# ISO 11095-1996

TERNATIONAL STANDARD ISO 11095 First edition 1996-02-0’1 Linear calibration using reference materials Etalonnage /inkaire utilisant des matbriaux de rbfbence ISO 11095:1996(E) Contents Page 1 Scope . . . . . . . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . . *. 1 2 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s. 1 4 General principles . . 2 5 Basic method . . 2 6 The Steps of the basic method . 4 7 Control method . 10 8 Two alternatives to the basic method 13 9 Example . 16 Annexes A List of Symbols and abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 B Basic method when the number of replicates is not constant 27 C Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 o ISO 1996 All nghts r-eserved. Uniess otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronie or mechanicac, including photocopying and mtcrofilm, without Permission in writing from the publisher. International Organization for Standardization Case Postale 56 l CH-l 211 Geneve 20 l Switzerland Printed in SwitzerIand ii 0 ISO ISO 11095:1996(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national Standards bodies (ISO member bedies). The work of preparing International Standards is normally carried out through ISO technical committees. Esch 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 Ciaison 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 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 sfafistical methods, Subcommittee SC 6, Measurement methods and results. Annexes A and B form an integral part of this International Standard. An- nex C is for information only. ISO 11095:1996(E) @Zl ISO Introduction Calibration is an essential part of most measurement procedures. lt is a set of operations which establish, under specified conditions, the re- lationship 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 established sufficiently well to validate a measure- ment 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) d an external ref tha n the User; erence material is an RM provided by someone other a certif ied reference material is an RM issued and certified by an or- ganization recognized as competent to do so. INTERNATIONAL STANDARD 0 ISO ISO 11095:1996(E) Linear calibration using reference materials 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 basic method - for estimating a linear calibration function un- der 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 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 measured 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 measure- ment Systems for which reference materials are available. lt is applicable to measurement Systems with an as- sumed linear calibration function. lt offers a method for examining the assumption of Iinearity. If it is known that the calibration function is nonlinear, then this International Standard is not applicable unless one uses the “bracketing technique” described in 8.3. This International Standard does not make a dis- tinction among the various types of RMs and consid- ers that the accepted values of the RMs selected to calibrate the measurement System are without error. 2 Normative references The following Standards contain provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publica- tion, 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 possibility of applying the most re- cent editions of the Standards indicated below. Members of IEC and ISO maintain registers of cur- rently valid International Standards. ISO 3534-1 :1993, Statistics - Vocabulary and sym- bols - Part 7: Probability and general statistical terms. ISO 3534-2:1993, Statistics - Vocabulary and sym- bols - Part 2: Statistical quality control. ISO Guide 30:1992, Terms and definitions used in connection with reference ma terials. 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 reference material: A substance or an artifact for which one or more properties are established suf- 1 ISO 11095:1996(E) a 1FJ-J ficiently weil to be used to validate a measurement System. 4 General principles Calibration is a procedure that determines the sys- tematic differente that may exist between a measurement System and a “reference” System rep- resented by the reference materials and their ac- cepted 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 en- vironment conditions associated with that instrument. The output of a calibration procedure is a calibration function that is used to make transformations of fu- ture measurement results. In this International Stan- dard, the term “transformation” refers to - either a correction of the future measurements if both the accepted values of the reference ma- terials (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 the 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 en- Sure that Point a) is met. The control method deter- mines, as soon 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 during the calibration experiment. This is illustrated in the basic method. Using several RMs, the basic method provides a strategy and tech- niques to analyse the data collected during the cali- bration experiment. lf linearity is not in question, then an alternative method, simpler than the basic method, tan 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 previous exper- iments. If linearity is in question, then a second alternative tan 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 over which the cali- bration 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 values 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 (bracketingj each unknown quantity by two RMs 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 assumed 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 lin- ear calibration function when several (more than two) RMs are available. The availability of several RMs al- lows the linearity of the calibration function to be verified. 5.2 Assumptions 5.2.1 lt is assumed that there is no error in the ac- cepted values of the RMs (this assumption will not be checked ,in this International Standard). In practice, accepted values of RMs are quoted with their uncer- tainties. The assumption of no error in the accepted values of the RMs tan be considered valid if the un- certainties are small compared to the magnitude of the errors in the measured values of these RMs (see ref. [IJ. NOTE 1 In situations where the RMs have been treated chemically or, in some instances physically, before Instru- ment readings are taken, this International Standard may underestimate the uncertainty associated with the trans- formation of a new measurement result. 2 0 ISO ISO 11095:1996(E) 5.2.2 The calibration function is assumed to be linear The number of replicates should be the same for all (this assumption will be examined). RMs. 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- sidual Standard deviation. The time and conditions at which the replicates are taken should cover as wide a range as is necessary to ensure that all operating conditions are rep- resented. 5.4 Strategy for analysing the data 5.4.1 Plot the data to check 5.2.4 The residual Standard deviation is assumed to be either constant or proportional to the accepted value of the RM (this assumption will be examined). a) the state of control of the measurement System during the calibration experiment, 5.3 Calibration experiment 5.3.1 Experimental conditions b) the assumption of linearity, and cj the variability of the measurements as a function of the accepted values of the RMs. . Experimental conditions should be the Same as the normal operating conditions of the measurement System; i.e. if, for example, more than one Operator uses the measuring equipment then there should be more than one Operator represented in the calibration experiment. 5.3.2 Choice of RMs The range of values spanned by the selected RMs should include (as far as is possible) the range of val- ues encountered during normal operating conditions of the measurement System. The composition of the selected RMs should be as close as possible to the composition of the targeted material to be*measured. 5.4.2 Estimate the linear calibration function under the assumption of constant residual Standard devi- ation. 5.4.3 Plot the calibration function and the residuals. The residuals plot is a strong indicator of departure from either the assumption of linearity or from the assumption of constant residual Standard deviation. If the assumption of constant residual Standard devi- ation does hold, skip step 5.4.4 and continue with step 5.4.5. Otherwise, execute step 5.4.4. 5.4.4 Estimate the linear calibration function under the assumption of proportional residual Standard de- viation and plot the calibration function and the re- siduals. The values of the RMs should be distributed approxi- mately equidistantly over the range of values en- countered during normal operating conditions of the measurement System. 5.3.3 Number of RMs, N The number of RMs used to assess the calibration 5.4.5 Evaluate the lack of fit of the calibration func- tion. If the variability due to lack of fit is large relative to the variability due to replication of measurements, investigate the procedures followed during the cali- bration experiment and re-examine the assumption of linearity of the calibration function. If the assump- tion of linearity does not hold, then an alternative is to use the bracketing technique described in 8.3. function should be at least 3. For an initial assessment of the calibration function, a number larger than 3 is recommended (at least 3 over any subinterval where there is a doubt about the lin- earity of the calibration function). 5.3.4 Number of replicates, K Esch RM should be measured at least twice (as many replicates as is possible in practice is recommended). NOTE 2 There exist other techniques, beyond the scope of this International Standard, that allow the fitting of a quadratic or polynomial curve to the data (see refs. [Z] and VI)* 5.4.6 Transform future measured values with the calibration function. The next clause describes the six Steps of this strat- egy. Clause 9 illustrates the basic method with an example. ISO 11095:1996(E) G ISO 6 The Steps of the basic method 6.1 Plot of the data collected during the calibration experiment Figure 1 Shows a plot of the measured values versus the corresponding accepted values of the R