 2. Measurement Process Characterization
2.3. Calibration
2.3.6. Instrument calibration over a regime

## Uncertainties of calibrated values

Purpose The purpose is to quantify the uncertainty of a 'future' result that has been corrected by the calibration curve. In principle, the uncertainty quantifies any possible difference between the calibrated value and its reference base (which normally depends on reference standards).
Explanation in terms of reference artifacts Measurements of interest are future measurements on unknown artifacts, but one way to look at the problem is to ask: If a measurement is made on one of the reference standards and the calibration curve is applied to obtain the calibrated value, how well will this value agree with the 'known' value of the reference standard?
Difficulties The answer is not easy because of the intersection of two uncertainties associated with
1. the calibration curve itself because of limited data
2. the 'future' measurement

If the calibration experiment were to be repeated, a slightly different calibration curve would result even for a system in statistical control. An exposition of the intersection of the two uncertainties is given for the calibration of proving rings ( Hockersmith and Ku).

ISO approach to uncertainty can be based on check standards or propagation of error General procedures for computing an uncertainty based on ISO principles of uncertainty analysis are given in the chapter on modeling.

Type A uncertainties for calibrated values from calibration curves can be derived from

An example of type A uncertainties of calibrated values from a linear calibration curve are analyzed from measurements on linewidth check standards. Comparison of the uncertainties from check standards and propagation of error for the linewidth calibration data are also illustrated.

An example of the derivation of propagation of error type A uncertainties for calibrated values from a quadratic calibration curve for loadcells is discussed on the next page. 