The classification and solution of regression problems for calibration

Abstract

Many experiments in metrology involve the use of instruments or measuring systems that measure values of a response variable corresponding to given values of a stimulus variable. The calibration of such instruments requires using a set of measurements of stimulus and response variables, along with their associated uncertainties, to determine estimates of the parameters that best describe the relationship between them, along with their associated uncertainty matrix. Algorithms for determining the calibration parameters for problems where measurements of the stimulus variable can be assumed to be accurate relative to those of the response variable are well known. However, there is much less awareness in the metrology community of solution algorithms for more generalised problems. Many standards that deal with calibration, while identifying the types of regression problems to be solved, offer only limited advice regarding the selection and use of solution algorithms. There is also a need for guidance regarding uncertainty evaluation. The aim of this report is to provide more assistance to the metrologist, allowing the calibration problem to be easily classified according to the uncertainty structure associated with the measurement data, providing solution algorithms for the main types of calibration problems, and describing the evaluation of uncertainties associated with the calibration parameters. The report will also act as input to JCGM-WG1 and ISO TC69/SC6/WG7.

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