Optimization techniques

1. Presented by :
PRASHIK S SHIMPI
M. Pharm 2nd Semester
Department of Quality Assurance
R.C.Patel Institute of Pharmaceutical
Education & Research, Shirpur.
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2. Contents
 Introduction
 Optimization parameters
 Classic optimization
 Optimization methods
 Application
 Reference
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3. Introduction
 Optimize:
To make as perfect, effective or functional as possible.
 Optimization :
It is the process of finding the best way of using the existing
resources while taking into account all of the factors that
influence decisions in any experiment.
 The composition of pharmaceutical formulation is often subject
to trial & error.
 Optimization by means of an experimental design may be
helpful in shortening the experimenting time.
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4. Optimization Parameters
A. Problem type
i) Constrained – Restrictions placed on the system due to
physical limitations or perhaps due to simple practicality.
ii) Unconstrained- No restrictions, but almost nonexistent in
pharmaceuticals.
B. Variable type
i) Independent variable:-
ii) Dependent variable:-
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5. Classic Optimization
 Result from application of calculus to the basic problem of
finding the maximum or minimum of a function.
 Useful for problems that are not too complex and do not
involve more than a few variables.
 Y=f (X)
 Y=f(X1, X2)
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6. Input Real System Output
Response
Mathematical
Model of
System
Input Factor
Levels
Optimization
Procedure
Applied Optimization Methods
 These general optimization techniques can be described
by following flowchart-
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7. Design of experiment
 Factorial designs
 Full Factorial designs
 Fractional Factorial designs
 Plackett-Burman design
 Response surface(second order) designs
• Central Composite designs
• Box-Behnken designs
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8. Factorial Design
 A full factorial design for n factors requires runs; with 10
factors that would mean 1024 runs!
 In fractional factorial designs the number of runs N is a power
of 2 (N = 4, 8, 16, 32, and so forth)
 In Plackett-Burman designs the number of runs N is a multiple
of 4 (N = 4, 8, 12, 16, 20, 24, and so forth)
 Plackett-Burman designs fill in the gaps in the run sizes
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9. Factorial Experiments
3-FACTOR
 3 main effects
(A, B, C)
 3, 2-way Interactions
A X B, A X C, B X C
 1, 3-way Interaction
A X B X C
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4-FACTOR
 4 main effects
(A, B, C, D)
 6, 2-way Interactions
A X B, A X C, A X D,
B X C, B X D, C X D
 4, 3-way Interactions
A X B X C, A X B X D,
A X C X D, B X C X D
 1, 4-way Interaction
A X B X C X D

10. - 23 level Factorial Design
- Full / Fractional Factorial Design
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2 level Full Factorial Design Fractional Factorial Design
Classifications
x1 x1
x2
x2
x3 x3
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11. Plackett-Burman Design
 Plackett and Burman (1946) showed how full factorial designs
can be fractionalized in a different manner than traditional 2k
fractional factorial designs, in order to screen the max number
of (main) effects in the least number of experimental runs.
 Fractional factorial designs for studying k = N – 1 variables in
N runs, where N is a multiple of 4.
 Only main effects are of interest.
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12. When to use PB designs:
 Screening
 Possible to neglect higher order interactions
 2-level multi-factor experiments.
 More than 4 factors, since for 2 to 4 variables a full factorial
can be performed.
 To economically detect large main effects.
 Particularly useful for N = 12, 20, 24, 28 and 36.
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13. Box-Behnken Design
 Box-Behnken designs are the equivalent
of Plackett-Burman designs for the case
of 3-level multi-factor.
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x1
x2
x3
 When to use Box-Behnken designs:
• With three-level multi-factor experiments.
• When it is required to economically detect large main effects,
especially when it is expensive to perform all the necessary runs.
• When the experimenter should avoid combined factor extremes.
This property prevents a potential loss of data in those cases.

14. Number of runs required by Central
Composite and Box-Behnken designs
Number
of factors
Box Behnken Central Composite
2 - 13 (5 center points)
3 15 20 (6 center point runs)
4 27 30 (6 center point runs)
5 46 33 (fractional factorial) or
52 (full factorial)
6 54 54 (fractional factorial) or
91 (full factorial)
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15. Example: Improving Yield of a
Chemical Process
Factor
Levels
– 0 +
Time (min) 70 75 80
Temperature (°C) 127.5 130 132.5
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16. Use a 23 Factorial Design With
Central Points
Run Factors in original
units
Factors in coded
units
Response
Time(min.)
X1
Temp.(°C)
X2 X1 X2
Yield(gms)
Y
1 70 127.5 - - 54.3
2 80 127.5 + - 60.3
3 70 132.5 - + 64.6
4 80 132.5 + + 68.0
5 75 130.0 0 0 60.3
6 75 130.0 0 0 64.3
7 75 130.0 0 0 62.3
Results From First Factorial Design
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18. Results of Second Factorial Design
Run Factors in original
units
Factors in coded
units
Response
Time(min.)
X1
Temp.(°C)
X2 X1 X2
Yield(gms)
Y
11 80 140 - - 78.8
12 100 140 + - 84.5
13 80 150 - + 91.2
14 100 150 + + 77.4
15 90 145 0 0 89.7
16 90 145 0 0 86.8
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20.  Improve process yield
 Reduce variability
 Reduce development time
 Reduce overall costs
 Evaluate and compare alternatives
 Evaluate material alternatives
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Applications of Optimization Techniques

21. Applications of Optimization Techniques
Optimization techniques are widely used in pharmacy especially
used in-
 Pharmaceutical suspension
 Controlled release formulations
 In tablet coating operation
 In Enteric film coating
 In HPLC analysis
 To study formulation of culture medium in virology
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22. Softwares for Optimization Techniques
 Design Expert 7.1.3
 SYSTAT SigmaStat 3.11
 SPSS 13
 DeltaGraph 5.6
 EquivTest
 PASS 2005 Quickstart manual
 Prism GraphPad 4.03
 CYTEL East 3.1
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23. Reference
1. Banker GS & Rhodes TS. Modern Pharmaceutics. 2nd ed.
vol-40, p. 803-828.
2. Hirmath SR. Industrial Pharmacy. Orient Longman Private
Ltd. p. 158-168.
3. Lewis GA, Roger DM, Phan-Tan-Luu. Pharmaceutical
Experimental Design. vol-92. p.247- 292.
4. Parikh DM. Handbook Of Pharmaceutical Granulation
Technology. vol-81. p.253-258.
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24. 5. Alderborn GF & Nystrom CS. Pharmaceutical Powder
Compaction Technology. vol-71. p.580-590.
6. Banker GS & Rhodes CT. Modern Pharmaceutics.4th ed. Vol-
121, p. 606-625.
7. Bolton SA. Pharmaceutical Statistics Practical & Clinical
Application. 3rd ed. vol-80. p. 590-625.
8. Nielloud F & Marti-Mestres G. Pharmaceutical Emulsion
&Suspensions. vol-105, p.51,540,543,549.
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25. Thank You
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