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Complex-Systems Design MethodologyCollaborative for Systems-Engineering Collaborative Environment Complex-Systems Design Methodology for Systems-Engineering Environment 1
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Fig. 4. Scatterplots of sampling points in a 2-dimensional design space based on (a) random sampling, (b) Latin Hypercube sampling, (c) sub-optimized Latin hypercube sampling, (Viana et al., 2010), (d) modified Sobol LPτ sequence. • Initial sample, 100 points. ◦ Additional sample, 100 points.
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Fig. 5. Full factorial design with (a) 2 variable-levels and (b) 3 variable-levels in a 3-dimensional design space. also ordinal and categorical variables can be used in the analysis, rather than only cardinal (i.e., continuous) variables as in the previously described sampling techniques. In this case the values of the variables are more properly called levels. 4.1.1 Factorial design
Factorial design, or full factorial design, is a sampling method that foresees one experiment for each possible combination of the levels of the factors. If factor A has a levels, factor B has b levels and factor C has c levels, the total number of experiments is N = a · b · c. There are special cases of factorial design where for all the factors only 2 or 3 levels are considered. They are usually called 2k and 3k factorial designs respectively, where k indicates the number of factors. The experimental structure obtained for 2k and 3k factorial designs is shown in Fig. 5 where the dots indicate the sample points. Full-factorial design requires a number of experiments that increases with the power of the number of factors. Thus, already in the case of 2k or 3k factorial designs, the experimentation (i.e., the simulation of the model) can become cumbersome very soon. Therefore, fractional factorial designs were introduced as an attempt to reduce the computational effort for the analysis. As the name suggests, fractional-factorial designs only foresee a fraction of the