This International Standard: outlines the general principles needed to calibrate a measurement system and to maintain that \'calibrated\' measurement system in a state of statistical control: provides a basic method for estimating a linear calibration function under either one of two assumptions relating to the variability of the measurements, for checking the assumption of linearity of the calibration function and the assumptions on the variability of the measurements, and for estimating the value of a new unknown quantity by transforming the measured values obtained on that quantity with the calibration function; provides a control method for extended use of a calibration function for detecting when the calibration function needs to be updated, and for estimating the uncertainty of the measured values after transformation with the calibration function; provides two alternatives to the basic method under special conditions; illustrates the basic method and the control method with an example. This International Standard is applicable to measurement systems for which reference materials are available. It is applicable to measurement systems with an assumed linear calibration function. It offers a method for examining the assumption of linearity. If it is known that the calibration function is nonlinear, then this International Standard is not applicable unless one uses the \'bracketing technique\' described in 8.3. This International Standard does not make a distinction among the various types of RMs and considers that the accepted values of the RMs selected to calibrate the measurement system are without error.