and basic states ISO 2013 All rights reserved 3BS ISO 11843-6:2013ISO

49、 11843-6:2013(E)5.2 Determination of the critical value of the response variableIf the response variable follows a Poisson distribution with a sufficiently large mean value, the standard deviation of the repeated measurements of the response variable in the basic state is estimated as yb. This is an estimate of b. The standard deviation of the repeated measurements of the response variable in the actual state of the sample is yg, giving an estimate of g(see Annex B).The critical value, yc, of