Factorial Design:- It identifies the chance variation ( present in the process due to accident) and the assignable variations ( which are due to specific cause.) • Factorial design are helpful to deduce IVIVC. • IVIVC are helpful to serve a surrogate measure of rate and extent of oral absorption. • BCS classification is based on solubility and permeability issue of drugs, which are predictive of IVIVC. • Sound IVIVC omits the need of bioequivalence study. • IVIVC is predicted at three levels: • Level A- point to point relationship of in vitro dissolution and in vivo performance. • Level B- mean in vitro and mean in vivo dissolution is compared and co-related. • Level C- correlation between the amount of drug dissolved at one time and one pharmacokinetic parameter is deduced. TYPES OF FACTORIAL DESIGN (FD) 1. Full Factorial Design(FD) a. Two Levels Full FD b. Three level Full FD 2. Fractional Factorial Design a. Homogenous fractional b. Mixed level fractional c. Box-Hunter d. Plackett - Burman e. Taguchi f. Latin square Full 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 (Levels)factor zk Factorial Design :22 23 32 33 22 FD = 2 Factors , 2 Levels = 4 runs 23 FD = 3 Factors , 2 Levels = 8 runs 32 FD = 2 Factors , 3 Levels = 9 runs 33 FD = 3 factors , 3 Levels = 27 runs • TWO Levels Full FD : 2 factors : X1 and X2 (Independent variables) 2 levels : Low and High + - Coding : (-1) LOW , (+1) HIGH Three level Full FD : In three level factorial design , three levels are use , 1) low (-1) 2) intermediate (0) 3) high (+1) • It is written as 3k factorial design. • It means that k factors are considered each at 3 levels. • These are usually referred to as low, intermediate • & high values. • These values are usually expressed as 0, 1 & 2 • The third level for a continuous factor facilitates investigation of a quadratic relationship between the response and each of the factors Factorial Design :22 23 32 33 22 FD = 2 Factors , 2 Levels = 4 runs 23 FD = 3 Factors , 2 Levels = 8 runs 32 FD = 2 Factors , 3 Levels = 9 runs 33 FD = 3 factors , 3 Levels = 27 runs • TWO Levels Full FD : 2 factors : X1 and X2 (Independent variables) 2 levels : Low and High + - Coding : (-1) LOW , (+1) HIGH Three level Full FD : In three level factorial design , three levels are use , 1) low (-1) 2) intermediate (0) 3) high (+1) • It is written as 3k factorial design. • It means that k factors are considered each at 3 levels. • These are usually referred to as low, intermediate • & high values. • These values are usually expressed as 0, 1 & 2 • The third level for a continuous factor facilitates investigation of a quadratic relationship between the response and each of the factors Homogenous fractional • Useful when large number of factors must be screened Mixed level fractional • Useful when variety of factors needed to be evaluated fo

1. Contents
• INTRODUCTION
• TYPES OF FACTORIAL DESIGN (FD)
• APPLICATION
• SUMMARY

2. INTRODUCTION
• Factorial experiment is an experiment whose
design consist of two or more factor each with
different possible values or “levels”.
• FD technique introduced by “Fisher” in 1926.
• Factorial design applied in optimization
techniques.
• Effect of disintegrant & lubricant conc . on tablet
dissolution .
• It is based on theory of probability and test of
significance

3. • It identifies the chance variation ( present in the process
due to accident) and the assignable variations ( which
are due to specific cause.)
• Factorial design are helpful to deduce IVIVC.
• IVIVC are helpful to serve a surrogate measure of rate
and extent of oral absorption.
• BCS classification is based on solubility and permeability
issue of drugs, which are predictive of IVIVC.
• Sound IVIVC omits the need of bioequivalence study.
• IVIVC is predicted at three levels:
• Level A- point to point relationship of in vitro
dissolution and in vivo performance.
• Level B- mean in vitro and mean in vivo dissolution is
compared and co related.
• Level C- correlation between amount of drug dissolved
at one time and one pharmacokinetic parameter is
deduced.

4. BCS classification and its expected
outcome on IVIVC for Immediate
release formulation
BCS Class Solubility Permeability IVIVC
I High High Correlation( if
dissolution is rate
limiting
II Low High IVIVC is expected
III High Low Little or no IVIVC
IV Low Low Little or no IVIVC

5. TYPES OF FACTORIAL DESIGN (FD)
1. Full Factorial Design(FD)
a. Two Levels Full FD
b. Three level Full FD
2. Fractional Factorial Design
a. Homogenous fractional
b. Mixed level fractional
c. Box-Hunter
d. Plackett - Burman
e. Taguchi
f. Latin square

6. Full 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
(Levels)factor zk

7. • Factorial Design :22 23 32 33
22 FD = 2 Factors , 2 Levels = 4 runs
23 FD = 3 Factors , 2 Levels = 8 runs
32 FD = 2 Factors , 3 Levels = 9 runs
33 FD = 3 factors , 3 Levels = 27 runs
• TWO Levels Full FD :
2 factors : X1 and X2 (Independent variables)
2 levels : Low and High + -
Coding : (-1) LOW , (+1) HIGH +
- -
++ +-
-+ --

8. Three level Full FD :
In three level factorial design ,
three levels are use ,
1) low (-1)
2) intermediate (0)
3) high (+1)
• It is written as 3k factorial design.
• It means that k factors are considered each at 3
levels.
• These are usually referred to as low, intermediate
• & high values.
• These values are usually expressed as 0, 1 & 2
• The third level for a continuous factor facilitates
investigation of a quadratic relationship between the
response and each of the factors

9. Factorial design
• These are the designs of choice for simultaneous determination of
the effects of several factors & their interactions.
• Used in experiments where the effects of different factors or
conditions on experimental results are to be elucidated.
 FRACTIONAL FACTORIAL DESIGNS
• It is used to examine multiple factors efficiently with fewer
runs than corresponding full factorial design
• Type of fractional factorial designs
 Homogenous fractional
 Mixed level
 Box-Hunter
 Plackett - Burman
 Taguchi
 Latin squares

10. Homogenous fractional
• Useful when large number of factors must be
screened
Mixed level fractional
• 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.
 Box-hunter
• Fractional designs with factors of more than two
levels can be specified as homogenous fractional or
mixed level fractional

11. Plackett-Burman
• It is a 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.

12. 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

14. APPLICATIONS:
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