Some New Three Level Designs for the Study of Quantitative Variables

1960/11/01 by George E. P. Box, G. E. P. Box, D. W. Behnken · 3,882 citations
Decision Sciences · Mathematics · #Artificial intelligence #Class (philosophy) #Computer science #Degree (music) #Factorial #Factorial experiment #Fractional factorial design #Mathematical analysis #Mathematics #Optimal Experimental Design Methods #Polynomial #Statistics

paper · doi:10.1080/00401706.1960.10489912

published in Technometrics 2(4), 455-475 (Taylor & Francis)

openalex publication_date 1960/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

A class of incomplete three level factorial designs useful for estimating the coefficients in a second degree graduating polynomial are described. The designs either meet, or approximately meet, the criterion of rotatability and for the most part can be orthogonally blocked. A fully worked example is included.

Citations

• THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTS

Cited by

• Comprehensive development, uncertainty and sensitivity analysis of a model for the hydrolysis of rapeseed oil
• The Impact of Classifier Configuration and Classifier Combination on Bug Localization
• Integrated RSM and micromechanical RVE–FEA approach for optimizing indentation behavior of HEA-reinforced AA7075 alloy fabricated via friction stir processing
• Optimization of Ultrasound-Assisted Acid Hydrolysis of Total Isoflavones in Radix puerariae Using Response Surface Methodology
• A new approach to the construction of optimal designs
• 11 Response surface designs
• Application of Box—Behnken Design to Modeling the Effect of Smectite Content on Swelling to Hydrocyclone Processing of Bentonites with Various Geologic Properties
• Response surface experiments: A meta-analysis
• Self-Validated Ensemble Models for Design of Experiments
• Optimal Bayesian experimental design for subsurface flow problems
• Effects of abiotic stressors on lutein production in the green microalga Dunaliella salina. [europepmc]
• Influence of surface chemistry on cytotoxicity and cellular uptake of nanocapsules in breast cancer and phagocytic cells. [europepmc]
• Optimization of ultrasound-assisted extraction parameters of chlorophyll from Chlorella vulgaris residue after lipid separation using response surface methodology. [europepmc]
• Optimizing microencapsulation of nisin with sodium alginate and guar gum. [europepmc]
• IPO: a tool for automated optimization of XCMS parameters. [europepmc]
• Development of chitosan based edible films: process optimization using response surface methodology. [europepmc]
• Biodegradation of feather waste keratin by a keratinolytic soil fungus of the genus Chrysosporium and statistical optimization of feather mass loss. [europepmc]
• Effects of nutritional conditions on growth and biochemical composition of Tetraselmis sp. [europepmc]
• Optimization of melanin production by Brevundimonas sp. SGJ using response surface methodology. [europepmc]
• Optimization of rhamnolipid production by Pseudomonas aeruginosa OG1 using waste frying oil and chicken feather peptone. [europepmc]
• High-pressure assisted extraction of bioactive compounds from industrial fermented fig by-product. [europepmc]
• Glucansucrase (mutant) enzymes from Lactobacillus reuteri 180 efficiently transglucosylate Stevia component rebaudioside A, resulting in a superior taste. [europepmc]
• Optimized microwave extraction, characterization and antioxidant capacity of biological polysaccharides from Eucommia ulmoides Oliver leaf. [europepmc]
• Ultrasound-Assisted Extraction of Polysaccharides from Volvariella volvacea : Process Optimization and Structural Characterization. [europepmc]
• Lipids modulate acetic acid and thiol final concentrations in wine during fermentation by Saccharomyces cerevisiae × Saccharomyces kudriavzevii hybrids. [europepmc]
• The application of Box-Behnken-Design in the optimization of HPLC separation of fluoroquinolones. [europepmc]
• A Sight to Wheat Bran: High Value-Added Products. [europepmc]
• Extraction of Metal Ions with Metal-Organic Frameworks. [europepmc]
• Assessment of the heavy metal bioremediation efficiency of the novel marine lactic acid bacterium, Lactobacillus plantarum MF042018. [europepmc]
• In vitro dual (anticancer and antiviral) activity of the carotenoids produced by haloalkaliphilic archaeon Natrialba sp. M6. [europepmc]
• Optimization of Mesoporous Silica Nanoparticles through Statistical Design of Experiment and the Application for the Anticancer Drug. [europepmc]
• Simultaneous bioremediation of cationic copper ions and anionic methyl orange azo dye by brown marine alga Fucus vesiculosus. [europepmc]
• Lipid-Based Nanocarriers for Ophthalmic Administration: Towards Experimental Design Implementation. [europepmc]
• Biological treatment of hazardous heavy metals by Streptomyces rochei ANH for sustainable water management in agriculture. [europepmc]
• Polyaniline/Biopolymer Composite Systems for Humidity Sensor Applications: A Review. [europepmc]

Related

• Construction of Blocked Factorial Designs to Estimate Main Effects and Selected Two-Factor Interactions
• Indicator function and complex coding for mixed fractional factorial designs
• Generation of Fractional Factorial Designs
• The algebraic method in experimental design
• Characterizations of indicator functions and contrast representations of fractional factorial designs with multi-level factors