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# ISO TS 28037

## Determination and use of straight-line calibration functions

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 Organization: ISO Publication Date: 1 September 2010 Status: active Page Count: 72 ICS Code (Application of statistical methods): 03.120.30
##### scope:

This Technical Speci cation 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 of this Technical Speci cation is on choosing the least squares method most appropriate for the type of measurement data, in particular methods that reect 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.

The Technical Speci cation 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.

NOTE 1 The Technical Speci cation does not give a general treatment of outliers in measurement data, although the validation tests given can be used as a basis for identifying discrepant data.

NOTE 2 The Technical Speci cation describes a method to evaluate the uncertainties associated with the measurement data in the case that those uncertainties are known only up to a scale factor (Annex E).

### Document History

ISO TS 28037
September 1, 2010
Determination and use of straight-line calibration functions
This Technical Speci cation 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...

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