Introduction to Design of Experiments (DOE) Series v1.0
From Orthogonal Arrays to Response Surface Methodology and Taguchi Methods - Complete Practical Guide for Process Optimization
Series Overview
This series is a comprehensive 5-chapter educational content that allows you to progressively learn Design of Experiments (DOE) in process industries from fundamentals to practice. It comprehensively covers everything from factor screening using orthogonal arrays, optimization using Response Surface Methodology (RSM), to robust design using Taguchi Methods.
Features:
- ✅ Practice-Oriented: 40 executable Python code examples
- ✅ Systematic Structure: 5-chapter structure progressing from basics to applications
- ✅ Industrial Applications: Rich examples from chemical plants and manufacturing processes
- ✅ Automation: Complete automation of experimental design generation and analysis with Python
Total Learning Time: 120-150 minutes (including code execution and exercises)
How to Learn
Recommended Learning Sequence
For Beginners (learning DOE for the first time):
- Chapter 1 → Chapter 2 → Chapter 3 → Chapter 4 → Chapter 5
- Required Time: 120-150 minutes
For Those with Statistics Experience (knowledge of ANOVA):
- Chapter 2 → Chapter 3 → Chapter 4 → Chapter 5
- Required Time: 90-120 minutes
For Practical Skills Enhancement (familiar with DOE concepts):
- Chapter 3 (RSM) → Chapter 4 (Taguchi) → Chapter 5 (Automation)
- Required Time: 60-80 minutes
Chapter Details
Chapter 1: Fundamentals of Design of Experiments and Orthogonal Arrays
Learning Content
- Fundamentals of Design of Experiments (DOE)
- Purpose and history of DOE
- Differences from traditional one-variable-at-a-time experiments
- Three principles of DOE: Replication, Randomization, Blocking
- One-way and Two-way Experiments
- One-way experiment (One-way ANOVA)
- Two-way experiment (Two-way ANOVA)
- Concept of interaction
- Fundamentals of Orthogonal Arrays
- What are orthogonal arrays (L8, L16, L27, etc.)
- Properties and advantages of orthogonal arrays
- How to assign factors
- Main Effects Plots and Interaction Plots
- Visualization of main effects
- Interpretation of interactions
- Searching for optimal conditions
- Chemical Reaction Yield Optimization Case Study
- Three-factor experiment: temperature, pressure, catalyst amount
- Experimental design using orthogonal array L8
- Analysis of results and determination of optimal conditions
Learning Objectives
- ✅ Explain basic concepts and benefits of DOE
- ✅ Conduct one-way and two-way experiments
- ✅ Design experimental plans using orthogonal arrays
- ✅ Create and interpret main effects plots and interaction plots
- ✅ Search for optimal conditions in chemical processes
Chapter 2: Factorial Experiments and Analysis of Variance
Learning Content
- Full Factorial Design
- 2³ design (3 factors, 2 levels)
- Calculation of number of experiments
- Evaluation of all interactions
- Fractional Factorial Design
- Principle of reducing number of experiments
- Concept of Resolution
- Understanding Confounding
- Analysis of Variance (ANOVA)
- One-way ANOVA with F-test
- Two-way ANOVA with interaction
- Interpretation of F-values and p-values
- Multiple Comparison Tests
- Tukey HSD test
- Bonferroni correction
- Visualization with box plots
- Decomposition of Variance Components
- Decomposition of total sum of squares
- Calculation of contribution ratios
- Identification of significant factors
- Case Study: Exploring Factors Affecting Catalyst Activity
- Evaluation of 4 factors (temperature, pressure, catalyst concentration, reaction time)
- Application of fractional design
- Analysis of main factors and interactions
Learning Objectives
- ✅ Distinguish between full factorial and fractional factorial experiments
- ✅ Conduct ANOVA and perform F-tests
- ✅ Evaluate significant differences between levels using multiple comparison tests
- ✅ Calculate contribution ratios of variance components and identify significant factors
- ✅ Design and analyze factor screening experiments in real processes
Chapter 3: Response Surface Methodology (RSM)
Learning Content
- Fundamentals of Response Surface Methodology
- Purpose and application scenarios of RSM
- Two-stage approach (screening → optimization)
- Necessity of surface models
- Central Composite Design (CCD)
- Arrangement of factorial points, axial points, and center points
- Rotatability
- Determination of alpha value
- Box-Behnken Design
- Design of 3-level plans
- Comparison with CCD
- Reduction of number of experiments
- Fitting Second-Order Polynomial Models
- Linear terms, quadratic terms, interaction terms
- Coefficient estimation using least squares method
- Model significance testing
- Visualization of Response Surfaces
- 3D response surface plots
- Contour plots
- Searching for optimal conditions
- Model Validation
- Coefficient of determination (R², Adjusted R²)
- Root Mean Square Error (RMSE)
