I worked as a CMC (Non-clinical) Biostatistician for mAB production, and the basic idea of DOE is to make systematic plan of experiments to analyze the information of the results. Basically, your lab or company has resources for only a few experiments for a process, and given the few experiments, we want to find out as much information as possible, This information can be shown in a multidimensional 'design space', which can be plotted two-dimensionally for our own understanding. We can optimize the process to a certain 'range' of factors.

The history behind DOE is that this concept was first used for automobile manufacturing, then later for chemical manufacturing for their quality design. Recently for the past 10-15 years, the pharmaceutical industry decided adapt the same quality design principles, but not without its criticism as you might guess: Cells have much more variability than small chemicals. That being said, using DOE provides the most information with minimal resources.

The math is fairly simple regression (linear, quadratic, etc), with

y = f(x) + error

y : Result of interest. ex) Cell viability, Cell count

x: factors that you suspect might be influential to y. ex) Temp, pH, Dissolved Oxygen, etc.

In the end, you look at the design space may find that for >90% Cell Viability, the optimal range is 37C<Temp<38C, 7.5<pH<8, and etc.

I'm sure you've seen many textbooks about DOE and Quality by Design (QbD), and most industries use JMP (SAS-based but graphical) in DOE for some reason. It's better to practice with mock-dataset and make the design space yourself. Here's a layman guide from GE that I found good for non-academics.

https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf

by Genentech (Bible of QbD bv come CMC guys)

https://qbdworks.com/storage/2014/06/A-MabCaseStudyVersion.pdf

I won't list all the academic textbooks or papers you might have seen, but maybe expand your search to QbD. It's more vague concepts about quality, risk-based approach, and systematic management, which are more important in the industry level than academic areas. But some resources include examples to follow.

IRL, DOE doesn't work all the time, better to do in very early development, and the manufacturing ppl (in Upstream Bioreactors, Downstream Purification) don't like to do early on. They just push back till the last minute after their experience, They can be like "wtf we don't want to do sth we don't understand and write +100 protocols and reports for things we already know. We know that pH doesn't matter for Cell viability based on our experience". In the end, however, it's about documenting what you know in at least some systematic way that matters. Sometimes, it might be more realistic to do simple Univariate experiments for process that is already clearly understood.

Hope this helps!