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

10. THANK YOU