Factorial Design ; Modern Pharmaceutics; M. Pharmacy- 1st Semester (Pharmaceutics)

1. GURU GOBIND SINGH COLLEGE OF PHARMACY
Presented To: Dr. Priyanka Kriplani
Presented By: Prabhjot Kaur
M-507
FACTORIAL DESIGN
FACTORIAL
DESIGN

2. CONTENT
Introduction
1
Types Of Factorial Design
2
Factorial Design Advantages and Disadvantages
3
4
References
5
Factorial Design Applications

3. Introduction
• Optimisation Techniques
Optimization is choosing the best element from some set of available alternative. It is
the process of finding the best way of using the existing resources while taking in to
account all the factors that influence decision in any experiment. It is used for quality
selection.
• Factorial Design
Factorial design is an experiment which consist of two or more factors each with
different possible values or levels. It was introduced by fisher in 1926. It is applied in
optimization techniques.

4. Introduction
• Factorial Design
- By a factorial design , it is meant that in each complete trial or replication of the
experiment all possible combination of the levels of the factors are investigated.
- Eg: This is an example of a 2×2 factorial design because there are two independent
variables, each with two levels:
Dependent variable: Plant Growth
Independent variable #1: Sunlight
Levels: Low, High
Independent variable #2: Watering Frequency
Levels: Daily, Weekly

5. Terms Related to Factorial Design
Factors : The term factor is broadly used to include the independent variable that is manipulated
by the investigator in the experiment or that is manipulated through selection.
Main Effect : This is the simplest effect of a factor on a dependent variable. It is the effect of the
factor alone averaged across the level of other factors.
Interaction : When the effect of one independent variable depends on the level of another
independent variable. Types of interactions include: Antagonistic, Synergistic and Celling effect
interaction.
Randomisation : Randomisation is the process by which experimental units are allocated to
treatment; that is by a random process and not by any subjective process. The treatment should be
allocated to units in such a way that each treatment is equally likely to be applied to each unit.
Blocking: This is the procedure by which experimental units are grouped into homogenous cluster
in an attempt to improve the comparison of treatment by randomly allocating the treatment within
each cluster or block.

6. Types Of Factorial Design
Full Factorial and fractional factorial designs are two common methods of design of experiments
(DOE) in industrial engineering. DOE is a systematic approach to plan, conduct, and analyze
experiments that involve multiple factors and responses.
Full Factorial Design Fractional Factorial Design
- A design in which every setting of
every factor appears with setting of
every other factor is full factorial
design.
- If there is k factor, each at Z level,
a full FD has Zk.
- Number of runs (N) = y x
where , y = number of levels,
x = number of factors
E.g. 3 Factors, 2 levels each 23= 8
-In full FD, as a number of factor or
level increases ,the number of
experiment required exceeds to
unmanageable levels. In such cases ,
the number of experiment can be
reduced systematically and resulting
design is called as Fractional
Factorial Design (FFD).
-Applied if no. of factors are more
than 5.

7. Full Factorial Design Types
Two Levels Full FD
2 Factors: X1 and X1 (Independent variables)
2 levels : Low and High
Coding : (-1),(+1)
22 = 4 Runs
FACTORS INTERACTIONS
Runs tc A B AB
1 (1) -1 -1 +1
2 a +1 -1 -1
3 b -1 +1 -1
4 ab +1 +1 +1

8. Full Factorial Design Types
Three level Full FD
3 factors: X1, X 2and X3 3 levels : low(-1), intermediate (0), high (+1)
32= 8 Runs
FACTORS INTERACTIONS
Runs tc A B C AB AC BC ABC
1 (1) -1 -1 -1 +1 +1 +1 -1
2 a +1 -1 -1 -1 -1 +1 +1
3 b -1 +1 -1 -1 +1 -1 +1
4 ab +1 +1 -1 +1 -1 -1 -1
5 c -1 -1 +1 +1 -1 -1 +1
6 ac +1 -1 +1 -1 +1 -1 -1
7 bc -1 +1 +1 -1 -1 +1 -1
8 abc +1 +1 +1 +1 +1 +1 +1

9. Fraction Factorial Design Types
1. Homogenous fractional
Useful when large number of factors must be screened
2. Mixed level
Useful when variety of factors needed to be evaluated for main effects and higher level interactions
can be assumed to be negligible. Ex-objective is to generate a design for one variable, A, at 2
levels and another, X, at three levels , mixed &evaluated.
3. Box-Hunter
Fractional designs with factors of more than two levels can be specified as homogenous fractional
or mixed level fractional

10. Fraction Factorial Design Types
4. Plackett - Burman
Popular class of screening design. These designs are very efficient screening designs when only the
main effects are of interest. These are useful for detecting large main effects economically,
assuming all interactions are negligible when compared with important main effects. Used to
investigate n-1 variables in n experiments proposing experimental designs for more than seven
factors.
5. Taguchi
It is similar to PBDs. It allows estimation of main effects while minimizing variance.
Taguchi Method treats optimization problems in two categories,
STATIC PROBLEMS: Generally, a process to be optimized has several control factors which
directly decide the target or desired value of the output.
DYNAMIC PROBLEMS: If the product to be optimized has a signal input that directly decides
the output.

11. Advantages and Disadvantages of Factorial Design
Type Advantages Disadvantages
Full Factorial Design More efficient and
informative; more
robust and realistic;
more flexible and
adaptable
Costly; complex
analysis and
interpretation
Fraction Factorial
Design
More economical and
feasible
Complex and technical;
sensitive and
dependent on the
assumptions and
judgments of the
experimenter

12. Applications of Factorial Design
1. Formulation and processing
2. Clinical Chemistry
3. Medicinal chemistry
4. HPLC Analysis
5. Formulation of culture medium in virological studies
6. Study of pharmacokinetic parameters

13. THANK YOU