2. Measurement Process Characterization
2.3. Calibration
2.3.5. Control of artifact calibration

## Control of bias and long-term variability

Control parameters are estimated using historical data A control chart procedure is used for controlling bias and long-term variability. The procedure is designed to be implemented in real time after a baseline and control limits for the check standard of interest have been established from the database of check standard values. A separate control chart is required for each check standard. The control procedure outlined here is based on a Shewhart control chart with upper and lower control limits that are symmetric about the average. The EWMA control procedure that is sensitive to small changes in the process is discussed on another page.
For a Shewhart control procedure, the average and standard deviation of historical check standard values are the parameters of interest The check standard values are denoted by $$C_k \, (k=1, \, \ldots, \, K) \, .$$ The baseline is the process average which is computed from the check standard values as $$\overline{C} = \frac{1}{K} \sum_{k=1}^K C_k \,\,.$$ The process standard deviation is $${\large s}_2 =\sqrt{\frac{1}{K-1} \sum_{k=1}^K (C_k - \overline{C})^2}$$ with K - 1 degrees of freedom.
The control limits depend on the t
distribution and the degrees of freedom in the process standard deviation
If $$\overline{C}$$ has been computed from historical data, the upper and lower control limits are: \begin{eqnarray} UCL &=& \overline{C} + t_{1-\alpha/2, \, K-1} \cdot s_2 \\ & & \\ LCL &=& \overline{C} - t_{1-\alpha/2, \, K-1} \cdot s_2 \end{eqnarray} where $${\large t}_{1-\alpha/2, \, K-1}$$ denotes the 1-α/2 critical value from the t table with v = K - 1 degrees of freedom.
Sample code Sample code for computing the t value for a conservative case where α= 0.05, J = 6, and K = 6, is available for both Dataplot and R.
Simplification for large degrees of freedom It is standard practice to use a value of 3 instead of a critical value from the t table, given the process standard deviation has large degrees of freedom, say, v > 15.
The control procedure is invoked in real-time and a failure implies that the current calibration should be rejected The control procedure compares the check standard value, C, from each calibration run with the upper and lower control limits. This procedure should be implemented in real time and does not necessarily require a graphical presentation. The check standard value can be compared algebraically with the control limits. The calibration run is judged to be out-of-control if either:

C > UCL

or

C < LCL
Actions to be taken If the check standard value exceeds one of the control limits, the process is judged to be out of control and the current calibration run is rejected. The best strategy in this situation is to repeat the calibration to see if the failure was a chance occurrence. Check standard values that remain in control, especially over a period of time, provide confidence that no new biases have been introduced into the measurement process and that the long-term variability of the process has not changed.
Out-of-control signals that recur require investigation Out-of-control signals, particularly if they recur, can be symptomatic of one of the following conditions:
• Change or damage to the reference standard(s)
• Change or damage to the check standard
• Change in the long-term variability of the calibration process

For more guidance, see Remedies and strategies for dealing with out-of-control signals.

Caution - be sure to plot the data If the tests for control are carried out algebraically, it is recommended that, at regular intervals, the check standard values be plotted against time to check for drift or anomalies in the measurement process.