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

## Shewhart control chart

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 short-term 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 short-term repetitions which can characterize the precision of the instrument but not the long-term variability of the process. In measurement science, the interest is in assessing individual measurements (or averages of short-term 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

k = 2

in which case approximately 5% of the measurements from a process that is in control will produce out-of-control 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

k = 3

in which case approximately 1% of the measurements from an in-control process will produce out-of-control signals. 