- Residual analysis
- Case Study: Optimization of Distillation Column Operating Conditions
- Two-factor optimization: reflux ratio and heating rate
- Simultaneous optimization of product purity and yield
- Optimal solution search using scipy.optimize
Learning Objectives
- ✅ Understand the principles and application scenarios of RSM
- ✅ Design CCD and Box-Behnken plans
- ✅ Fit second-order polynomial models
- ✅ Create 3D response surfaces and contour plots
- ✅ Search for optimal conditions using scipy.optimize
- ✅ Statistically evaluate model validity
Chapter 4: Taguchi Methods and Robust Design
Learning Content
- Fundamentals of Taguchi Methods
- Concept of quality engineering
- Purpose of robust design
- Differences from traditional DOE
- Control Factors and Noise Factors
- Classification of factors (control factors, noise factors, signal factors)
- Inner array and outer array
- Design of cross-product experiments
- Signal-to-Noise Ratio (SN Ratio)
- SN ratio for nominal-the-best characteristics (with target value)
- SN ratio for smaller-the-better characteristics
- SN ratio for larger-the-better characteristics
- Parameter Design
- Determining optimal conditions by maximizing SN ratio
- Adjusting sensitivity
- Conducting confirmation experiments
- Loss Function
- Quantification of quality loss
- Concept of societal loss
- Calculation of Taguchi loss function
- Case Study: Robust Design of Injection Molding Process
- Optimization of control factors (temperature, pressure, time)
- Evaluation of noise factor effects (material lot, environmental temperature)
- Minimization of product dimension variation
Learning Objectives
- ✅ Explain the purpose and characteristics of Taguchi Methods
- ✅ Appropriately classify control factors and noise factors
- ✅ Calculate three types of SN ratios
- ✅ Determine optimal conditions through parameter design
- ✅ Quantify quality loss using loss function
- ✅ Implement robust design in real processes
Chapter 5: Experimental Design and Analysis Automation with Python
Learning Content
- Utilizing pyDOE3 Library
- Automatic generation of various experimental designs
- Generation and validation of orthogonal arrays
- Generation of CCD and Box-Behnken designs
- Automated Experimental Results Analysis Pipeline
- From data loading to result output
- Automation of ANOVA
- Model fitting and evaluation
- Interactive Response Surface Visualization
- 3D plots with Plotly
- Interactive graphs with sliders
- Simultaneous visualization of multiple responses
- Automated Experimental Design Report Generation
- Automatic creation of experimental plans
- Automatic analysis result reports
- HTML/PDF output
- Robustness Evaluation using Monte Carlo Simulation
- Consideration of uncertainty
- Probabilistic evaluation
- Estimation of confidence intervals
- Multi-objective Optimization (Pareto frontier)
- Simultaneous optimization of multiple objective functions
- Search for Pareto optimal solutions
- Trade-off analysis
- Complete DOE Workflow Integration Example
- Experimental design → Implementation → Analysis → Optimization
- Comprehensive optimization project for chemical processes
- Reusable Python scripts
Learning Objectives
- ✅ Automatically generate various experimental designs with pyDOE3
- ✅ Build analysis pipelines for experimental data
- ✅ Create interactive response surfaces with Plotly
- ✅ Automatically generate experimental plans and analysis reports
- ✅ Conduct robustness evaluation with Monte Carlo simulation
- ✅ Search for Pareto solutions in multi-objective optimization
- ✅ Automate complete DOE workflows
Overall Learning Outcomes
Upon completing this series, you will acquire the following skills and knowledge:
Knowledge Level (Understanding)
- ✅ Can explain the basic principles and historical background of DOE
- ✅ Understand the characteristics of orthogonal arrays, factorial experiments, RSM, and Taguchi Methods
- ✅ Understand the theory of Analysis of Variance (ANOVA) and statistical testing
- ✅ Understand the concept of robust design and the meaning of SN ratio
Practical Skills (Doing)
- ✅ Can design experimental plans (orthogonal arrays, CCD, Box-Behnken, etc.) according to objectives
- ✅ Can conduct ANOVA and multiple comparison tests
- ✅ Can fit second-order polynomial models and create response surfaces
- ✅ Can calculate SN ratios and determine robust conditions
- ✅ Can automate from experimental design generation to analysis with Python
- ✅ Can search for Pareto optimal solutions in multi-objective optimization
Application Ability (Applying)
- ✅ Can plan and conduct efficient experiments in real processes
- ✅ Can draw statistically valid conclusions and determine optimal conditions
- ✅ Can minimize product variation through robust design
- ✅ Can handle experimental design tasks as a process engineer
FAQ (Frequently Asked Questions)
Q1: What is the difference between DOE and machine learning-based optimization?
