FACTORIAL DESIGN
DEPARTMENT OF PHARMACEUTICS AND PHARMACEUTICAL TECHNOLOGY,L.M.COLLEGE OF PHARMACY, AHMEDABAD.
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Research Process:
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Require intelligence planning and approach.
Research scientist Against
the Person who Invest in Stock Market,.,.
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Traditional Trend Randomized fashion of research Required More number of trials..,
Take more time Cant predict the extension… i.e. cant say what happen if such change are made within
that particular system.
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e.g. In process of Extrusion Spheronization,
Three attributes… Binder (%)
Granulation time (Min) Spheronization speed (RPM)
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No of trials are more.,.,.
Man Money Material Time
And still for output ???We are not sure !!
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Optimization Designing experiments to yield the most information
from the fewest runs Reduce the number of trial to minimum but in
logical manner Carry out research in systematic way
Identify the characteristic you want in your product
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Factorial design Fractional Factorial design
Simplex lattice design Plackett-burman design Central composite design Constrained mixture design
Box Behnken design Face centered cubic design (FCC)
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Basic Terminology:
In scientific language those attributes
are called as variables..
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Significant variableMore important..
Go on changing level..
E.g. Polymer Conc,
Granulation time
Insignificant variableNot that much importance
you can keep it at constant level also..
E.g. Effect of lubricant on floating tablet
Independent variable may positive or negative result on
to the dependent variable
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Also Known as Response variable. Its output of our experiment.
Not limit for dependent variable.
This variable depends on independent variable.
Keep as many as you wish.
e.g. Angle of repose, Disintegration time,
Friability, Hardness.
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LEVEL
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In General Factor and Level are keep below 3. No of trial depend upon...
No of independent variableNo of level
So choosing the independent variable and no of level that is the crucial step in optimization…
What is level?? Level of factor are the values or designations assigned to the factors.
Factor Associated variable
Lower level(coded -
1)
Upper level(coded
+1)
Conc. Of Bile salts
X1 0.075 0.125
Lecithin-Cholate Molar
ratio
X2 0.6:1 1.4:1
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No. X1 X2 Conc. Of Bile salts
Lecithin-Cholate
Molar ratio
Solubility (mg/ml)
1 -1 -1 0.075 0.6:1 6.58
2 +1 -1 0.125 0.6:1 10.18
3 -1 +1 0.075 1.4:1 9.41
4 +1 +1 0.125 1.4:1 14.15
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First order or additive linear model:
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Complete model:
Y= 10.40 + 2.08 X1 + 1.92 X2
Y= 10.40 + 2.08 X1 + 1.92 X2 + 0.28 X1X2
Full factorial design for 3 factors(2^3)
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Factor Associated variable
Lower level
(coded -1)
Upper level
(coded +1)
Polysorbate 80(%)
X1 3.7 4.3
Propylene glycol(%)
X2 17 23
Sucrose invert
medium(%)
X3 49 61
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No.
X1 X2 X3 Polysorbate 80(%)
Propylene
glycol(%)
Sucrose(ml)
Turbidity y(ppm)
1 -1 -1 -1 3.7 17 49 3.1
2 +1 -1 -1 4.3 17 49 2.8
3 -1 +1 -1 3.7 23 49 3.9
4 +1 +1 -1 4.3 23 49 3.1
5 -1 -1 +1 3.7 17 61 6.0
6 +1 -1 +1 4.3 17 61 3.4
7 -1 +1 +1 3.7 23 61 3.5
8 +1 +1 +1 4.3 23 61 1.8
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Complete synergistic model:
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Y= 3.45 -0.675 X1 – 0.375 X2 + 0.225 X3 + 0.05 X1X2 - 0.4 X1X3 – 0.65 X2X3 + 0.175 X1X2X3
32 FULL FACTORIAL DESIGN
GELLAN GUM-ALGINATE BEADS
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Why 3 level factorial design???
IndependentFactors
Levels
-1 0 +1
X1: Gellan gum Concentration
1.5 2 2.5
X2: Sodium alginate Concentration
0.5 1 1.5
Percentage entrapment efficiency (Y1), swelling ratio (Y2) and T90 (time taken for 90% drug to be released) (Y3) was selected as dependant factors
Design matrix for 32 full factorial designRun
Coded value
Uncoded value Responses
Batch code
X1 X2Gellan gum
conc.
Sodiumalginate Conc.
Entrapment efficiency
swelling ratio
T90
S1 -1 -1 1.5 0.5 91.84 4.65 5.2
S2 0 -1 2 0.5 93.1 5.92 7.5
S3 1 -1 2.5 0.5 96.44 6.34 9.4
S4 -1 0 1.5 1 94.18 5.39 5.2
S5 0 0 2 1 96.83 6.28 8.2
S6 1 0 2.5 1 98.09 6.85 9.1
S7 -1 1 1.5 1.5 98.4 5.38 7.3
S8 0 1 2 1.5 99.79 6.54 9.5
S9 1 1 2.5 1.5 99.68 7.56 11.1Vipul Patel/ Pharmaceutics and Pharmaceutical Technology
The polynomial equations for three
responses are shown below:Y1= 96.48+1.63X1+2.75X2-0.83X1X2
Y2= 6.15+0.83X1+0.50X2Y3= 7.50+1.98X1+0.96X2+0.83X22
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It’s a graphical representation of results. From the Full model equation, eliminate
insignificant terms gives refined equation or
reduced equation. This refined equation or Full equation is
transferred in form of graphs. That is known as contour plot or response surface
methodology plot.
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Run Coded value Uncoded value Responses
Batch code X1 X2 X1 X2 Y1 Y2 Y3
S1 -1 -1 1.5 0.5 91.84 4.65 5.2S2 0 -1 2 0.5 93.1 5.92 7.5S3 1 -1 2.5 0.5 96.44 6.34 9.4S4 -1 0 1.5 1 94.18 5.39 5.2S5 0 0 2 1 96.83 6.28 8.2S6 1 0 2.5 1 98.09 6.85 9.1S7 -1 1 1.5 1.5 98.4 5.38 7.3S8 0 1 2 1.5 99.79 6.54 9.5S9 1 1 2.5 1.5 99.68 7.56 11.1
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99
98
97
93
9495 96
Y1 Y2
7
6.5
6
5.5
5
10
9
8
7.
6
Y3
Maximum efficiency in estimating main effects.
Identification of interaction.Conclusions apply to a wide range of
conditions.Maximum use of the data.Saves time and money.
Vipul Patel/ Pharmaceutics and Pharmaceutical Technology
References Gareth A. Lewis, Didier Mathieu, Roger Phan-Tan-Luu.
Pharmaceutical Experimental Design. Marcel Dekker
1999. Sanford Bolton, Charles Bon. Pharmaceutical statistics,
Practical and Clinical applications. Drugs and Pharmaceutical Sciences Vol-135.
Pritesh C. Mistry. Development Of Gellan Gum Alginate Bead of Aceclofenac, 2006; LMCP THESIS.
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