2.
Measurement Process Characterization
2.2. Statistical control of a measurement process 2.2.2. How are bias and variability controlled?


Example of Shewhart control chart for mass calibrations  The Shewhart control chart has a baseline and upper and lower limits, shown as dashed lines, that are symmetric about the baseline. Measurements are plotted on the chart versus a time line. Measurements that are outside the limits are considered to be out of control.  
Baseline is the average from historical data  The baseline for the control chart is the accepted value, an average of the historical check standard values. A minimum of 100 check standard values is required to establish an accepted value.  
Caution  control limits are computed from the process standard deviation  not from rational subsets 
The upper (UCL) and lower (LCL) control limits are:
UCL = Accepted value + k*process standard deviation LCL = Accepted value  k*process standard deviation where the process standard deviation is the standard deviation computed from the check standard database.


Individual measurements cannot be assessed using the standard deviation from shortterm repetitions  This procedure is an individual observations control chart. The previously described control charts depended on rational subsets, which use the standard deviations computed from the rational subsets to calculate the control limits. For a measurement process, the subgroups would consist of shortterm repetitions which can characterize the precision of the instrument but not the longterm variability of the process. In measurement science, the interest is in assessing individual measurements (or averages of shortterm repetitions). Thus, the standard deviation over time is the appropriate measure of variability.  
Choice of k depends on number of measurements we are willing to reject 
To achieve tight control of the measurement process, set
in which case approximately 5% of the measurements from a process that is in control will produce outofcontrol signals. This assumes that there is a sufficiently large number of degrees of freedom (>100) for estimating the process standard deviation. To flag only those measurements that are egregiously out of control, set
in which case approximately 1% of the measurements from an incontrol process will produce outofcontrol signals. 