2.
Measurement Process Characterization
2.3. Calibration 2.3.3. What are calibration designs? 2.3.3.1. Elimination of special types of bias


Bias caused by linear drift over the time of measurement  The requirement that reference standards and test items be stable during the time of measurement cannot always be met because of changes in temperature caused by body heat, handling, etc.  
Representation of linear drift 
Linear drift for an even number of measurements is represented by
and for an odd number of measurements by
 
Assumptions for drift elimination 
The effect can be mitigated by a driftelimination scheme
(Cameron/Hailes) which
assumes:


Example of driftelimination scheme  An example is given by substitution weighing where scale deflections on a balance are observed for X, a test weight, and R, a reference weight. \begin{eqnarray} Y_1 = X  3d_1 + error_1 \\ Y_2 = R  1d_2 + error_2 \\ Y_3 = R + 1d_3 + error_3 \\ Y_4 = X + 3d_4 + error_4 \end{eqnarray}  
Estimates of driftfree difference and size of drift  The driftfree difference between the test and the reference is estimated by $$ D = \frac{1}{2} \left[(Y_1  Y_2)  (Y_3  Y_4)\right] $$ and the size of the drift is estimated by $$ \widehat{d} = \frac{1}{4} \left( Y_1 + Y_2  Y_3 + Y_4 \right) $$  
Calibration designs for eliminating linear drift  This principle is extended to create a catalog of driftelimination designs for multiple reference standards and test items. These designs are listed under calibration designs for gauge blocks because they have traditionally been used to counteract the effect of temperature buildup in the comparator during calibration. 