Lecture.
5
Design of Experiments: Design
types and construction
Dr. Salma M. Abdel-Hafez
Lecturer
Department of Pharmaceutics and Industrial Pharmacy
Faculty of Pharmacy, Ain Shams University
Full Factorial Design
▪ It is recommended when you have low number of factors and low number of levels so that the overall
number of runs or experiments is not excessive.
▪ Useful for investigating main factor effects as well as their interactions.
▪ Number of experiments = (Number of levels) Number of factors
▪ e.g. 2 factors varied at 3 levels, number of experiments = 32 = 9
3 factors varied at 2 levels, number of experiments = 23 = 8
3 factors varied at 3 levels, number of experiments = 33 = 27
▪ Note: additional centre points may be added. 33 full factorial design
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Full Factorial Design, cont.
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Full Factorial Design, cont.
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Fractional Factorial Designs
▪ An attempt to reduce the number of experiments obtained from the 2-level full
factorial design by subtracting numbers from the power.
▪ e.g. 23-1 instead of 23
Fractional factorial
▪ Useful for screening of factors to select significant factors and study their main design
effects.
▪ May not be sensitive for estimating the factor interactions according to its resolution.
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Fractional Factorial Designs, cont.
▪ In Design Expert® software, different color codes are given for different resolutions:
Green: High resolution, yellow: Medium resolution and red: Low resolution
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Fractional Factorial Designs, cont.
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Fractional Factorial Designs, cont.
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Fractional Factorial Designs, cont.
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Fractional Factorial Designs, cont.
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Response Surface Designs
▪ These designs extract what is called rich-information
points.
▪ This selection saves us the use of all the combinations Central composite
design
however they cover the whole space of the experiment.
▪ They have a smaller number of experiments than the full
Box-Behnken
factorial design design
D-optimal
design
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Central Composite Design (CCD)
▪ Each numeric factor is varied over 5 levels.
▪ e.g. -1, 0, +1, - alpha (-1.4), + alpha (+1.4).
▪ Alpha levels are denoted by the program.
Central composite
design
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Central Composite Design (CCD), cont.
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Central Composite Design (CCD), cont.
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Box-Behnken Design (BBD)
▪ The BBD usually takes factors at three levels and all the design points fall within
the safe operating zone.
▪ In each run, the levels of two factors are held at their extreme levels and the third Box-Behnken
design
at its middle level, thereby eliminating the experimental runs performed at the
extreme conditions.
▪ This is useful in case of delicate systems where it is unfavourable to work them at
harsh conditions such as the liposomes or proteins for example.
▪ However, this implies poor coverage because you don’t have any corner points,
therefore BBD may introduce errors when extrapolated to extremes of the design
space.
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Box-Behnken Design (BBD), cont.
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Box-Behnken Design (BBD), cont.
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D-optimal Design
▪ It contains the best subset of all possible experiments
▪ It works by space filling sampling. Briefly, the design works by maximizing
the determinant obtained from the information matrix generated from all D-optimal
the possible combinations of the involved factors. This explains the use of design
the letter “D” in the D-optimal designs.
▪ The D-optimal was found to be highly sensitive and more predictive with
the least bias percentage.
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D-optimal Design, cont.
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D-optimal Design, cont.
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Simplex Lattice
Mixture Designs chooses the
points in this
▪ When you have components of a mixture or a system e.g. domain
microemulsions or HPLC mobile phases (their sum of
percentages will be 100%).
▪ If the space of experiment is triangular, you can use the
Simplex Lattice or the Simplex Centroid (simplex means
triangle). To model this area of lipid
nanocapsule formation,
use D-optimal mixture
▪ If the space of your experiment is irregular, then you can use design
the D-optimal Mixture Design.
▪ Simplex Lattice is more accurate than Simplex Centroid.
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