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


Control parameters from historical data 
A modified control chart procedure is used for controlling instrument
precision. The procedure is designed to be implemented in real time
after a baseline and control limit for the instrument of interest have
been established from the database of shortterm standard deviations.
A separate control chart is required for each instrument  except
where instruments are of the same type with the same basic precision,
in which case they can be treated as one.
The baseline is the process standard deviation that is pooled from \( k = 1, \, \ldots, \, K \) individual repeatability standard deviations, \( {\large s}_k \), in the database, each having \( \nu_k \) degrees of freedom. The pooled repeatability standard deviation is $$ {\large s}_1 = \sqrt{ \frac{1}{\nu} \sum_{k=1}^K \nu_k \, {\large s}_k^2 } $$ with degrees of freedom $$ \nu = \sum_{k=1}^K \nu_k \,\, .$$ 

Control procedure is invoked in realtime for each calibration run  The control procedure compares each new repeatability standard deviation that is recorded for the instrument with an upper control limit, UCL. Usually, only the upper control limit is of interest because we are primarily interested in detecting degradation in the instrument's precision. A possible complication is that the control limit is dependent on the degrees of freedom in the new standard deviation and is computed as follows: $$ UCL = s_1 \sqrt{F_{\alpha, \, \nu_{new}, \, \nu}} $$ The quantity under the radical is the upper α percentage point from the F table where α is chosen small to be, say, 0.05. The other two terms refer to the degrees of freedom in the new standard deviation and the degrees of freedom in the process standard deviation.  
Limitation of graphical method 
The graphical method of plotting every new estimate of repeatability on
a control chart does not work well when the UCL can change with
each calibration design, depending on the degrees of freedom. The
algebraic equivalent is to test if the new standard deviation exceeds
its control limit, in which case the shortterm precision is judged
to be out of control and the current calibration run is rejected.
For more guidance, see
Remedies and strategies for dealing
with outofcontrol signals.
As long as the repeatability standard deviations are in control, there is reason for confidence that the precision of the instrument has not degraded. 

Case study: Mass balance precision  It is recommended that the repeatability standard deviations be plotted against time on a regular basis to check for gradual degradation in the instrument. Individual failures may not trigger a suspicion that the instrument is in need of adjustment or tuning. 