Knowledge Management and Process Monitoring of Pharmaceutical Processes in the Quality by Design Paradigm - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 233

and there are no special causes involved. A value lying outside this region signifies
the presence of special causes for the resulting process variability, making the
corresponding batch an outlier among the rest of the batches. There are various
rules, such as the Nelson rules and Western Electric rules, that when applied to the
control chart give an indication about the trends and systematic patterns that can
ultimately lead to an out-of-control situation. This makes the control chart an
important aid in preventing loss of future batches caused by some special cause of
variation.
Figure 13 shows a control chart. There is one horizontal line each for the
average, ±1SD, ±2SD, and ±3SD. The various data points that violate the Nelson
rules are marked according to the rule that they violate.
Though univariate Statistical Process Control (SPC) charts are easy to generate
and interpret, they are susceptible to giving false positives if the monitored vari-
ables are highly interrelated. For this reason, the bioprocessing industry is rapidly
adopting more sophisticated tools such as multivariate statistics for deeper insights
into the process. These tools, however, require advanced algorithms for data pre-
processing and modelling [ 4 , 13 , 20 ]. This has enabled analysis of multidimen-
sional data in an efficient way in the form of various multivariate control charts.
Multivariate control charts are used to monitor several related parameters at the
same time. In univariate control charts, the focus is on one parameter at a time,
whereas multivariate control charts take into account the fact that most of these
parameters are related to each other and therefore it is essential to investigate these
interactions and correlations to benchmark the process performance. These charts
combine the principles of multivariate analysis and statistical process control to
trend and analyse the process data. Most of these are based on principal component
analysis (PCA) and partial least squares (PLS) techniques. These are projection
methods that project the data into lower-dimensional spaces to facilitate analysis.
PCA is mainly used to reduce the number of variables that require monitoring by
combining the variables to generate new variables called principal components
that are fewer in number than the original variables and are less correlated com-
pared with the original variables. In this way, it focuses on deriving a model based
on the data where the variance between the projection coordinates is maximum.
PLS, on the other hand, analyses the covariance between a set of variables with the
focus on finding the directions that represent variation in process variables as well
as how such variation in process variables affects quality variables.
Most of these methods operate by first constructing a process model based on
historical data. Subsequent batches are then studied based on that model to detect
shifts and deviations in the process. There are several charts based on these
principles that can be used for multivariate process monitoring:
• T 2 control charts based on Hotelling's statistics are used to detect shifts and
deviations of principal components from the normal behaviour defined by the
model;
• Score plots are used to detect out-of-control behaviour of the latent variables
from the control limits defined by the reference data;