1、BRITISH STANDARD BS ISO 11095:1996 Implementation of ISO 11095:1996 Linear calibration using reference materials ICS 03.120.30; 17.020BS ISO 11095:1996 This British Standard, having been prepared under the direction of the Management Systems Sector Board, was published under the authority of the Sta
2、ndards Board and comes into effect on 15 December 1996 BSI 10-1998 The following BSI references relate to the work on this standard: Committee reference SS/6 Draft for comment 93/408389 DC ISBN 0 580 27015 7 Committees responsible for this British Standard The preparation of this British Standard wa
3、s entrusted to Technical Committee SS/6, Precision of test methods, upon which the following bodies were represented: British Gas plc Chemical Industries Association Consumers Association GAMBICA (BEAMA Ltd.) Institute of Quality Assurance Laboratory of the Government Chemist Ministry of Agriculture
4、, Fisheries and Food Ministry of Defence National Physical Laboratory Royal Society of Chemistry University of London Amendments issued since publication Amd. No. Date CommentsBS ISO 11095:1996 BSI 10-1998 i Contents Page Committees responsible Inside front cover National foreword ii Foreword iii Te
5、xt of ISO 11095:1996 1 List of references Inside back coverBS ISO 11095:1996 ii BSI 10-1998 National foreword This British Standard reproduces verbatim ISO 11095:1996 and implements it as the UK national standard. This British Standard is published under the direction of the Management Systems Secto
6、r Board whose Technical Committee SS/6 has the the responsibility to: aid enquirers to understand the text; present to the responsible international committee any enquiries on interpretation, or proposals for change, and keep UK interests informed; monitor related international and European developm
7、ents and promulgate them in the UK. NOTEInternational and European Standards, as well as overseas standards, are available from Customer Services, BSI, 389 Chiswick High Road, London W4 4AL. A British Standard does not purport to include all the necessary provisions of a contract. Users of British S
8、tandards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Cross references Publication referred to Corresponding British Standard ISO 3534-1:1993 BS ISO 3534 Statistics. Vocabulary and symbols Part 1:1993 Pro
9、bability and general statistical terms ISO 3534-2:1993 Part 2:1993 Statistical quality control Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, theISO title page, pages ii to iv, pages 1 to 26, an inside back cover and a back cover. This standard has bee
10、n updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on theinside front cover.BS ISO 11095:1996 ii BSI 10-1998 Contents Page Introduction 1 1 Scope 1 2 Normative references 1 3 Definitions 1 4 General principles 1 5 Basic method 2 6 T
11、he steps of the basic method 3 7 Control method 10 8 Two alternatives to the basic method 13 9 Example 16 Annex A (normative) List of symbols and abbreviations 24 Annex B (normative) Basic method when the number of replicates is not constant 25 Annex C (informative) Bibliography 26 Figure 1 Schemati
12、c diagram of data collected during the calibration experiment 4 Figure 2 Schematic diagram of a calibration curve 6 Figure 3 Schematic diagram of a plot of residuals versus fitted values 6 Figure 4 Schematic diagram of a control chart to validate the calibration curve under the assumption of constan
13、t residual standard deviation 12 Figure 5 Schematic diagram of the data in a one-point calibration experiment 14 Figure 6 Data collected during the calibration experiment for line-spacing 17 Figure 7 The calibration curve for line-spacing under the assumption of constant residual standard deviation
14、18 Figure 8 Residuals versus fitted values for line-spacing under the assumption of constant residual standard deviation 19 Figure 9 Standard deviations of replicated measurements for line-spacing versus NIST values 19 Figure 10 Calibration curve for line-spacing under the assumption of proportional
15、 residual standard deviation 20 Figure 11 Weighted residuals versus weighted fitted values for line-spacing under the assumption of proportional residual standard deviation 21 Figure 12 Control chart to validate the calibration curve for line-spacings underthe assumption of proportional residual sta
16、ndard deviation 23 Table 1 ANOVA table to compare lack of fit and pure error under the assumption of constant residual standard deviation 9 Table 2 ANOVA table to compare lack of fit and pure error under the assumption of proportional residual standard deviation 10 Table 3 Calibration experiment for
17、 line-spacing 16 Table 4 Values of y i 17 Table 5 Linear calibration under the assumption of constant residual standard deviation 17 Table 6 Values of z i 19 Table 7 Linear calibration under the assumption of proportional residual standard deviation 20 Table 8 ANOVA table to compare lack of fit and
18、pure error for line-spacing under the assumption of proportional residual standard deviation 21 Table 9 Data collected for the control method 22BS ISO 11095:1996 BSI 10-1998 iii Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (
19、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 the right to be represented on that committee. International organizations, go
20、vernmental 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. Draft International Standards adopted by the technical committees are circulated to
21、the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. International Standard ISO 11095 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee SC 6, Measurement methods a
22、nd results. Annexes A and B form an integral part of this International Standard. Annex C is for information only.iv blankBS ISO 11095:1996 BSI 10-1998 1 Introduction Calibration is an essential part of most measurement procedures. It is a set of operations which establish, under specified condition
23、s, the relationship between values indicated by a measurement system and the corresponding accepted values of some “standards”. In this International Standard, the standards are reference materials. A reference material (RM) is a substance or an artifact for which one or more properties are establis
24、hed sufficiently well to validate a measurement system. There exist several kinds of RMs: a) an internal reference material is an RM developed by a user for his/her own internal use; b) an external reference material is an RM provided by someone other than the user; c) a certified reference material
25、 is an RM issued and certified by an organization recognized as competent to do so. 1 Scope This International Standard: a) outlines the general principles needed to calibrate a measurement system and to maintain that “calibrated” measurement system in a state of statistical control; b) provides a b
26、asic method for estimating a linear calibration function under either one of two assumptions relating to the variability of the measurements, for checking the assumption of linearity of the calibration function and the assumptions on the variability of the measurements, and for estimating the value
