Introduction & Basics of DoE Terminologies Key steps in DOE Softwares used for DOE Factorial Designs ( Full and Fractional) Mixture Designs Response Surface Methodology Central Composite Design Box -Behnken Design Conclusion References

1. DESIGN OF EXPERIMENTS
(Factorial, Composite, Mixture and
Response Surface designs)
Presented By:-
Vaishnavi Bhosale
M.S. Pharmaceutics (2nd Semester)
NIPER Hyderabad

2. CONTENTS
• Introduction & Basics of DoE
• Terminologies
• Key steps in DOE
• Softwares used for DOE
• Factorial Designs ( Full and Fractional)
• Mixture Designs
• Response Surface Methodology
• Central Composite Design
• Box -Behnken Design
• Conclusion
• References

3. BASICS OF DOE
• Design of experiments (DOE) is defined as a branch of applied statistics that deals
with planning, conducting, analyzing, and interpreting controlled tests to evaluate
the factors that control the value of a parameter or group of parameters.
• Design of experiments (DOE) is a systematic method to determine the relationship
between factors affecting a process and the output of that process
WHY DOE ???
FIND CAUSE & EFFECT
RELATIONSHIPS

4. TERMINOLOGIES
• FACTORS – INPUTS to the process.
Quantitative: A numerical factor is assigned to it. Example: Concentration-1%, 2%, 3% etc.
Qualitative: These are non-numerical. Example-Polymer grade, humidity condition etc.
• LEVELS- These represent settings of each factor in the study
• RESPONSE: It is OUTCOME of an experiment. It is the effect, which we are going to evaluate
i.e., disintegration time, duration of buoyancy, thickness, etc. It is an outcome of the
experiment.
• RESPONSE SURFACE: Response surface representing the relationship between the
independent variables X1 and X2 and the dependent variable Y.
• RUN OR TRIALS: Experiments conducted according to the selected experimental designs

5. KEY STEPS FOR EXPERIMENTAL DESIGN
1.Setting solid
objectives
2. Selection of
process variables
(factors) and
responses (CQAs):
3. Selection of an
experimental design
4. Execution of the
design
5. Checking that the
data are consistent
with the
experimental
assumptions
6. Analyzing the
results
7. Use and
interpretation of the
results

6. TYPES OF DOE
FACTORIAL
DESIGNS
• Full Factorial
• Fractional Factorial
MIXTURE
DESIGNS
• Simplex lattice
• Simplex centroid
SCREENING
DESIGNS
• Plackett Burman
designs
• Taguchis array
RESPONSE
SURFACE
METHODOLOGY
• Central composite
design
• Box Behnken designs

7. SOFTWARES USED FOR DOE
• Design Expert
• DE PRO XL
• MATREX
• Mini Tab
• OPTIMA
• OMEGA
• FACTOP
• GRG2

8. FACTORIAL DESIGNS
• A factorial design allows the effect of several factors and even interactions between them
to be determined with the same number of trials as are necessary to determine any one of
the effects by itself with the same degree.
• First, whenever we are interested in examining treatment variations, factorial designs
should be strong candidates as the designs of choice.
• Second, factorial designs are efficient. Instead of conducting a series of independent
studies we are effectively able to combine these studies into one.
• Finally, these are the only effective way to examine interaction effects
• The fitting of an empirical polynomial equation to the experimental result facilitates the
optimization procedure. The general polynomial equation is as follows:
• Where Y is the response, X1, X2, X3 are the levels (concentration) of the 1, 2, 3 factors
and B1, B2, B3, B12, B13, B23, are the polynomial coefficients, B0 is the intercept
Y = B0+B1X1+B2 X2+B3 X3++B12 X1X2+B13X1X3+ B23X2X3 —
-

9. FULL FACTORIAL DESIGN
• In a Full factorial design (FFD), the effect of all the factors and
their interactions on the outcomes is investigated.
• In FFD, each setting of every factor appears with every setting
of another factor.
• If there are ‘k’ factors with each having ‘p’ levels, the design
consists of (p) K Runs/ trails
23
8 runs
22
4 runs
32
9 runs
33
27 runs

10. FFD APPLICATION

12. FRACTIONAL FACTORIAL DESIGNS
• Fractional factorial designs represent a part of the relevant full
design, typically ½ or 1/4 … of the full factorial.
• They are typically used when the number of factors exceeds 4–5, for
screening purposes.
• Their main limitation is related to confounding or alias of main
effects and interactions.
• The term “resolution” refers to the ability of a design to estimate
effects and interactions without confounding
RESOLUTION III RESOLUTION IV
RESOLUTIONV

13. FRACTIONAL FACTORIAL DESIGN

16. MIXTURE DESIGNS
• In a mixture experiment, the independent factors are proportions of different
components of a blend
• In mixture experiments, the measured response is assumed to depend only
on the relative proportions of the ingredients or components in the mixture
and not on the amount of the mixture.
• In mixture problems, the purpose of the experiment is to model the blending
surface with some form of mathematical equation so that:
• Some measure of the influence on the response of each component singly
and in combination with other components can be obtained
X1+X2+X3+X4......=1

