SANS 11843-5-2009 Capability of detection Part 5 Methodology in the linear and non-linear calibration cases《检测能力 第5部分：线性和非线性校准事例的方法学》.pdf

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1、 Collection of SANS standards in electronic format (PDF) 1. Copyright This standard is available to staff members of companies that have subscribed to the complete collection of SANS standards in accordance with a formal copyright agreement. This document may reside on a CENTRAL FILE SERVER or INTRA

2、NET SYSTEM only. Unless specific permission has been granted, this document MAY NOT be sent or given to staff members from other companies or organizations. Doing so would constitute a VIOLATION of SABS copyright rules. 2. Indemnity The South African Bureau of Standards accepts no liability for any

3、damage whatsoever than may result from the use of this material or the information contain therein, irrespective of the cause and quantum thereof. ISBN 978-0-626-23475-1 SANS 11843-5:2009Edition 1 ISO 11843-5:2008Edition 1 SOUTH AFRICAN NATIONAL STANDARD Capability of detection Part 5: Methodology i

4、n the linear and non-linear calibration cases This national standard is the identical implementation of ISO 11843-5:2008 and is adopted with the permission of the International Organization for Standardization. Published by SABS Standards Division 1 Dr Lategan Road Groenkloof Private Bag X191 Pretor

5、ia 0001Tel: +27 12 428 7911 Fax: +27 12 344 1568 www.sabs.co.za SABS SANS 11843-5:2009 Edition 1 ISO 11843-5:2008 Edition 1 Table of changes Change No. Date Scope National foreword This South African standard was approved by National Committee SABS TC 169, Applications of statistical methods, in acc

6、ordance with procedures of the SABS Standards Division, in compliance with annex 3 of the WTO/TBT agreement. This SANS document was published in September 2009. Reference numberISO 11843-5:2008(E)ISO 2008INTERNATIONAL STANDARD ISO11843-5First edition2008-06-01Capability of detection Part 5: Methodol

7、ogy in the linear and non-linear calibration cases Capacit de dtection Partie 5: Mthodologie des talonnages linaire et non linaire SANS 11843-5:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO 11843-5:2008(E) PDF disclaimer This PDF fi

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11、 2008 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member body in the

12、country of the requester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2008 All rights reservedSANS 11843-5:2009This s tandard may only be used and printed by approved subsc

13、ription and freemailing clients of the SABS .ISO 11843-5:2008(E) ISO 2008 All rights reserved iiiContents Page Foreword iv Introduction v 1 Scope . 1 2 Normative references . 2 3 Terms and definitions. 2 4 Precision profile of the net state variable 4 5 Critical value and minimum detectable value of

14、 the net state variable 5 5.1 General. 5 5.2 Calculation relating to probability . 6 5.3 Calculation relating to probability 6 5.4 Differential method . 6 6 Examples . 7 6.1 General. 7 6.2 Law of propagation of uncertainty 7 6.3 Model fitting. 10 6.4 Application to competitive ELISA . 11 Annex A (no

15、rmative) Symbols and abbreviations used in this part of ISO 11843 12 Annex B (informative) Derivation of Equation (9) . 13 Annex C (informative) Derivation of Equation (13) . 14 Bibliography . 15 SANS 11843-5:2009This s tandard may only be used and printed by approved subscription and freemailing cl

16、ients of the SABS .ISO 11843-5:2008(E) iv ISO 2008 All rights reservedForeword ISO (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 through ISO techni

17、cal 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 collaborates closely w

18、ith 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. Draft Int

19、ernational 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 document m

20、ay be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 11843-5 was prepared by Technical Committee ISO/TC 69, Application of statistical methods, Subcommittee SC 6, Measurement methods and results. ISO 11843 consists of the following

21、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 the minim

22、um detectable value with a given value Part 5: Methodology in the linear and non-linear calibration cases SANS 11843-5:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO 11843-5:2008(E) ISO 2008 All rights reserved vIntroduction Both lin

23、ear and non-linear calibration functions are encountered in practice. This part of ISO 11843 treats both cases equally in the context of the capability of detection, by paying attention to the probability distributions of the net state variable (measurand), rather than the calibration functions them

24、selves. The basic concepts of ISO 11843-2 including the probability requirements, and , and the linear calibration cases are retained by this part of ISO 11843. In the interval of values between the basic state and minimum detectable value, a linear calibration function may be applied. In this manne

25、r, compatibility with ISO 11843-2 is assured. In the case that an analytical method characterized with a linear calibration function is compared with a method with a non-linear calibration function, this part of ISO 11843 is recommended. In a linear calibration case, ISO 11843-2 and this part of ISO

26、 11843 are both available. ISO 11843-2 which uses the precision profile for the response variable alone will give the same result as this part of ISO 11843 which requires the precision profiles for both the response variable and net state variable, since the precision profile for the response variab

27、le is the same as that for the net state variable in the linear case. SANS 11843-5:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .SANS 11843-5:2009This s tandard may only be used and printed by approved subscription and freemailing clien

28、ts of the SABS .INTERNATIONAL STANDARD ISO 11843-5:2008(E) ISO 2008 All rights reserved 1Capability of detection Part 5: Methodology in the linear and non-linear calibration cases 1 Scope This part of ISO 11843 is concerned with calibration functions that are either linear or non-linear. It specifie

