01 — Scientific Foundations
Why DOE in Industry?
Statistical Design of Experiments (DOE) is a core scientific methodology to understand, control,
and optimize complex production systems. Unlike one-factor-at-a-time empirical tuning (OFAT),
DOE enables simultaneous exploration of multiple factors and interactions with proven statistical
efficiency.
Montgomery (2017), in Design and Analysis of Experiments - the global reference text in
this field - documents that full and fractional factorial designs can
identify significant factors with 50% to 80% fewer runs
than OFAT (One Factor At a Time) approaches, while preserving equivalent statistical power and
detecting factor interactions that classical approaches systematically miss.
In the Latin American industrial context, where experimental resources are limited and pilot
testing costs are significant, DOE efficiency is not just a methodological advantage: it is an
operational requirement. Antony (2014) estimates that organizations implementing systematic DOE
reduce process-improvement cycles by 40-60%.
2k
Factorial designs
2 levels, k factors
RSM
Response Surface
Methodology · Box-Behnken / CCD
Taguchi
Robust designs
for manufacturing
[1] Montgomery DC. (2017). Design and Analysis of Experiments (9th ed.). John Wiley & Sons. ISBN: 978-1-119-11347-8.
[2] Antony J. (2014). Design of Experiments for Engineers and Scientists (2nd ed.). Elsevier. doi:10.1016/B978-0-08-099417-8.00001-9
[3] Box GEP, Hunter JS, Hunter WG. (2005). Statistics for Experimenters (2nd ed.). Wiley-Interscience.
02 — Methodological Framework
Taxonomy of Experimental
Designs
Selecting the right experimental design depends on research objective, number of factors,
available resources, and response variable type. OphirIAn uses a four-level methodological
decision tree aligned with ISO 5725 standards for measurement-method accuracy and precision.
| Design |
Objective |
Factors |
Minimum runs |
Typical application |
| Screening (Plackett-Burman) | Identify vital factors | 5-20 | N+1 | Initial process exploration |
| Factorial 2k | Main effects + interactions | 2-7 | 2k | Critical-parameter optimization |
| Fractional Factorial 2k-p | Efficiency with many factors | 5-15 | 2k-p | Formulation and industrial recipes |
| RSM - CCD / Box-Behnken | Response surface and optimum | 2-5 | Variable | Maximize/minimize quality KPI |
| Taguchi L-Array | Robustness to noise | 3-8 | Orthogonal | Manufacturing quality control |
| D-Optimal | Irregular regions and constraints | Variable | Computational | Constrained mixture processes |
For agroindustrial and light-manufacturing processes - the core of the Colombian MSME ecosystem -
Box-Behnken and Central Composite Design (CCD) under Response Surface
Methodology (RSM) provide the best balance between statistical power, number of runs, and
objective-function modeling capacity.
[4] Myers RH, Montgomery DC, Anderson-Cook CM. (2016). Response Surface Methodology (4th ed.). Wiley. ISBN: 978-1-118-91601-8.
[5] Plackett RL, Burman JP. (1946). The design of optimum multifactorial experiments. Biometrika, 33(4), 305–325.
[6] ISO 5725-1:2023. Accuracy of measurement methods and results. Geneva: ISO.
03 — Implementation Protocol
DOE Pipeline in Industrial
Environments
OphirIAn developed a five-phase DOE implementation pipeline that combines scientific rigor
with real operational constraints in Colombian industrial plants: variable equipment,
limited historical data, and operators without formal statistical training.
01
Problem and Variable Definition
Identify response variable (Y) through process analysis and VOC (Voice of the Customer). Map controllable factors, noise sources, and operational constraints. Validate the measurement system with R&R studies (Repeatability & Reproducibility) under MSA (Measurement System Analysis). Without a reliable measurement system, any DOE will produce misleading conclusions.
Deliverable: MSA Report + Variable Map
02
Screening and Pre-Experiment
For processes with more than 5 potential factors, a screening design (Plackett-Burman or Resolution III fractional factorial) is applied to identify the vital few (effect Pareto). This phase reduces the experimental space by 60-80% before formal optimization, preserving critical resources in MSME environments.