17. MIXTURE DESIGN APPLICATION

18. SIMPLEX LATTICE DESIGN
• The simplex-lattice design selects points spread evenly over the factor space. They
are defined to support a polynomial model of degree m in q components over the
lattice. This is denoted as a { q, m} simplex-lattice. Thus, q=2 is a line, q=3 is an
equilateral triangle, and q=4 is a tetrahedron.
• We will have m+1 equally spaced values from 0 to 1 on each axis such that
x = 0, 1/m, 2/m, ......1
where, x are the sampled points of each factor
• The possible designs for q=3 and m=2, the possible designs are
• (x1, x2, x3) = (1,0,0) (0,1,0) (0,0,1) (½ , ½, 0) (½, 0, ½) (0, ½, ½)

19. SIMPLEX CENTROID DESIGN
• A simplex centroid design of q components is composed of pure mixture
runs, all combinations of 2 to the k factors at equal levels, and a center
point run with equal amounts of all ingredients.
• Therefore, the design will consist of 2𝑞 − 1 distinct design points. Figure 5
shows an example for q=3 and q=4

20. RESPONSE SURFACE METHODOLOGY
• A response surface design is a set of advanced design of experiments (DOE) techniques that
help you better understand and optimize your response.
• The difference between a response surface equation and the equation for a factorial design is
the addition of the squared (or quadratic) terms that lets you model curvature in the response,
making them useful for:
• Understanding or mapping a region of a response surface. Response surface equations model
how changes in variables affect a response of interest.
• Finding the levels of variables that optimize a response.
• Selecting the operating conditions to meet specifications.
• Two main types of RSM
CENTRAL
COMPOSITE DESIGN
BOX BEHNKEN
DESIGN
Y= B0 + B1X1+ B2X2+ B3X3+ B12X1X2+ B13X1X3+ B23 X2X3+ B11X12
+B22X22 + B33X32

21. CENTRAL COMPOSITE DESIGN
• Central composite designs are a factorial or fractional factorial design with center points,
augmented with a group of axial points (also called star points) that let you estimate curvature.
You can use a central composite design to:
• Efficiently estimate first- and second-order terms.
• Model a response variable with curvature by adding center and axial points to a previously-
done factorial design.
• Central composite designs are especially useful in sequential experiments because you can
often build on previous factorial experiments by adding axial and center points.

22. TYPES OF CCD
• Alpha (α) is the distance of each axial point (also called star point) from the center in a central
composite design
• A value less than one puts the axial points in the cube; a value equal to one puts them on the
faces of the cube; and a value greater than one puts them outside the cube.

23. CCD APPLICATION

24. BOX BEHNKEN DESIGNS
( 3 level 3 factor design)
• A Box-Behnken design is a type of response surface design that does not contain an embedded
factorial or fractional factorial design.
• Box-Behnken designs have treatment combinations that are at the midpoints of the edges of
the experimental space and require at least three continuous factors. The following figure
shows a three-factor Box-Behnken design. Points on the diagram represent the experimental
runs that are done:
• Because Box-Behnken designs often have fewer design points, they can be less expensive to do
than central composite designs with the same number of factors.

27. CONCLUSION
• Designed experiments are an advanced and powerful analysis tool during
projects.
• An effective experimenter can discover significant process factors.
• The factors can then be used to control response properties in a process and
teams can then engineer a process to the exact specification the product
requires.
• A well built experiment can save not only time but also solve critical
problems which have remained unseen in processes.
• Specifically, interactions of factors can be observed and evaluated.
• Ultimately, what factors matter and what factors do not is studied

28. REFERENCES
• Stavros N. Politis, Paolo Colombo, Gaia Colombo & Dimitrios M. Rekkas (2017) Design of experiments (DoE)
in pharmaceutical development, Drug Development and Industrial Pharmacy, 43:6, 889-901
• Nazia khanam, Md irshad alam, Quazi md aamer Iqbal md yusuf ali, Aquil-ur-rahman siddiqui, Vol 2 2018,
A review on optimization of drug delivery system with experimental designs, International Journal of applied
Pharmaceutics, 7-12
• Cory Natoli, An Introduction to mixture designs, 2020, Scientific Test and Analysis Techniques STAT COE
• Vaddemukkala Y, Syed M, Srinivasarao. A research article on optimization of olmesartan tablet formulation
by 23 factorial design. Int J Res Pharm Nano Sci 2015;4:188-95.
• K. Narayanan, V.M. Subrahmanyam, and J. Venkata Rao, 2014, A Fractional Factorial Design to Study the
Effect of Process Variables on the Preparation of Hyaluronidase Loaded PLGA Nanoparticles, Hindawi
Publishing Corporation Enzyme Research
• Enneffah wafaa, Vassir el-alaoui, Mustapha bouatia,Abdelkader laatiris, Naoual cherkaoui, Vounes rahali,
2016, Solubilization of celecoxib using organic cosolvent and nonionicsurfactants optimized by experimental
design, International journal of pharmacy and pharmaceutical sciences
• Preeti Kush, Jitender Madan, and Parveen kumar, 2019, Application of central composite design and
response surface methodology for optimization of metal organic framework: novel carrier for drug delivery”,
Asian journal of pharmaceutical and clinical research, pp.121-7
• K.M. Ranch, F.A. Maulvi, M.J. Naik, A.R. Koli, R.K. Parikh, D.O. Shah, 2018, Optimization of a novel in situ
gel for sustained ocular drug delivery using Box-Behnken Design: In vitro, ex vivo, in vivo and human
studies, International Journal of Pharmaceutics
• Minitab 18 support