Design of
Experiments.
The method itself, from the vocabulary up to response surfaces. Start at the top if the subject is new to you, or jump to the design you are about to run.
Foundations.
7 parts- Part 1
What is Design of Experiments? (DoE Basics) Start here
What a designed experiment is, and why it gets you more information from fewer runs than changing one factor at a time.
- Part 2
Key DoE Terms
The words you need before you can read a design: factor, level, response, run, effect, and the rest.
- Part 3
Principles of DoE: Randomization, Replication, Blocking
The three habits that make experimental data worth trusting: randomize the order, repeat the runs, block out what you cannot control.
- Part 4
Main Effects & Interaction Effects Explained
How a factor moves the result on its own, and how two factors together can do something neither of them does alone.
- Part 5
The Basics of Designing Better Experiments
Why changing one factor at a time hides the interactions, and how covering the design space finds them in fewer runs.
- Part 6
Understanding Systematic and Random Errors
The difference between error that shifts every result the same way and error that just scatters them, and what each costs you.
- Part 7
Why You Should Always Code Your Variables Python
Coefficients in raw units cannot be compared. Coding puts every factor on the same scale so the model can be read.
Full factorial designs.
3 parts- Part 8
A step by step example of a full factorial design
A full factorial worked through on real filtration data, from the run sheet to the main effect and interaction plots.
- Part 9
Create a Full Factorial Design in Python Python
Build a 2^k design with pyDOE3: name your factors, map coded levels to real units, randomize the order, export the run sheet.
- Part 10
A full factorial design in Python from beginning to end Python
One dataset, start to finish in Python: build the design, plot the effects, run ANOVA, check the model, draw the surface.
Blocking.
2 parts- Part 11
Why Blocking Matters
An epoxy coating experiment where batch-to-batch variation buried the real effect, and what blocking would have saved.
- Part 12
Blocking in Practice: How to Actually Do It Python
How a block is actually built into a design through confounding, with blocked and unblocked versions of one experiment.
Fractional factorial designs.
4 parts- Part 13
Introducing Fractional & Central Composite Designs
When a full factorial gets too big: fractional designs to screen many factors, central composite designs to optimize a few.
- Part 14
Example of a Fractional Factorial Design
A fractional factorial worked through end to end: which runs you drop, what you give up, and what you can still conclude.
- Part 15
Create a Fractional Factorial Design in Python Python
Build a fractional design in pyDOE3, choose the resolution, and see which effects end up confounded with which.
- Part 16
Foldover Designs
A second, mirrored set of runs that breaks the confounding in a fractional design, shown on an effect that misled.
Models & ANOVA.
9 parts- Part 17
Mathematical Models in DOE
Turning a table of runs into an equation that predicts the response, and knowing how far you can trust it.
- Part 18
How to perform ANOVA
The test that tells you which factors really moved the response, and which ones only look like they did.
- Part 19
Understanding the ANOVA Table Output
What every column in the ANOVA table means, and which numbers you actually read to decide what matters.
- Part 20
Testing ANOVA Assumptions
ANOVA only holds if your residuals behave. What to check, what it looks like when it fails, and what to do then.
- Part 21
QQ-Plots Explained
How to read a QQ-plot, and what the common shapes tell you about whether your residuals are normal enough.
- Part 22
Residual Analysis
What is left over once the model has done its work, and why those leftovers tell you whether to believe it.
- Part 23
How to Perform ANOVA with Python Python
Run ANOVA in Python with statsmodels: fit the model, drop the dead terms, add curvature, check the diagnostics.
- Part 24
Active Effects: Not Everything Matters Equally
Most factors do nothing. Effect sparsity and effect hierarchy explain why, and how to tell the live ones from the dead.
- Part 25
All-Subset Regression
Rather than dropping terms one at a time, fit every possible combination and pick the best model. How it compares to ANOVA.
Response surfaces.
6 parts- Part 26
Response Surface Methodology (RSM)
How a run of small designs walks you toward better process conditions instead of guessing where the optimum sits.
- Part 27
The Path of Steepest Ascent
Once a model points uphill, this is how far you walk along it and where you stop to run the next set of experiments.
- Part 28
A step by step example of a Central Composite Design (CCD)
A central composite design worked through step by step, including how it picks up the curvature a factorial misses.
- Part 29
Create a Central Composite Design in Python Python
Build a central composite design in Python, set the axial distance, and get a run sheet you can take to the bench.
- Part 30
Central Composite Design vs. Box-Behnken Design
Two response surface designs side by side. What each one costs in runs, and when to pick one over the other.
- Part 31
How to create a Box-Behnken Design in Python Python
Build a Box-Behnken design in pyDOE3, and see how it finds curvature with fewer runs than a central composite.