Design: Plackett-Burman / 2k-p Res. III
03
Design and Execution of the Main Experiment
Build the optimal design with identified significant factors. Fully randomize run order to control confounding. Add blocks for uncontrollable noise factors (shifts, lots, operators). Add replicates to estimate pure experimental error. Execute with real-time statistical process control (SPC).
Standard: ASTM E2281 / ISO 3534-3
04
Statistical Analysis and Modeling
Use multifactor ANOVA with assumption checks (Shapiro-Wilk normality, Levene homogeneity, DW independence). Build polynomial regression models. Perform cross-validation and residual analysis. For nonlinear behavior: use robust regression (Huber) or Gaussian Process-based models when response space is complex.
Software: R/Python + Minitab/JMP
05
Optimization and Verification
Locate optimum using desirability functions (Derringer & Suich, 1980) for multi-response settings. Confirm experimentally with verification runs (minimum n=5). Run sensitivity analysis and 95% confidence intervals around predicted optimum. Standardize and statistically control the optimal operating point.
Deliverable: Operating Protocol + SPC Chart
[7] Derringer G, Suich R. (1980). Simultaneous optimization of several response variables. Journal of Quality Technology, 12(4), 214–219.
[8] ASTM E2281-15. (2015). Standard Practice for Process and Measurement Capability Indices. ASTM International.
[9] ISO 3534-3:2021. Statistics — Vocabulary and symbols — Part 3: Design of experiments. Geneva: ISO.
[10] Automotive Industry Action Group (AIAG). (2010). Measurement Systems Analysis (MSA) Reference Manual (4th ed.).
04 — ML Integration
DOE + Machine Learning:
The Hybrid Paradigm
The current methodological frontier in industrial optimization combines classical DOE with
machine-learning methods to overcome limitations in high-dimensional spaces, complex nonlinear
relationships, and noisy process data. This hybrid paradigm, known as
Model-Based Design of Experiments (MBDoE), is central to the OphirIAn approach.
Shahriari et al. (2016), in Bayesian Optimization (IEEE Proceedings), and Snoek et al. (2012)
showed that Bayesian optimization with Gaussian Processes outperforms classical DOE in
continuous parameter spaces with 5+ factors, reducing required evaluations
by up to 70% to reach global optima while estimating predictive uncertainty simultaneously.
Classical DOE Approach
Strengths: Confounding control, efficient main-effect estimation,
solid statistical grounding, direct interpretability.
Limitations: Linearity assumptions, combinatorial explosion in high dimensions,
discretized response curves.
ML / Bayesian Approach
Strengths: Nonlinearity handling, sequential updates (active learning),
uncertainty estimation, high-dimensional capability.
Limitations: Requires more initial data, lower causal interpretability,
overfitting risk without regularization.
Integrated OphirIAn Pipeline
Phase 1: DOE screening (Plackett-Burman) -> identify vital factors.
Phase 2: Centered factorial RSM -> build base polynomial model.
Phase 3: Gaussian Process Regression on residuals -> capture nonlinearities.
Phase 4: Bayesian optimization with acquisition function (EI / UCB) -> explore global optimum.
Phase 5: Experimental confirmation + SPC control -> transfer to production.
Classical DOE is the map;
machine learning is the real-time navigator.
[11] Shahriari B et al. (2016). Taking the Human Out of the Loop: A Review of Bayesian Optimization. Proc. IEEE, 104(1), 148–175. doi:10.1109/JPROC.2015.2494218
[12] Snoek J, Larochelle H, Adams RP. (2012). Practical Bayesian Optimization of Machine Learning Algorithms. NeurIPS 2012.
[13] Gregorutti B et al. (2017). Correlation and variable importance in random forests. Stat Comput, 27, 659–678.
[14] Forrester AIJ, Keane AJ. (2009). Recent advances in surrogate-based optimization. Prog Aerosp Sci, 45(1-3), 50–79.
[15] Garud SS et al. (2017). Design of computer experiments: A review. Comput Chem Eng, 106, 71–95.
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