Optimization involves systematically designing experiments to improve formulations by accounting for all influencing factors. Factorial design is a technique used in optimization that involves studying the effect of multiple factors simultaneously. It depends on factors, their levels, and variables. There are two main types of factorial design: full factorial design and fractional factorial design. Full factorial design tests every combination of factors and levels but becomes impractical with more than 5 factors. Fractional factorial design reduces the number of runs needed to study many factors.

1. To:
Dr. Gururaj S. Kulkarni
Department of Pharmaceutics
MALLIGE COLLEGE OF PHARMACY
By: Manikant Prasad
Shah
Mpharm II Sem.
Concept of Optimization,
Optimization Parameters and
Factorial Design
05-04-20181

2. Optimization Concept:
2
 The term Optimize is defined as to make perfect , effective , or as functional
as possible.
 It is the process of finding the best way of using the existing resources while
taking in to the account of all the factors that influences decisions in any
experiment
 Traditionally, optimization in pharmaceuticals refer to changing one variable
at a time, so to obtain solution of a problematic formulation.
 Modern pharmaceutical optimization involves systematic design of
experiments (DoE) to improve formulation irregularities.
05-04-2018

3.  Optimization is used in pharmacy relative to
formulation and processing .
 It is the process of finding the best way of using the
existing resources while taking in to the account of all
the factors that influences decisions in any
experiment.
 Final product not only meets the requirements from
the bioavailability but also from the practical mass
production criteria. .
In development projects , one generally
experiments by a series of logical steps, carefully
controlling the variables & changing one at a
time, until a satisfactory system is obtained
05-04-20183

4.  Target processing parameters – ranges for each
excipients & processing factors .
Questions optimization requires:
• How we can make Formulation perfect ?
 What should be characteristics?
 What should be the conditions?
05-04-20184

5. Why is Optimization necessary?
5
OPTIMIZATION
Reducing
cost
Safety &
Reducing
error
Reproducib
ility
Save
Time
Primary objective may not be to optimize absolutely but to compromise
effectively & thereby produce the best formulation under a given set of
restrictions .
05-04-2018

6. 6
Formulation and Processing
Clinical Chemistry
Medicinal Chemistry
High Performance Liquid Chromatographic
Analysis
Formulation of Culture Medium in Virological
Studies.
Study of Pharmacokinetic Parameters.
APPLICATIONS:
05-04-2018

7. Terms Used
7
o FACTOR: It is an assigned variable such as concentration , Temperature
etc..,
• Quantitative: Numerical factor assigned to it
Ex- Concentration- 1%, 2%,3% etc.
• Qualitative: Which are not numerical
Ex- Polymer grade, humidity condition etc.
o LEVELS: Levels of a factor are the values or designations assigned to
the factor.
o RESPONSE: It is an outcome of the experiment.
• It is the effect to evaluate.
Ex- Disintegration time.
05-04-2018

8. Terms Used
8
o EFFECT: It is the change in response caused by
varying the levels
 It gives the relationship between various factors
& levels.
o INTERACTION: It gives the overall effect of two
or more variables
Ex- Combined effect of lubricant and glidant on
hardness of the tablet
FACTOR LEVELS
Temperature 300 , 500
Concentration 1%, 2% 05-04-2018

9. Advantages
o Yield the “Best Solution” within the domain of study.
o Require fewer experiments to achieve an optimum
formulation.
o Can trace and rectify problem in a remarkably easier
manner.
9 05-04-2018

10. 05-04-201810

11. Softwares for Optimization
 Design Expert 7.1.3
 SYSTAT Sigma Stat 3.11
 CYTEL East 3.1
 Minitab
 Matrex
 Omega
 Compact 21-Apr-15 O
05-04-201811

12. 05-04-2018
PARAMETERS
PROBLEM TYPE
CONSTRAINED
UNCONSTRAINED
VARIABLES DEPENDENT
INDEPENDENT
Optimization Parameters
12

13. Problem Types
05-04-2018
Unconstrained
• In unconstrained optimization problems there are no restrictions.
• For a given pharmaceutical system one might wish to make the hardest
tablet possible.
• The making of the hardest tablet is the unconstrained optimization problem.
Constrained
• The constrained problem involved in it, is to make the hardest tablet possible,
but it must disintegrate in less than 15 minutes.
13

14. Variables
05-04-2018
• Independent variables : The independent variables are under the control of
the formulator. These might include the compression force or the die cavity
filling or the mixing time.
• Dependent variables : The dependent variables are the responses or the
characteristics that are developed due to the independent variables. The
more the variables that are present in the system the more the
complications that are involved in the optimization.
14

15. Example of Variables
05-04-201815

16.  Once the relationship between the variable
and the response is known, it gives the
response surface as represented in the Fig. 1.
Surface is to be evaluated to get the
independent variables, X1 and X2, which
gave the response, Y. Any number of
variables can be considered, it is impossible
to represent graphically, but mathematically it
can be evaluated.
05-04-201816

17. 05-04-201817

18. Factorial Design (FD)
 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.
 Factors : Factors can be “Quantitative” (numerical
number) or they are qualitative. They may be
names rather than numbers like Method 1, site B,
or present or absent .
05-04-201818

19.  Factorial design depends on independent
variables for development of new formulation .
 Factorial design also depends on Levels as well
as Coding
 There are three types of levels : 1) LOW
2)INTERMEDIATE 3) HIGH
 Simultaneously CODING takes place for Levels :
1) for LOW = (-1)
2)For intermediate = (0)
3) for HIGH =(+1)
05-04-201819

20.  FD is for the evaluation of multiple factors
simultaneously.
 2 3 means 2 is level while 3 is factor .
 Factorial Design is divided into two types
1.Full Factorial Design
2.Fractional factorial design
05-04-201820

21. 1.Full Factorial Design
 A design in which every setting of every factor
appears with setting of every other factor is full
factorial design.
 Simplest design to create, but extremely
inefficient.
 If there is k factor , each at Z level , a Full FD has
ZK
Number of runs (N)
N = y x Where, y = number of levels, x = number of
factors E.g.- 3 factors, 2 levels each, N = 23 = 8
runs 05-04-201821

22.  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
05-04-201822

23. TWO Levels Full FD :
 2 factors : X1 and X2 (Independent variables)
 2 levels : Low and High
 Coding : (-1) , (+1)
Three level Full FD :
In three level factorial design ,
• 3 factors: X1, X2 and X3
• 3 levels are use ,
1) low (-1)
2) intermediate (0)
3) high (+1)
05-04-201823

24. FRACTIONAL FACTORIAL
DESIGN
 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 experiments can
be reduced systemically and resulting design is
called as Fractional factorial design (FFD).
 Applied if no. of factor are more than 5 .
 Means “less than full”
 Levels combinations are chosen to provide
sufficient information to determine the factor
effect
 More efficient
05-04-201824

25. Types of Fractional Factorial
Design
 Homogeneous fractional
 Mixed level fractional
 Plackett-Burman
Homogenous fractional
Useful when large number of factors must be
screened
Mixed level fractional
Useful when variety of factors need to be
evaluated for main effects and higher level
interactions can be assumed to be negligible.
05-04-201825

26. 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
18.03.201826

27. summary
 Factorial design depends on Factors and Levels.
 Factorial design also depends on Variables.
 Factorial design divide in either in Full FD and
Fractional FD (FFD)
 Full FD have two types : Two levels and Three
level Full FD
 Full FD not applicable to factors more than 5.
 Fractional FD overcome on the limitation of Full
FD (applicable to factors more than 5)
05-04-201827

28. Thank you..
05-04-201828