29、s basic methods to construct a precision profile for the response variable, namely a description of the standard deviation (SD) or coefficient of variation (CV) of the response variable as a function of the net state variable, transform this precision profile into a precision profile for the net sta

30、te variable in conjunction with the calibration function, and use the latter precision profile to estimate the critical value and minimum detectable value of the net state variable. The methods described in this part of ISO 11843 are useful for checking the detection of a certain substance by variou

31、s types of measurement equipment to which ISO 11843-2 cannot be applied. Included are assays of persistent organic pollutants (POPs) in the environment, such as dioxins, pesticides and hormone-like chemicals, by competitive ELISA (enzyme-linked immunosorbent assay), and tests of bacterial endotoxins

32、 that induce hyperthermia in humans. The definition and applicability of the critical value and minimum detectable value of the net state variable are described in ISO 11843-1 and ISO 11843-2. This part of ISO 11843 extends the concepts in ISO 11843-2 to the cases of non-linear calibration. The crit

33、ical value, xc, and minimum detectable value, xd, are both given in the units of the net state variable. If xcand xdare defined based on the distribution for the response variable, the definition should include the calibration function to transform the response variable to the net state variable. Th

34、is part of ISO 11843 defines xcand xdbased on the distribution for the net state variable independently of the form of the calibration function. Consequently, the definition is available irrespective of the form of this function, whether it is linear or non-linear. The calibration function should be

35、 continuous, differentiable, and monotonically increasing or decreasing. A further method is described for the cases where the SD or CV is known only in the neighbourhood of the minimum detectable value. Examples are provided. SANS 11843-5:2009This s tandard may only be used and printed by approved

36、subscription and freemailing clients of the SABS .ISO 11843-5:2008(E) 2 ISO 2008 All rights reserved2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the late

37、st edition of the referenced document (including any amendments) applies. ISO 3534-1, Statistics Vocabulary and symbols Part 1: General statistical terms and terms used in probability ISO 3534-2, Statistics Vocabulary and symbols Part 2: Applied statistics ISO 3534-3, Statistics Vocabulary and symbo

38、ls Part 3: Design of experiments ISO 5725-1, Accuracy (trueness and precision) of measurement methods and results Part 1: General principles and definitions ISO 11843-1:1997, Capability of detection Part 1: Terms and definitions ISO 11843-2:2000, Capability of detection Part 2: Methodology in the li

39、near calibration case 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 3534 (all parts), ISO 5725-1, ISO 11843-1, ISO 11843-2 and the following apply. 3.1 critical value of the net state variable xcvalue of the net state variable, X, the exceeding of

40、which leads, for a given error probability, , to the decision that the observed system is not in its basic state ISO 11843-1:1997, definition 10 See Figure 1. 3.2 minimum detectable value of the net state variable xdvalue of the net state variable in the actual state that will lead, with probability

41、 1 , to the conclusion that the system is not in the basic state NOTE Adapted from ISO 11843-1:1997, definition 11 and ISO 11843-1:1997/Cor.1:2003. See Figure 1. 3.3 precision detection capability standard deviation (SD) of the observed response variable or SD of the net state variable when estimate

42、d by the calibration function NOTE 1 Coefficient of variation (CV) may be used as precision instead of SD where appropriate. NOTE 2 In this part of ISO 11843, precision is defined under repeatability conditions (ISO 3534-2). NOTE 3 The terms, precision and precision profile, are used in this part of

43、 ISO 11843, rather than imprecision and imprecision profile, because of a tradition to use the former terms in a number of situations. SANS 11843-5:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO 11843-5:2008(E) ISO 2008 All rights re

44、served 3Key xccritical value of the net state variable xdminimum detectable value of the net state variable X net state variable probability of an error of the first kind at X = 0 probability of an error of the second kind at X = xdaProbability density. NOTE Figure 1 in ISO 11843-1:1997 illustrates

45、the distributions of response variables and the non-linear calibration line. Figure 1 of this part of ISO 11843 includes the distributions of net state variables which are transformed through the slope of the calibration line from the distributions of the response variable shown in ISO 11843-1. Figu

46、re 1 Distributions of the estimated net state variable in the basic state, X = 0, (left) and in the state of xd(right) 3.4 precision profile detection capability mathematical description of the standard deviation or coefficient of variation of the response variable or net state variable as a functio

47、n of the net state variable 3.5 response variable Y variable representing the outcome of an experiment ISO 3534-3:1999, definition 1.2 NOTE 1 For the purposes of ISO 11843, this general definition is understood in the following specialized form: directly observable surrogate for the state variable,

48、Z. NOTE 2 The response variable, Y, is a random variable in any stage of analysis and if transformed by the calibration function, its precision profile is expressed as the standard deviation and coefficient of variation, X(X) and X(X), respectively, of the net state variable. SANS 11843-5:2009This s

49、 tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO 11843-5:2008(E) 4 ISO 2008 All rights reserved3.6 precision profile of response variable continuous plot in this part of ISO 11843 on the basis of the uncertainty of the response variable which comes from the random properties of analytical steps such as pipetting and instrumental baseline noise, and not from the systematic error often known as the knowledge of instrumental im