It's important to acknowledge that the amount of data available in a development setting is often limited. Therefore, the
ability to conduct statistical analysis is affected and a modified approach to analysis may be required. However, as a product
moves into manufacturing and production runs mount, the amount of data available for statistical analysis increases and improves
one's understanding of the process and one's ability to detect CQAs and understand how they interact. In the example below,
we applied QbD tools to a manufacturing process to solve a problem with bulk substance yield at a company we will refer to
as PharmaCo. The product being produced was a monoclonal antibody produced in a standard mammalian cell expression system
in a bioreactor.
Run charts and control charts. First, the historical data on yield were plotted on a run chart in order to graphically represent the batch-to-batch variability
and shift in output over time. The chart depicted a sequence of batches, at different scales, with the standardized yield
in grams on the vertical (y) axis and the time series, represented by the batch numbers, on the horizontal (x) axis (as in Figure 1,
a control chart that has the run chart as its basis). In the underlying run chart, we see a few indications of atypical behavior.
First, there is a shift in the average yield from about 900 grams to about 700 grams. Something, unknown to this point, has
happened in the process to cause this shift. We also see instances of outliers—or points that breached the lower control limit
(LCL). These points also point to some special cause.
Figure 1. A control chart that plots batch-to-batch variability in yield.
Control charts add the control limits of the process to support a wider range of analytical techniques. The control limits,
as in Figure 1, are statistically derived based on the data. An analysis of the control chart showed that over time a significant
shift in the process occurred that resulted in a drop in yield of 18%. Moreover, the chart shows a high number of out-of-control
points, including three extreme outliers that occurred three consecutive times, which were traced to a single raw material
lot. In other words, the process is not in "statistical control." Further, patterns that the chart uncovers—in this case,
problems with a raw material lot, among other things—may offer some clues to the source of the out-of-control variations in
PharmaCo's manufacturing personnel acknowledged the three extreme outliers in the data points but were unable to provide an
explanation of them because those three batches had been produced in precisely the same fashion as the three preceding batches.
This is not an uncommon situation, but it is telling that there are elements of the process that are not well understood.
In the language of QbD, there is a lack of process understanding.
Bivariate analysis. To help understand the sources of the variation indicated by the control chart, the available data were subjected to bivariate
analysis in which pairs of variables extracted from the historical data were examined and depicted on a scatter plot. In PharmaCo's
case, bivariate analysis might plot yield against raw material lots or against process parameters to find correlations. Figure
2 plots the yield of the PharmaCo fermentation process against one of the key raw material parameters and shows that this
process parameter correlates strongly with yield. At this point, however, this correlation does not imply cause and effect;
further study is warranted. In fact, bivariate analysis conducted over a number of pairs of variables typically finds only
weak correlations, not a strong correlation between two variables that might point to a magic bullet to solve the problem.
Figure 2. A scatter plot of a bivariate analysis comparing a key raw material parameter to yield.