ADD a bunch of fluff about how doe's work

tex/thesis.tex

@@ -719,7 +719,7 @@ themselves express \il{15} and all three of its receptor components ().
 Additionally, blocking \il{15} itself or \il{15R$\upalpha$} \invitro{} has been
 shown to inhibit homeostatic proliferation of resting human T cells ().
 
-\subsection*{strategies to optimize cell manufacturing}
+\subsection*{overview of design of experiments}
 
 The \gls{dms} system has a number of parameters that can be optimized, and a
 \gls{doe} is an ideal framework to test multiple parameters simultaneously. The
@@ -729,7 +729,60 @@ resources. It was developed in many non-biological industries throughout the
 engineers needed to minimize downtime and resource consumption on full-scale
 production lines.
 
-% TODO add a bit more about the math of a DOE here
+At its core, a \gls{doe} is simply a matrix of conditions to test where each row
+is usually called a `run' and corresponds to one experimental unit to which the
+conditions are applied, and each column represents a parameter of concern to be
+tested. The values in each cell represent the level at which each parameter is
+to be tested. When the experiment is performed using this matrix of conditions,
+the results are be summarized into one or more `responses' that correspond to
+each run. These responses are then be modeled (usually using linear regression)
+to determine the statistic relationship (also called an `effect') between each
+parameter and the response(s).
+
+Collectively, the space spanned by all parameters at their feasible ranges is
+commonly referred to as the `design space', and generally the goal of a
+\gls{doe} is to explore this design space using using the least number of runs
+possible. While there are many types of \glspl{doe} depending on the nature
+of the parameters and the goal of the experimenter, they all share common
+principles:
+
+% BACKGROUND cite montgomery, because I feel like it
+\begin{description}
+\item [randomization --] The order in which the runs are performed should
+  ideally be as random as possible. This is to mitigate against any confounding
+  factors that may be present which depend on the order or position of the
+  experimental runs. For an example in context, the evaporation rate of media in
+  a tissue culture plate will be much faster at the perimeter of the plate vs
+  the center. While randomization does not eliminate this bias, it will ensure
+  the bias is `spread' evenly across all runs in an unbiased manner.
+\item [replication --] Since the analysis of a \gls{doe} is inherently
+  statistical, replicates should be used to ensure that the underlying
+  distribution of errors can be estimated. While this is not strictly necessary
+  to conclude results using a \gls{doe}, failure to use replications requires
+  strong assumptions about the model structure (particularly in the case of
+  high-complexity models which could easily fit the data perfectly) and also
+  precludes the use of statistical tests such as the lack-of-fit test which can
+  be useful in rejecting or accepting a particular analysis. Note that the
+  subject of replication is within but not the same as power analysis, which
+  concerns the number of runs required to estimate a certain effect size.
+\item [orthogonality --] Orthogonality refers to the independence of each
+  parameter in the design matrix. In other words, the levels tested in any given
+  parameter add mutually-exclusive information about the response(s). Again,
+  while not strictly necessary, orthogonality drastically simplifies the
+  analysis of the experiment by allowing each parameter to be treated
+  separately. In cases where orthogonality is impossible (which is often true in
+  experiments with many categorical variables) strategies exist to maximize
+  orthogonality.
+\item [blocking --] In the case where the experiment must be non-randomly spread
+  over multiple groups, runs are assigned to `blocks' which are not necessarily
+  relevant to the goals of the experiment but nonetheless could affect the
+  response. A key assumption that is (usually) made in the case of blocking is
+  that there is no interaction between the blocking variable and any of the
+  experimental parameters. For example, in T cell expansion, if media lot were a
+  blocking variable and expansion method were a parameter, we would by default
+  assume that the effect of the expansion method does not depend on the media
+  lot (even if the media lot itself might change the mean of the response).
+\end{description}
 
 \Glspl{doe} served three purposes in this dissertation. First, we used them as
 screening tools, which allowed us to test many input parameters and filter out
@@ -738,7 +791,9 @@ used to make a robust response surface model to predict optimums using
 relatively few resources, especially compared to full factorial or
 one-factor-at-a-time approaches. Third, we used \glspl{doe} to discover novel
 effects and interactions that generated hypotheses that could influence the
-directions for future work.
+directions for future work. To this end, the types of \glspl{doe} we generally
+used in this work were fractional factorial designs with three levels, which
+enable the estimation of both main effects and second order quadratic effects.
 
 \subsection*{strategies to characterize cell manufacturing}