27、of a new unknown quantity by transforming the measured values obtained on that quantity with the calibration function; c) provides a control method for extended use of a calibration function for detecting when the calibration function needs to be updated, and for estimating the uncertainty of the me
28、asured values after transformation with the calibration function; d) provides two alternatives to the basic method under special conditions; e) illustrates the basic method and the control method with an example. This International Standard is applicable to measurement systems for which reference ma
29、terials are available. It is applicable to measurement systems with an assumed linear calibration function. It offers a method for examining the assumption of linearity. If it is known that the calibration function is nonlinear, then this International Standard is not applicable unless one uses the
30、“bracketing technique” described in 8.3. This International Standard does not make a distinction among the various types of RMs and considers that the accepted values of the RMs selected to calibrate the measurement system are without error. 2 Normative references The following standards contain pro
31、visions which, through reference in this text, constitute provisions of this International Standard. At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this International Standard are encouraged to investigate the
32、possibility of applying the most recent editions of the standards indicated below. Members of IEC and ISO maintain registers of currently valid International Standards. ISO 3534-1:1993, Statistics Vocabulary and symbols Part 1: Probability and general statistical terms. ISO 3534-2:1993, Statistics V
33、ocabulary and symbols Part 2: Statistical quality control. ISO Guide 30:1992, Terms and definitions used in connection with reference materials. 3 Definitions For the purposes of this International Standard, the definitions given in ISO 3534-1 and ISO 3534-2 and the following definition apply. 3.1 r
34、eference material a substance or an artifact for which one or more properties are established sufficiently well to be used to validate a measurement system 4 General principles Calibration is a procedure that determines the systematic difference that may exist between a measurement system and a “ref
35、erence” system represented by the reference materials and their accepted values. In this International Standard, the term system (measurement system or reference system) is used to represent not only a measuring instrument but also the set of procedures, operators and environment conditions associat
36、ed with that instrument.BS ISO 11095:1996 2 BSI 10-1998 The output of a calibration procedure is a calibration function that is used to make transformations of future measurement results. In this International Standard, the term “transformation” refers to either a correction of the future measuremen
37、ts if both the accepted values of the reference materials (RMs) and the observed values have the same units, or a translation from the units of the observed measurements to the units of the RMs. The validity of the calibration function depends on two conditions: a) that the measurements from which t
38、he calibration function was calculated are representative of the normal conditions under which the measurement system operates; and b) that the measurement system is in a state of control. The calibration experiment must be designed to ensure that point a) is met. The control method determines, as s
39、oon as possible, when the system has to be considered out of control. The procedure in this International Standard is only applicable to measurement systems which are linearly related to their reference systems. To check whether the assumption of linearity is valid, more than two RMs must be used du
40、ring the calibration experiment. This is illustrated in the basic method. Using several RMs, the basic method provides a strategy and techniques to analyse the data collected during the calibration experiment. If linearity is not in question, then an alternative method, simpler than the basic method
41、, can be used to estimate a linear calibration function based on one point. This “one-point calibration” method (following a zero-level transformation) does not allow for any test of assumptions, but it is a quick and easy method to “recalibrate” a system that has been studied more thoroughly during
42、 previous experiments. If linearity is in question, then a second alternative can be used, called “bracketing”. The basic method and the one-point method are based on the assumption that the effort invested in calibration will be valid over a period of stability of the process. To study the period o
43、ver which the calibration is valid, a control method has to be in place. The control method is designed to detect whether changes have taken place in the system that justify an investigation and/or a recalibration. The control method also provides a simple way to determine the precision of the value
44、s that have been transformed with a given calibration function. The bracketing method is labour intensive but may provide greater accuracy in the determination of the values of unknown quantities. This method consists of surrounding as tightly as possible (bracketing) each unknown quantity by two RM
45、s and extracting a transformed value for the unknown quantity from measurements of both the unknown quantity and the values of the two RMs. Only short-term stability of the measurement process is assumed (stability during the measurement of the unknown quantity and of the two RMs). Linearity is assu
46、med solely in the interval between the values of the two RMs. 5 Basic method 5.1 General This clause describes how to estimate and use a linear calibration function when several (more than two) RMs are available. The availability of several RMs allows the linearity of the calibration function to be
47、verified. 5.2 Assumptions 5.2.1 It is assumed that there is no error in the accepted values of the RMs (this assumption will not be checked in this International Standard). In practice, accepted values of RMs are quoted with their uncertainties. The assumption of no error in the accepted values of t
48、he RMs can be considered valid if the uncertainties are small compared to the magnitude of the errors in the measured values of these RMs (see ref. 1). NOTE 1In situations where the RMs have been treated chemically or, in some instances physically, before instrument readings are taken, this Internat
49、ional Standard may underestimate the uncertainty associated with the transformation of a new measurement result. 5.2.2 The calibration function is assumed to be linear (this assumption will be examined). 5.2.3 Repeated measurements of a given RM are assumed to be independent and normally distributed, with variance referred to as “residual variance” (the independence and normality assumptions will not be checked in this International Standard). The square root of the residual variance is referred to as the re
