Factorial Design
PRESENTED BY
MR. SAGAR NAGNATH MORE
ROLL NO – 2406951214817010
F.Y.M PHARM (PHARMACEUTICS)
MANDESH INSTITUTE OF PHARMACEUTICAL SCIENCE
AND RESEARCH CENTER MHASWAD
Presented By
Mr. JADHAV PRADEEP MADHUKAR
Factorial Design
&
It’s Application in Formulation
Introduction to Factorial Design
What is Factorial Design? (DEFINITION)
Factorial design is a powerful statistical technique used to study the effects of
It involves systematically varying each factor at different levels, allowing for the
• OBJECTIVES •
1. Evaluate Multiple Factors: Study the effects of two or more factors (e.g., drug
concentration, pH, temperature) on a pharmaceutical response simultaneously.
2. Identify Interactions: Analyze interactions between factors to understand how
they influence the formulation or process outcomes.
3. Optimize Formulations: Develop optimal drug formulations with improved
efficacy, stability, or release profiles using minimal experiments.
4. Enhance Process Efficiency: Improve manufacturing processes by identifying
key factors that affect quality and performance.
5. Reduce Costs and Time: Minimize experimental runs while obtaining reliable
and comprehensive data for decision-making.
Types of Factorial Design (FD)
# Full Factorial Design (FD):
1. Two-Level Full FD
2. Three-Level Full FD
# Fractional Factorial Design:
1. Homogeneous fractional
2. Mixed-level fractional
3. Box-Hunter
4. Plackett-Burman
5. Taguchi
6. Latin Square
Full Factorial Design
• A design where every factor's settings appear
with every other factor.
• For k factors, each at z levels, Full FD has zk
combinations:
• 22: Two factors, two levels = 4 runs
• 23: Three factors, two levels = 8 runs
• 32: Two factors, three levels = 9 runs
• 33: Three factors, three levels = 27 runs
Two-Level Full Factorial Design
• Two factors: X1 and X2 (independent
variables).
• Two levels: Low (-1) and High (+1).
Three-Level Full Factorial Design
• Three levels: Low (-1), Intermediate (0), High
(+1).
• Written as 3k, where k factors are at three
levels.
• Enables investigation of quadratic
relationships.
Fractional Factorial Designs
• Examines multiple factors efficiently with fewer
runs.
• Types of Fractional Factorial Designs:
1. Homogeneous fractional
2. Mixed-level fractional
3. Box-Hunter
4. Plackett-Burman
5. Taguchi
6. Latin Square
Homogeneous and Mixed-Level And
Box-Hunter Fractional Designs
• Homogeneous: Screens a large number of
factors.
• Mixed-Level: Evaluates a mix of factors
assuming negligible higher-level interactions.
• Box-Hunter: Fractional designs for factors
with more than two levels.
Plackett-Burman Design
• Efficient screening design focusing on main
effects.
• Detects significant main effects economically.
• Suitable for investigating n-1 variables in n
experiments.
Taguchi Method
• Similar to Plackett-Burman designs.
• Treats optimization problems as static or
dynamic:
• - Static: Control factors directly influence
output.
• - Dynamic: Signal inputs decide outputs.
Latin Square Design
• Handles two sources of blocking.
• Requires t2 experimental units for t
treatments.
• Includes randomization restrictions for
precise experimental designs.
Advantages of Factorial Design
1. Allows the study of interaction effects between
factors.
2. Efficient use of experimental runs compared to
one-factor-at-a-time methods.
3. Provides comprehensive information about
factor behavior.
4. Facilitates optimization of multiple factors
simultaneously.
5. Useful for screening important factors in
complex systems.
Disadvantages of Factorial Design
1. Can require a large number of runs for many
factors.
2. Analysis and interpretation become complex
with more factors.
3. Not suitable for factors with insignificant
interactions.
4. May be resource-intensive in terms of time and
cost.
5. Assumes factors are independent, which may
not always be valid.
Applications in Formulation
1. Tablet Formulation:
Optimizing binder, disintegrant, and lubricant concentrations.
Studying the impact of these factors on hardness, friability, and dissolution.
2. Controlled Release Systems:
Analyzing the effects of polymer type, polymer concentration, and plasticizer
level on drug release rate.
3. Nanoformulations:
Optimizing factors like surfactant concentration, sonication time, and stirring
speed for nanoparticle size and stability.
4. Emulsion/Suspension Formulation:
Investigating the influence of surfactants, stabilizers, and homogenization
conditions on stability and particle size.
5. Drug-Excipient Compatibility:
Evaluating how excipient interactions affect stability or bioavailability.
