Developer Tutorial: Using JMP to Create Orthogonal Mixed-level Screening Designs

Orthogonal Mixed-level Screening Designs introduced in JMP 18 are useful for JMP DOE users who need to test the effectiveness of many interventions simultaneously in a single experiment with minimal runs. See how to use JMP 18 orthogonal mixed-level screening designs to mix continuous and two-level categorical factors and use special constructions for mixed-level screening designs where continuous factors have some levels at the center. The three-level factors must be continuous, and the two-level factors can be either continuous or categorical. Additionally, these designs supply substantial bias protection of the main effects estimates due to active two-factor interactions.

The video includes a discussion with Tom Donnelly  @tom_donnelly  (~ time 49:24) about JMP design choices related to orthogonal mixed-level designs.  Tom's slides are included in the attachments to this video post.

See how to:

• Find the designs in JMP using DOE->Classical->Factor Screening->Screening Design path
• Understand the motivation for Orthogonal Mixed-Leve Designs
  • Main effects screening primary goal
  • Mix of three-level and two-level factors
  • Three-level factors are continuous (we’re not looking for balance)
  • Almost as many factors as runs (saturated, main effects screening), to 3/4 run size
  • DSD-like, but with more 2-level factors
• Understand and view demo of Method/Option 3, where n is a multiple of 16
• Understand and view demo of Method/Option 2, where n is a multiple of 8
• Understand and view demo of Method/Option 1, where n is a multiple of 2
• Delve into issues
  • Screening important factors, DSD too expensive, not all 3-levels
  • Detecting LARGE quadratics
  • Determining how much to go after quadratics

Resources

• Choosing the Right Design - with an Assist from JMP's Design Explorer, white Paper by Christine Anderson Cook
• Ares, Jose Nunez, Eric Schoen, and Peter Goos (2023). “Orthogonal minimally aliased response surface designs for three-level quantitative factors and two-l...”. In: Statistica Sinica.
• Jones, B., Lekivetz, R., Majumdar, D, and Nachtsheim, C.J. (2024) "Screening designs for continuous and categorical factors". To appear in Technometrics.
• Jones, B., Lekivetz, R., & Nachtsheim, C. (2023). “A family of orthogonal main effects screening designs for mixed-level factors”. Journal of Quality Technology, 55(5), 527-534.
• Jones, Bradley and Christopher J. Nachtsheim (Apr. 2013). “Definitive Screening Designs with Added Two-Level Categorical Factors”. In: Journal of Quality Technology 45.2, pp. 121–129.
• Jones, Bradley and Christopher J. Nachtsheim (Jan. 2011). “A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects”. In: Journal of Quality Technology 43.1, pp. 1–15.
• Lekivetz, R., Sitter, R., Bingham, D., Hamada, M. S., Moore, L. M., & Wendelberger, J. R. (2015).”On algorithms for obtaining orthogonal and near-orthogonal arrays for main-effects screening”. Journal of Quality Technology, 47(1), 2-13.
• Nachtsheim, Abigael C., Weijie Shen, and Dennis K. J. Lin (Apr. 2017). “Two-Level Augmented Definitive Screening Designs”. In: Journal of Quality Technology 49.2, pp. 93–107.
• Nguyen, Nam-Ky, Tung-Dinh Pham, and Phuong Vuong Mai (Jan. 2020). “Constructing D-Efficient Mixed-Level Foldover Designs Using Hadamard Matrices”. In: Technometrics 62.1, pp. 48–56.
• Taguchi, Genichi (Jan. 1987). The System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs. English. 1st edition. White Plains, N.Y. Dearborn, Mich: Quality Resources.