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1、 Reference number ISO 11843-5:2008(E) ISO 2008 INTERNATIONAL STANDARD ISO 11843-5 First edition 2008-06-01 Capability of detection Part 5: Methodology in the linear and non-linear calibration cases Capacit de dtection Partie 5: Mthodologie des talonnages linaire et non linaire Copyright Internationa
2、l Organization for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 01:58:20 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO 11843-5:2008(E) PDF disclaimer This PDF file may contain embedded typefaces. In ac
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5、inting. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. COPYRIGHT PROTECTED DOCUMENT ISO 2008 All rights reserved. Unless otherw
6、ise 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 country of the requester. ISO copyright
7、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 reserved Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/59
8、10770001 Not for Resale, 07/25/2008 01:58:20 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO 11843-5:2008(E) ISO 2008 All rights reserved iii Contents Page Foreword iv Introduction v 1 Scope . 1 2 Normative references. 2 3 Terms and definitions. 2 4 Precision profile of
9、 the net state variable 4 5 Critical value and minimum detectable value of 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.
10、3 Model fitting. 10 6.4 Application to competitive ELISA. 11 Annex A (normative) 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 Copyright International Organizat
11、ion for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 01:58:20 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO 11843-5:2008(E) iv ISO 2008 All rights reserved Foreword ISO (the International Organization
12、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 technical committees. Each member body interested in a subject for which a technical committee has been established has t
13、he 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 with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. Interna
14、tional 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 International Standards adopted by the technical committees are circulated to the member bodies for voting. Publicatio
15、n 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 may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights
16、. 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 parts, under the general title Capability of detection: Part 1: Terms and definitions Part 2: Methodology in the li
17、near 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 minimum detectable value with a given value Part 5: Methodology in the linear and non-linear calibration cases Copyright
18、 International Organization for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 01:58:20 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO 11843-5:2008(E) ISO 2008 All rights reserved v Introduction Both line
19、ar 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 thems
20、elves. 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 manner
21、, 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
22、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 variabl
23、e is the same as that for the net state variable in the linear case. Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 01:58:20 MDTNo reproduction or networking permitted without license from IHS -
24、,-,- Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 01:58:20 MDTNo reproduction or networking permitted without license from IHS -,-,- INTERNATIONAL STANDARD ISO 11843-5:2008(E) ISO 2008 All rig
25、hts reserved 1 Capability 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 specifies basic methods to construct a precision profile for the response variable
26、, 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 state variable in conjunction with the calibration function, and use the latt
27、er 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 various types of measurement equipment to which ISO 11843-2 cannot be applied. I
28、ncluded 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 that induce hyperthermia in humans. The definition and applicability of t
29、he 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 critical value, xc, and minimum detectable value, xd, are both given in the un
30、its of the net state variable. If xc and xd are 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. This part of ISO 11843 defines xc and xd based on the distribution for the
31、 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 continuous, differentiable, and monotonically increasing or decreasin
32、g. 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. Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/5910770001 Not for Resale, 0
33、7/25/2008 01:58:20 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO 11843-5:2008(E) 2 ISO 2008 All rights reserved 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cit
34、ed applies. For undated references, the latest 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
35、 ISO 3534-3, Statistics Vocabulary and symbols 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, Capabilit
36、y of detection Part 2: Methodology in the linear 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 xc value of
37、 the net state variable, X, the exceeding of 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 xd value of the net state variable in the
38、 actual state that will lead, with probability 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
39、 or SD of the net state variable when estimated 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 a
40、nd precision profile, are used in this part of ISO 11843, rather than imprecision and imprecision profile, because of a tradition to use the former terms in a number of situations. Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/5910
41、770001 Not for Resale, 07/25/2008 01:58:20 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO 11843-5:2008(E) ISO 2008 All rights reserved 3 Key xc critical value of the net state variable xd minimum detectable value of the net state variable X net state variable probabili
42、ty of an error of the first kind at X = 0 probability of an error of the second kind at X = xd a Probability density. NOTE Figure 1 in ISO 11843-1:1997 illustrates the distributions of response variables and the non-linear calibration line. Figure 1 of this part of ISO 11843 includes the distributio
43、ns 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. Figure 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 pr
44、ofile detection capability mathematical description of the standard deviation or coefficient of variation of the response variable or net state variable as a function of the net state variable 3.5 response variable Y variable representing the outcome of an experiment ISO 3534-3:1999, definition 1.2
45、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, Z. NOTE 2 The response variable, Y, is a random variable in any stage of analysis and if transformed by the calibration function, its p
46、recision profile is expressed as the standard deviation and coefficient of variation, X(X) and X(X), respectively, of the net state variable. Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 01:58
47、:20 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO 11843-5:2008(E) 4 ISO 2008 All rights reserved 3.6 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 p
48、roperties of analytical steps such as pipetting and instrumental baseline noise, and not from the systematic error often known as the knowledge of instrumental imperfections 3.7 net state variable X difference between the state variable, Z, and its value in the basic state, z0 ISO 11843-1:1997, definition 4 NOTE The net state variable, X, is a deterministic variable in the s