# 3² full factorial design.pptx

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### 3² full factorial design.pptx

• 1. 3² FULL FACTORIAL DESIGN Presented By:- Jeel Parag Joshi Enrollment No. :- 222770820005 M Pharm Sem III SAL INSTITUTE OF PHARMACY
• 2. CONTENTS LIST  Introduction​ / Summary of Factorial Designs  What are Factorial Designs?  Process and Strategies Of using Factorial Designs  Design Of Experiments  Experimental Runs  Design Space  Final Polynomial Equation  Glance about Quadratic Equation
• 3. INTRODUCTION 3 Factorial Design is an approach that is used to minimize the following:- Experimental Runs Minimize Manpower Money And helps in:- Optimization of batches & Saves Time
• 4. WHAT ARE FACTORIAL DESIGNS FACTORIAL DESIGNS:- These are the designs of choice for the simultaneous determination of the effects of several factors and their interactions. Symbols to denote levels are:- When both variables are in low concentration  a- one low variable and second high variable  b- one high variable and second low variable  ab- both variables are high  Eg: Factorial designs are optimal to determine the effect of pressure and lubricant on the hardness of a tablet  Eg: Effect of disintegrant & lubricant conc. On tablet dissolution  Eg: It is based on the theory of probability and test of significance.
• 5. PROCESSES AND STRATEGIES USED IN FACTORIAL DESIGN 1. Problem Defination 2. Selectiion of factor and levels 3. Design of experiment protocol 4. Conduct Experiment and collect data 5. Analyse Data 6. Interpret Data 7. Prediction of optimum formula 8. Validation of optimisation
• 6. DESIGN OF EXPERIMENTS 3² FACTORIAL DESIGNS 6 Example:- How the effect of Dispersion Time and Disintegration Time impacts on the Dispersion and Disintegration Rate of ORO DISPERSIBLE TABLET (At 3 Levels and 2 Factors) FACTORS COMPOUNDS LEVEL (-1) LEVEL (0) LEVEL (+1) Concentration of Diluent Cross Carme lose Sodium 150mg 175mg 200mg Super Disintegrant Micro Crystalline Cellulose 25 mg 50 mg 75 mg
• 7. 7 RUNS Diluent Concentration Disintegrant Concenteration 1 -1 -1 2 0 -1 3 +1 -1 4 -1 0 5 0 0 6 +1 0 7 -1 +1 8 0 +1 9 +1 +1 EXPERIMENTAL RUNS
• 8. DESIGN SPACE 8 Design space of 3 ² FULL FACTORIAL DESIGN D I S P E R S I O N T I M E DISINTEGRATION TIME -1,+1 +1,+1 +1,-1 -1,-1 -1,0 +1,0 0,+1 0,0 0,-1
• 9. POLYNOMIAL EQUATION 9 Y= Ƀo+ B₁X₁+B₂X₂+B₃X₃+B₁₂X ₁₂+B ₁ ₃X ₁ ₃ +B ₂₃ X ₂₃+ B ₁₁X ₁²+ B ₂₂X ₂² Y= Results/Responses B ₀= Intercept B₁ = Coefficient of variable X₁ B₂= Coefficient of variable X₂ B₃= Coefficient of variable X₃ B₁₂X ₁₂= Interaction Effects between variables X₁ & X₂ B ₁₃ x ₁₃ = Interaction Effects between variables X ₁ & X ₃ B ₁₁X ₁²+ B ₂₂X ₂²= Quadratic Equation
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