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

Bias caused by instrument drift

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

..., -5d, -3d, -1d, +1d, +3d, +5d, ...

and for an odd number of measurements by

..., -3d, -2d, -1d, 0d, +1d, +2d, +3d, ... .
Assumptions for drift elimination The effect can be mitigated by a drift-elimination scheme (Cameron/Hailes) which assumes:
  • Linear drift over time
  • Equally spaced measurements in time
Example of drift-elimination 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 drift-free difference and size of drift The drift-free 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 drift-elimination 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 build-up in the comparator during calibration.
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