2.
Measurement Process Characterization
2.2. Statistical control of a measurement process 2.2.3. How is shortterm variability controlled?


Degradation of instrument or anomalous behavior on one occasion 
Changes in the precision of the instrument, particularly anomalies and
degradation, must be addressed. Changes in precision can be detected
by a statistical control procedure based on the Fdistribution
where the shortterm standard deviations are plotted on the control
chart.
The base line for this type of control chart is the pooled standard deviation, s_{1}, as defined in Data collection and analysis. 

Example of control chart for a mass balance  Only the upper control limit, UCL, is of interest for detecting degradation in the instrument. As long as the shortterm standard deviations fall within the upper control limit established from historical data, there is reason for confidence that the precision of the instrument has not degraded (i.e., common cause variations).  
The control limit is based on the Fdistribution 
The control limit is
$$UCL = {\large s}_1 \sqrt{F_{\alpha, \, J1, \, K(J1)}}$$
where the quantity under the radical is the upper α
critical value from the
F table with degrees of
freedom (J  1) and K(J  1). The numerator degrees of
freedom, v_{1} = (J 1), are associated with the standard deviation computed
from the current measurements, and the denominator degrees of freedom,
v_{2} = K(J  1), correspond to the pooled standard deviation of the
historical data. The probability α is chosen to be small, say 0.05.
The justification for this control limit, as opposed to the more conventional standard deviation control limit, is that we are essentially performing the following hypothesis test: $$H_0: \,\, \sigma_1 = \sigma_2$$ $$H_a: \,\, \sigma_1 < \sigma_2$$ where σ_{1} is the population value for the s_{1} defined above and σ_{2} is the value against which the standard deviation of the current value is being tested. Generally, s_{1} is based on sufficient historical data that it is reasonable to make the assumption that σ_{1} is a "known" value. The upper control limit above is then derived based on the standard F test for equal standard deviations. Justification and details of this derivation are given in Cameron and Hailes (1974). 

Sample Code 
Sample code for computing the F value for the case where α = 0.05, J = 6, and K = 6, is available for both Dataplot and R. 