# Box Behnken Design

Information about Box Behnken Design

Published on July 8, 2014

Author: director.anilsolanki

Source: authorstream.com

Box Behnken Statistical Design Dr. Anil Solanki, Professor APMC College of Pharmaceutical Edudation & Research, Himatnagar. Gujarat. India: Box Behnken Statistical Design Dr. Anil Solanki , Professor APMC College of Pharmaceutical Edudation & Research, Himatnagar. Gujarat. India Introduction: Introduction Box Behnken design is an experimental design derived by George Box and Donald Behnken in 1960 Itâ€™s a response surface approch As the no. of factor increases so does the complexity of the model equation and because of more eloborate experimental design needed. BBD is Ideal choice in this situation Box Behnken specially selected as:: Box Behnken specially selected as: It require fewer experiment run (15 run for 3 factors) Most effective technique Use to optimize the main effect, interaction effect and quadratic effect. Require minimum 3 factors and 3 levels Box Behnken design: Box Behnken design Design factor for 3 factor 3 level: Design factor for 3 factor 3 level Experiments X1 X2 X3 Remarks 1 -1 -1 0 2 2 full factorial design for X1 and X2 variable 2 +1 -1 0 3 -1 +1 0 4 +1 +1 0 5 -1 0 -1 2 2 full factorial design for X1 and X2 variable 6 +1 0 -1 7 -1 0 +1 8 +1 0 +1 9 0 -1 -1 2 2 full factorial design for X1 and X2 variable 10 0 +1 -1 11 0 -1 +1 12 0 +1 +1 13 0 0 0 Central Point replicated three times 14 0 0 0 15 0 0 0 Number of experiments (N): Number of experiments (N) The no. of experiments (N) required for the development of BBD is N= 2k (k-1) + C0 Where k = No. of factors C0 = No. of center points (3 in BBD) PowerPoint Presentation: No. of Factors (k) Runs 3 15 4 27 5 43 6 63 Mathematical Model: Mathematical Model Y = B0 +B1X1 +B2X2+B3X3(Main Effect) +B12X1X2+B13X1X3+B23X2X3+B123X1X2X3 (Interaction Effect) +B11X1 2 + B22X2 2 + B33X3 2 (Quadratic effect) + E (error) Y= Measured response