<p><span lang="EN-GB">This document is concerned with linear, that is, straight-line, calibration functions that describe the relationship between two variables </span> <span lang="EN-GB"> and </span> <span lang="EN-GB">, namely, functions of the form </span> <span lang="EN-GB">. Although many of the principles apply to more general types of calibration function, the approaches described exploit the simple form of the straight-line calibration function wherever possible.</span></p>
<p><span lang="EN-GB">Values of the parameters </span> <span lang="EN-GB"> and </span> <span lang="EN-GB"> are estimated based on measured data points </span> <span lang="EN-GB">, </span> <span lang="EN-GB"> Various cases are considered relating to the nature of the uncertainties associated with these data. No assumption is made that the errors relating to the </span> <span lang="EN-GB"> are homoscedastic (having equal variance), and similarly for the </span> <span lang="EN-GB"> when the errors are not negligible.</span></p>
<p><span lang="EN-GB">Estimates of the parameters </span> <span lang="EN-GB"> and </span> <span lang="EN-GB"> are determined using least‑squares’ methods. The emphasis of this document is on using the method most appropriate for the type of measured data, that is, respecting the associated uncertainties. The most general type of covariance matrix associated with the measured data is treated, but important special cases that lead to simpler calculations are described in detail.</span></p>
<p><span lang="EN-GB">For all cases considered, methods for validating the use of the straight-line calibration functions and for evaluating the uncertainties and covariance associated with the parameter estimates are given.</span></p>
<p><span lang="EN-GB">The document also describes the use of the estimates of the calibration-function parameters and their associated uncertainties and covariance to predict a value of </span> <span lang="EN-GB"> and its associated standard uncertainty given a measured value of </span> <span lang="EN-GB"> and its associated standard uncertainty.</span></p>
<p><span lang="EN-GB">NOTE 1 The document does not give a general treatment of outliers in measured data, although the validation tests given can be used to indicate discrepant data. </span><span lang="EN-GB">ISO</span> <span lang="EN-GB">16269</span><span lang="EN-GB">-</span><span lang="EN-GB">4</span><span lang="EN-GB"> can be consulted for guidance.</span></p>
<p><span lang="EN-GB">NOTE 2 The document describes a method to evaluate the uncertainties associated with the measured data when those uncertainties are known only up to a scale factor (see </span><span lang="EN-GB">Annex D</span><span lang="EN-GB">).</span></p>
Registration number (WIID)
84405
Scope
<p><span lang="EN-GB">This document is concerned with linear, that is, straight-line, calibration functions that describe the relationship between two variables </span> <span lang="EN-GB"> and </span> <span lang="EN-GB">, namely, functions of the form </span> <span lang="EN-GB">. Although many of the principles apply to more general types of calibration function, the approaches described exploit the simple form of the straight-line calibration function wherever possible.</span></p>
<p><span lang="EN-GB">Values of the parameters </span> <span lang="EN-GB"> and </span> <span lang="EN-GB"> are estimated based on measured data points </span> <span lang="EN-GB">, </span> <span lang="EN-GB"> Various cases are considered relating to the nature of the uncertainties associated with these data. No assumption is made that the errors relating to the </span> <span lang="EN-GB"> are homoscedastic (having equal variance), and similarly for the </span> <span lang="EN-GB"> when the errors are not negligible.</span></p>
<p><span lang="EN-GB">Estimates of the parameters </span> <span lang="EN-GB"> and </span> <span lang="EN-GB"> are determined using least‑squares’ methods. The emphasis of this document is on using the method most appropriate for the type of measured data, that is, respecting the associated uncertainties. The most general type of covariance matrix associated with the measured data is treated, but important special cases that lead to simpler calculations are described in detail.</span></p>
<p><span lang="EN-GB">For all cases considered, methods for validating the use of the straight-line calibration functions and for evaluating the uncertainties and covariance associated with the parameter estimates are given.</span></p>
<p><span lang="EN-GB">The document also describes the use of the estimates of the calibration-function parameters and their associated uncertainties and covariance to predict a value of </span> <span lang="EN-GB"> and its associated standard uncertainty given a measured value of </span> <span lang="EN-GB"> and its associated standard uncertainty.</span></p>
<p><span lang="EN-GB">NOTE 1 The document does not give a general treatment of outliers in measured data, although the validation tests given can be used to indicate discrepant data. </span><span lang="EN-GB">ISO</span> <span lang="EN-GB">16269</span><span lang="EN-GB">-</span><span lang="EN-GB">4</span><span lang="EN-GB"> can be consulted for guidance.</span></p>
<p><span lang="EN-GB">NOTE 2 The document describes a method to evaluate the uncertainties associated with the measured data when those uncertainties are known only up to a scale factor (see </span><span lang="EN-GB">Annex D</span><span lang="EN-GB">).</span></p>
