Definitive Screening Design (DSD)

This repository provides a lightweight Python implementation for constructing definitive screening designs with numerical factors and optional two-level categorical factors. A DSD is an economical experimental plan for identifying the few important effects among many candidate factors while retaining information about curvature and selected second-order effects. The package generates the coded run matrix; the accompanying notebooks show how to turn that matrix into a randomized experimental run sheet, assess what a proposed model can estimate before collecting responses, and analyze the responses afterward. DSDs are screening tools rather than automatic model-selection procedures, so conclusions should be checked against subject-matter knowledge and, when necessary, confirmed or refined with augmented experiments.

Why the Definitive Screening Design?

ELI5

Imagine having many knobs and not knowing which ones matter. A DSD tests carefully chosen combinations of low, middle, and high settings so you can find the important knobs - and notice when "more" is not simply better - with relatively few experiments. It is a first-pass map, not a universal recipe: it works best when most knobs are numeric, can be adjusted independently, and only a few effects are important.

ELI Scientist/Engineer

A DSD is an economical early-stage experiment for screening several factors, especially continuous ones. The three levels expose curvature while the design keeps estimates of main effects clear of bias from two-factor interactions and quadratic effects; a classical DSD for m continuous factors needs only 2m + 1 runs. It can also accommodate a few two-level categorical factors. Use another design when the region is constrained, factors form a mixture, many factors are categorical, a split-plot structure is required, or higher-order effects are expected.

ELI Statistician

DSDs combine foldover pairs with a center run to produce a second-order-friendly screening design. Linear main effects are mutually orthogonal and orthogonal to quadratic effects and two-factor interactions; all pure quadratics are estimable, and no two-factor interaction is completely confounded with another interaction or a quadratic, although such terms may be correlated. This alias structure supports joint screening for active first- and second-order terms under effect sparsity, but model selection degrades as the number of active terms approaches the run count; augmentation is advisable when many terms may be active or reliable second-order identification is the goal.

Main References

• Bradley Jones and Christopher J. Nachtsheim. "A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects" Journal of Quality Technology (2011) 43, 1–15. 10.1080/00224065.2011.11917841
• Lili Xiao, Dennis K. J. Lin, Fenghan Bai, "Constructing Definitive Screening Designs Using Conference Matrices" Journal of Quality Technology (2012) 44, 2-8. 10.1080/00224065.2012.11917877
• Bradley Jones and Christopher J. Nachtsheim. "Definitive screening designs with added two-level categorical factors" Journal of Quality Technology (2013) 45, 121-129. 10.1080/00224065.2013.11917921

Further References about the practical use of this design

• Bradley Jones - "Simulating Responses and Fitting Definitive Screening Designs"
• Bradley Jones - "Proper and Improper use of Definitive Screening Designs"
• Douglas Montgomery - Coursera lesson on "General Structure of a DSD with m Factors"
• Paul Nelson - "The Evolution of Definitive Screening Designs from Optimal (Custom) DoE"
• Errore, Jones, Nachtsheim (2016) - "Using Definitive Screening Designs to Identify Active First- and Second-Order Factor Effects"
• Jones, Nachtesheim (2017) "Effective Design-Based Model Selection for Definitive Screening Designs"
• Weese, Ramsey, Montgomery (2018) - "Analysis of definitive screening designs: Screening vs prediction"
• Other applications of the DSD from Google Scholar, Semantic Scholar, Web Of Science

Installation

pip install definitive_screening_design

Example

Generate a Definitive Design screening with three numerical and two 2-levels categoricals factors, using the protocol presented in the 2013 paper. The result is a Pandas DataFrame.

import definitive_screening_design as dsd
dsd.generate(n_num=3, n_cat=2)

See notebooks/ for examples using this package and notebooks_pydoe/ for paired examples using pydoe's DSD implementation. Both sets explain how design rows translate into experimental run sheets and distinguish design analysis from response-model selection.