{"id":4658,"date":"2026-08-12T16:59:38","date_gmt":"2026-08-12T14:59:38","guid":{"rendered":"https:\/\/ellistat.com\/?post_type=guide-dutilisateur&p=4658"},"modified":"2026-08-12T16:59:38","modified_gmt":"2026-08-12T14:59:38","slug":"response-surface","status":"publish","type":"guide-dutilisateur","link":"https:\/\/ellistat.com\/en\/guide-dutilisateur\/surface-de-reponse\/","title":{"rendered":"Response surface methodology (RSM)"},"content":{"rendered":"

This is the page for the full quadratic modeling<\/strong> : linear effects, interactions, and squares. This method alone makes it possible to locate an optimum within the domain and estimate its position.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The factors must be\u00a0quantitative<\/strong>, the page displays \u00abFactors must be quantitative\u00bb if a value is not numeric, and their number is\u00a0limited to 6<\/strong>. Beyond that, no tables are provided.<\/p>\n\n\n\n

1. Available tables<\/h2>\n\n\n\n
Table<\/strong><\/td>What She Is<\/strong><\/td>Quality<\/strong><\/td><\/tr><\/thead>
composite<\/strong><\/td>Centered composite design: factorial, star-shaped, and central points. The standard.<\/td>*****<\/td><\/tr>
Behnken Box<\/strong><\/td>Edge centers of the domain. Avoid simultaneous extreme combinations.<\/td>***<\/td><\/tr>
Hoke D1 \/ D4 \/ D6<\/strong><\/td>Economic designs with a small number of trials.<\/td>****<\/td><\/tr>
Hybrid A \/ B<\/strong><\/td>Very cost-effective plans for 3 and 4 factors.<\/td>***<\/td><\/tr>
DSD3 \u2026 DSD8<\/strong><\/td>Definitive Screening Designs, used here in modeling.<\/td>****<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The list depends on the number of factors: composite and Hoke designs with 2 factors; DSD, hybrid, and Box-Behnken designs with 3 and 4 factors; and Hoke and Box-Behnken designs with 5 and 6 factors.<\/p>\n\n\n\n

\ud83d\udca1 Box-Behnken rather than composite<\/strong> when extreme combinations are impossible or dangerous: maximum temperature and<\/strong> maximum pressure at the same time. Box-Behnken never visits two extremes simultaneously, whereas the composite method even goes beyond the boundaries of the cube (or hypercube) with its star-shaped points.<\/p>\n\n\n\n

2. The two composite settings<\/h2>\n\n\n\n

The composite view, and only the composite view, displays two settings:<\/p>\n\n\n\n

    \n
  • Number of central points<\/strong>\u00a0; <\/li>\n\n\n\n
  • Cube-to-Sphere Ratio<\/strong>\u00a0(\u03b1): the distance of the points in the star, in coded units. When \u03b1 = 1, the star is placed on the faces of the cube; when \u03b1 > 1, it is placed beyond the cube.<\/li>\n<\/ul>\n\n\n\n

    Ellistat calculates and displays the default values<\/strong> below the fields, recalculated each time the number of factors changes:<\/p>\n\n\n\n

    Factors<\/strong><\/td>Key Points<\/strong><\/td>Cube-to-Sphere Ratio<\/strong><\/td><\/tr><\/thead>
    2<\/td>5<\/td>1,414<\/td><\/tr>
    3<\/td>6<\/td>1,682<\/td><\/tr>
    4<\/td>7<\/td>2<\/td><\/tr>
    5<\/td>6<\/td>2<\/td><\/tr>
    6<\/td>9<\/td>2,28<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    \u26a0\ufe0f These values provide a plan\u00a0rotation-invariant<\/strong>\u00a0: The prediction accuracy depends only on the distance from the center, not on the direction. It is acceptable to adjust these parameters\u2014in particular, setting \u03b1 to 1 when the star-shaped points would extend beyond the physically feasible domain\u2014but doing so causes us to lose this property, and the accuracy becomes better in some directions than in others.<\/p>","protected":false},"featured_media":0,"menu_order":80,"template":"","meta":{"_acf_changed":true},"menu-guide-dutilisateur":[24],"class_list":["post-4658","guide-dutilisateur","type-guide-dutilisateur","status-publish","hentry","menu-guide-dutilisateur-7-doe-plans-dexperiences"],"acf":[],"yoast_head":"\nSurface de r\u00e9ponse - Ellistat<\/title>\n<meta name=\"description\" content=\"Mod\u00e9lisez interactions et courbure, trouvez l'optimum de votre process avec un plan composite, Box-Behnken ou Hoke, adapt\u00e9s \u00e0 vos contraintes de domaine.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ellistat.com\/en\/users-guide\/response-surface\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Surface de r\u00e9ponse - 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