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ISO 28037

Determination and use of straight-line calibration functions

Edition date: 2025-10-02
In Force
Available languages: English
Summary:

ISO/TS 28037:2010 is concerned with linear, that is, straight-line, calibration functions that describe the relationship between two variables X and Y, namely, functions of the form Y = A + BX. 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.

Values of the parameters A and B are determined on the basis of measured data points (xi, yi), i = 1, ... , m. 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 yi are homoscedastic (having equal variance), and similarly for the xi when the errors are not negligible.

Estimates of the parameters A and B are determined using least squares methods. The emphasis is on choosing the least squares method most appropriate for the type of measurement data, in particular methods that reflect the associated uncertainties. The most general type of covariance matrix associated with the measurement data is treated, but important special cases that lead to simpler calculations are described in detail.

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.

ISO/TS 28037:2010 also describes the use of the calibration function parameter estimates and their associated uncertainties and covariance to predict a value of X and its associated standard uncertainty given a measured value of Y and its associated standard uncertainty.



L'ISO/TS 28037:2010 traite des fonctions d'étalonnage linéaire, c'est-à-dire une droite, qui décrivent la relation entre deux variables X et Y, notamment les fonctions de la forme Y = A + BX. Bien que de nombreux principes s'appliquent à des types de fonction d'étalonnage plus généraux, les approches décrites utilisent dans la mesure du possible cette forme simple de la fonction d'étalonnage linéaire.

Les valeurs des paramètres A et B sont déterminées sur la base de paires de données mesurées (xi,yi), i = 1,?, m. Selon la nature des incertitudes associées à ces données, différents cas sont considérés. Aucune hypothèse n'est faite sur les erreurs relatives à yi pour savoir si elles sont homoscédastiques (de variances égales), et de même pour xi lorsque les erreurs ne sont pas négligeables.

Les estimations des paramètres A et B sont déterminées par les méthodes des moindres carrés. La présente Spécification Technique met l'accent sur le choix de la méthode des moindres carrés la plus appropriée au type de données de mesure, notamment les méthodes qui reflètent les incertitudes associées. Le cas le plus général de matrice de covariances associée aux données de mesure est traité, mais des cas particuliers importants, donnant lieu à des calculs plus simples, sont décrits en détail.

Pour tous les cas considérés, les méthodes de validation du choix de fonctions d'étalonnage linéaire et d'évaluation des incertitudes et de la covariance associées aux estimations des paramètres sont données.

L'ISO/TS 28037:2010 décrit aussi l'utilisation des estimations des paramètres de fonction d'étalonnage et de leurs incertitudes et covariance associées dans la prédiction d'une valeur de X et son incertitude-type associée pour une valeur mesurée de Y donnée avec son incertitude-type associée.
ICS: 03.120.30-Application of statistical methods
CTN: ISO/TC 69/SC 6 - 49808

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