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


Control parameters are estimated using historical data  A control chart procedure is used for controlling bias and longterm 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 $$ {\large s}_2 =\sqrt{\frac{1}{K1} \sum_{k=1}^K (C_k  \overline{C})^2} $$ 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, \, K1} \cdot s_2 \\ & & \\ LCL &=& \overline{C}  t_{1\alpha/2, \, K1} \cdot s_2 \end{eqnarray} where \( {\large t}_{1\alpha/2, \, K1} \) denotes the 1α/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 realtime 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
outofcontrol if either:
or


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 longterm variability of the process has not changed.  
Outofcontrol signals that recur require investigation 
Outofcontrol signals, particularly if they recur, can be symptomatic
of one of the following conditions:
For more guidance, see Remedies and strategies for dealing with outofcontrol 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. 