Biomedical Engineering Reference
In-Depth Information
) are the weighted summary of all the process variables used in the
model. The score biplots represent the operational space and each point in the plot
represents a single batch. The batches that are close to each other in the score biplots can
be concluded as operated in a similar operating space. These plots enable determining if
any group, pattern, or outlier exists in the data set.
Score contribution plots show why an observation in a score plot deviates from the
reference point. The reference point can be the average behavior of the process, another
observation, or a group of observations. Score contributions are typically depicted as bar
plots. The dominating bars indicate the variables that showmaximum deviation from the
reference point. The direction of the bars indicates in which direction the variables
deviate. The cause of the deviation can be determined by using the contribution plots and
the process knowledge.
Loadings plots (w
*
c) show both the X weights (w
*
) and Y weights (c) superimposed
in one plot. The (w
*
c) plot of one PLS component against another (e.g., 1 versus 2) shows
how the X variables correlate with Y variables and the correlation structure of the X's and
Y's. To interpret this plot, one can imagine a line passing through the origin and one of the
Y variables and project all the X and Y variables onto this line. The X variables near the Y
variables are positively correlated with Yand the X variables that are on the opposite side
of the Y variables are negatively correlated with Y. Also, the Y variables close to each
other are positively correlated and the ones on the opposite sides are negatively correlated
with each other.
Variable of importance in projection (VIP) plots summarize the importance of the
variables both to explain X and to correlate with Y. VIP values larger than 1 indicate
“important” X variables predicting Y.
The PLS regression coefficients show how strongly the Y variables are correlating
with X variables. The bars indicate the confidence intervals of the coefficients. The
directions of the bars show if the X variables are positively or negatively correlated with
the Y variables. The coefficients are considered significant if the confidence interval does
not cross zero. One should note that these coefficients are usually not independent unless
generated by design of experiments.
Scores (t
1
, t
2
,
...
12.7.1 Use of PCA and PLS in Multivariate Statistical
Process Monitoring
Construction of multivariate charts (as explained above) offers multivariate
statistical process monitoring (MSPM) capabilities for efficiently monitoring batch
biopharmaceutical (they are also used in other batch industries) processes. Typical
approach includes selecting a representative historical data set from a production
database. It can be at various scales (i.e., bench, pilot, or large). However, availability of
representative historical data is more probable at large scale due to routine production
campaigns comprised of many batches. Usually, 15-30 batches are good numbers for
constructing a reasonable process models via PCA and/or PLS. It is recommended
that batch selection for modeling is carried out via rational subgrouping if the
main objective is monitoring of successive batches. On the bass of our experience,
rational subgrouping should be combined with the process and characterization
