A BIOLOGIC EXAMPLE
Figure 2. Two views of chemical cleave data: batch release charts set at three sigma and using Shewhart limits. The top chart
is a run chart with specifications set at plus or minus three sigma. The bottom charts are the same data with Shewhart control
limits set and process shifts incorporated (moving range chart is omitted from the Shewhart chart).
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Figure 2 shows data from a chemical cleave step in a biologic process.2 The top chart shows the data with limits set at plus or minus three standard deviations. No points are observed beyond these
3 σ limits. Assuming the data are reasonably continuous, less than 1% of any data set can be expected to fall beyond 3 σ limits,
regardless of how unstable the system may be, and irrespective of the functional form of the distribution involved. This is
a central problem associated with the use of 3 σ limits. As the process is upset by special causes of variation or by drifts
in the process mean, the 3 σ limits will grow without bound, making the process under examination look stable even when it
is not.3
The lower charts in Figure 2 show control limits calculated and placed according to Shewhart's methods, and much more information
is available. It is important to note that in an individual point and moving range control chart, all the control limits are
developed from the average of the moving ranges, rather than from the individual data themselves. It is the special relationship
between the moving ranges chart and the control limits that allow control limits to be developed that are not significantly
widened by upsets to the system, as so often happens with 3 σ limits.2 The estimate for σ using Shewhart's methods is nearly half of that calculated by the more usual root mean square deviation
function found in calculators and spreadsheets.
The process in Figure 2 is unstable. It is not behaving in a predictable manner and sooner or later will record an OOS event.
The chart created using Shewhart's methods exposes several special causes and changes to the process mean. These signals provide
clues for detecting changes to both manufacturing and analytical processes in an attempt to reduce variation and improve quality
and productivity. In this case, the Shewhart chart has identified where something changed the process average, and where
upsets have introduced special cause events. Investigating these signals will lead to a better understanding of the process,
and to proper identification of causality as well as the appropriate corrective action.
The more traditional "average plus or minus three sigma" chart found no signals in the data. The Shewhart control chart found
seven.
The approach pioneered by Shewhart suggests that key variables be tracked in real time on a control chart.3 In this way, disturbances or changes to the process can be identified and corrected, often before an OOS result is recorded.
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