A: DOE is a method to efficiently evaluate the effects of factors with a small number of experiments and obtain statistically valid optimal conditions. Machine learning learns complex patterns from large amounts of data, but DOE is effective when the number of experiments is limited. Both can also be combined.
Q2: Can I understand this without knowledge of statistics?
A: It is desirable to understand basic statistics (mean, variance, concept of hypothesis testing). This series explains necessary statistical concepts, but foundational knowledge of statistics is helpful for interpreting F-tests and p-values.
Q3: How do I decide between using orthogonal arrays and RSM?
A: Orthogonal arrays are suitable for factor screening (identifying significant factors), while RSM is suitable for optimization after significant factors are identified. Typically, factors are narrowed down with orthogonal arrays, then detailed optimization is performed with RSM.
Q4: When should I use Taguchi Methods?
A: It is effective when you want to minimize variation in products or processes. For example, Taguchi Method's robust design is appropriate when you want to maintain stable quality even with variations in material lots or environmental conditions.
Q5: What should I be careful about when applying DOE in actual plants?
A: It is important to consider safety, cost, and operational impact. We recommend reducing the number of experiments with fractional designs or conducting preliminary evaluations with simulations. Collaboration with field operators is also essential.
Q6: What should I learn next after this series?
A: We recommend the following topics:
- Bayesian Optimization: Efficient optimization with few experiments
- Mixture Experimental Design: Optimization of blend ratios
- Model Predictive Control (MPC): Integration of optimization and control
- Fusion with Machine Learning: Surrogate models and active learning
Next Steps
Recommended Actions After Completing the Series
Immediate (within 1 week):
1. ✅ Try orthogonal array experiments in your own processes
2. ✅ Template ANOVA scripts
3. ✅ Publish Chapter 5 code on GitHub
Short-term (1-3 months):
1. ✅ Real process optimization project using RSM
2. ✅ Implementation of robust design using Taguchi Methods
3. ✅ Development of experimental design automation tools
4. ✅ Learning Bayesian optimization
Long-term (6 months or more):
1. ✅ Building integrated optimization systems for entire processes
2. ✅ Development of methods integrating machine learning and DOE
3. ✅ Conference presentations or paper writing
4. ✅ Career building as a process optimization engineer
Feedback and Support
About This Series
This series was created as part of the PI Knowledge Hub project under Dr. Yusuke Hashimoto at Tohoku University.
Created: October 26, 2025
Version: 1.0
We Welcome Your Feedback
We welcome your feedback to improve this series:
- Typos, errors, technical mistakes: Please report via GitHub repository Issues
- Improvement suggestions: New topics, additional code examples you'd like to see, etc.
- Questions: Sections that were difficult to understand, parts that need additional explanation
- Success stories: Projects using what you learned from this series
Contact: yusuke.hashimoto.b8@tohoku.ac.jp
License and Terms of Use
This series is published under CC BY 4.0 (Creative Commons Attribution 4.0 International) license.
What you can do:
- ✅ Free viewing and downloading
- ✅ Use for educational purposes (classes, study sessions, etc.)
- ✅ Modification and derivative works (translation, summarization, etc.)
Conditions:
- 📌 Author credit must be displayed
- 📌 Modifications must be indicated
- 📌 Commercial use requires prior contact
Details: CC BY 4.0 License Full Text
Let's Get Started!
Are you ready? Start with Chapter 1 and begin your journey into the world of Design of Experiments (DOE)!
Chapter 1: Fundamentals of Design of Experiments and Orthogonal Arrays →
Update History
- 2025-10-26: v1.0 Initial Release
Your DOE learning journey begins here!