QbD by central composite design

Valuable material regarding software

1. Design Of Expert
Prepared by...
Ms. Sushmita Rana
(Master in Pharmaceutics)

2. OFAT used that show fluctuation in the interaction effects
so now a days ICH add one new guidelines QbD in which We
use DoE that gives variables simultaneously vary and show
interaction effects ( Abdulaziz A. et.al)
The Central composite design was implemented for the
optimization of formulation, e.g.: ratio of (X
1)& (X
2) were
independent variables and (Y
1) and (Y
2) were selected as
response or dependent variables
Introduction

3. According to the design, nine formulations were prepared and
evaluated for response. All the factorial batches (F-1 to F-9) were
evaluated to calculated the response of given formulation.
Build Information
File Version 11.0.3.0
Study TypeResponse SurfaceSubtype Randomized
Design TypeCentral CompositeRuns 9
Design Model Quadratic Blocks No Blocks
Build Time (ms) 1.0000

4. Factors
Independent variables Dependent variables
X1Diluent ratio Y1 Disintegration time
X2 compressional force Y2 Hardness
X3 Disintegrant level Y3 Dissolution
X4 Binder level Y4 Friability
X5 Lubricant level Y5 weight uniformity

5. FactorName UnitsTypeMinimum Maxi
Coded
Low
Coded
High
MeanStd. Dev.
X1 A:B Numeric-1.00001.0000
-1 ↔ -
1.00
+1 ↔
1.00
0.00000.8660
X2 C Numeric-1.00001.0000
-1 ↔ -
1.00
+1 ↔
1.00
0.00000.8660
•We take two independent variables
•We have selected two factors e.g. A : B ratio
•Another factor is C

6. Responses
Respon
se
NameUnits
Observ
ations
Analysi
s
Minim
um
Maxim
um
Mean
Std.
Dev.
Ratio
Transf
orm
Model
R1EE% 9
Polyno
mial
17.858.837.7812.713.30None
Quadrat
ic
R2 VS 9
Polyno
mial
273.5857.7589.17204.063.14NoneLinear
R3 PDI 9
Polyno
mial
0.2190.3460.27090.04051.58NoneLinear
By using independent variables that depend upon
the formulation we have to be prepared
Consider some independent variables like entrapment efficiency,
vesicle size etc.

7. Evaluation
•Model Terms
Term
Standard
Error*
VIF Rᵢ² Power
A 0.4082 1 0.0000 39.5 %
B 0.4082 1 0.0000 39.5 %
AB 0.5000 1 0.0000 28.9 %
A^2 0.7071 1 0.0000 49.0 %
B^2 0.7071 1 0.0000 49.0 %
Power calculations are performed using response type "Continuous" and parameters:
Delta=2, Sigma=1
Power is evaluated over the -1 to +1 coded factor space.
Standard errors should be similar to each other in a balanced design. Lower standard errors are better.

8. •The ideal VIF value is 1.0. VIFs above 10 are cause for concern. VIFs above 100 are
cause for alarm, indicating coefficients are poorly estimated due to multicollinearity.
Ideal Rᵢ² is 0.0. High Rᵢ² means terms are correlated with each other, possibly leading to
poor models.
•If the design has multilinear constraints, then multicollinearity will exist to a greater
degree. This inflates the VIFs and the Rᵢ², rendering these statistics useless. Use FDS
instead.
•Power is an inappropriate tool to evaluate response surface designs.
Use prediction-based metrics provided in this program via Fraction of Design Space
(FDS) statistics.
•Click on the Graphs tab to find the FDS graph. More information about FDS is available
in the Help.
Be sure that the model you selected contains only terms you expect to be significant

9. Correlation matrix
InterceptA-A B-B AB A² B²
Intercept1.0000.000-0.0000.000-0.632-0.632
A-A 0.0001.000-0.0000.000-0.000-0.000
B-B -0.000-0.0001.000-0.0000.0000.000
AB 0.0000.000-0.0001.000-0.0000.000
A² -0.632-0.0000.000-0.0001.000-0.000
B² -0.632-0.0000.0000.000-0.0001.000
Pearson’s
InterceptA-A B-B AB A² B²
Intercept
A-A 1.0000.0000.0000.0000.000
B-B 0.0001.0000.0000.0000.000
AB 0.0000.0001.0000.0000.000
A² 0.0000.0000.0001.0000.000
B² 0.0000.0000.0000.0001.000

10. Matrix Measures
Description Value
Condition Number of Coefficient
Matrix
1.0000
Maximum Variance Mean 0.8056
Average Variance Mean 0.4502
Minimum Variance Mean 0.3556
G Efficiency 82.76
Scaled D-optimality Criterion 2.16
Determinant of (X'X)⁻¹ 1.92901E-4
Trace of (X'X)⁻¹ 2.14
I (Cuboidal) 0.4500
If the condition number is 100-1000, there is moderate to strong multicollinearity.
Values above 1000 indicate severe multicollinearity.
When comparing designs, a smaller Scaled D-optimality Criterion is better.
The determinant, trace, and 'I' values can only be used when comparing designs with the
same number of runs. A smaller value is better.

13. ANOVA for Linear model
Source
Sum of
Squares
df
Mean
Square
F-valuep-value
Model 0.0100 20.0050 9.510.0138significant
A-A 0.0000 10.00000.07160.7980
B-B 0.0099 10.009918.940.0048
Residual0.0031 60.0005
Cor Total0.0131 8
Factor coding is Coded.
Sum of squares is Type III -Partial
The Model F-value of 9.51 implies the model is significant. There is only a
1.38% chance that an F-value this large could occur due to noise.
P-values less than 0.0500 indicate model terms are significant. In this case
B is a significant model term. Values greater than 0.1000 indicate the model
terms are not significant. If there are many insignificant model terms (not
counting those required to support hierarchy), model reduction may
improve your model

14. Final Equation in Terms of Coded Factors
PDI =
+0.2709
-0.0025 A
-0.0407 B
The equation in terms of coded factors can be used to
make predictions about the response for given levels of
each factor.
By default, the high levels of the factors are coded as +1
and the low levels are coded as -1.
The coded equation is useful for identifying the relative
impact of the factors by comparing the factor coefficients

19. Point prediction
Two-sidedConfidence = 95%Population = 99%
Respons
e
Predicte
d Mean
Predicte
d
Median
Observe
d
Std Dev
SE
Mean
95% CI
low for
Mean
95% CI
high for
Mean
95% TI
low for
99%
Pop
95% TI
high for
99%
Pop
EE%37.445837.4458 1.698371.1377433.82541.066621.994152.8975
VS608.853608.853 103.31350.0231486.451731.2551.919741215.79
PDI0.2744580.274458
0.022886
4
0.011081
3
0.2473430.3015730.1400070.408908

20. Confirmation
Two-sidedConfidence = 95%
Respon
se
Predict
ed
Mean
Predict
ed
Median
Observ
ed
Std Devn
SE
Pred
95% PI
low
Data
Mean
95% PI
high
EE%37.445837.4458 1.6983712.0442330.9401 43.9515
VS608.853608.853 103.3131114.787327.98 889.726
PDI
0.27445
8
0.27445
8
0.02288
64
1
0.02542
8
0.21223
8
0.33667
8