![]() In addition, the structure of Symmetric Latin Hypercube provides good properties for fitting a polynomial model. Compared with the search in the family of Latin hypercubes using the CP algorithm, its search time is drastically reduced and the Latin hypercubes that can be realistically obtained are likely to be better. The CP algorithm due to Li and Wu (Technometric, 1997) is used to search for optimal Symmetric Latin Hypercubes. A class of Symmetric Latin Hypercube which has good geometric properties is proposed. The levels are spaced evenly from the lower bound to the upper bound of the factor. However, existing search methods are slow, especially for Latin hypercubes with large dimensions. In a Latin Hypercube, each factor has as many levels as there are runs in the design. A randomly generated Latin hypercube design (LHD) can be quite structured: the variables may be highly correlated or the design may not have good space-lling prop-erties. This results a scheme where each recipe is tested once in each furnace. Here the values (A, B and C) correspond to the three diffusion recipes and the parameter (p1 to p3) corresponds to three furnaces. Optimal Latin hypercube designs are widely used in computer experiments. and showed that the constructed Latin hypercube has the same rectangular distance as the single replicate full factorial design, where the rectangular. Sliced Latin hypercube designs (SLHDs) are LHDs that can be partitioned into some LHD slices 2, which means that the SLHDs have the optimal univariate uniformity for both the whole design and. Table 3.3 shows a Latin Hypercube design with three parameters. which actually motivated this research is also presented. A computer experiment using an OLH design conducted at Ford Motor Co. OLHs whose number of columns reaches the upper bound, are found for $m=3,4$ while the cases for $m>5$ are still unknown. Furthermore, the structure of Orthogonal Latin Hypercubes is established in the vector space $\.$ An upper bound on the number of columns of an OLH is given. Applying an Orthogonal Latin Hypercube design. Second, it can facilitate non-parametric fitting procedures, since a good space filling design within the class of Orthogonal Latin Hypercubes can be selected. A class of Orthogonal Latin Hypercubes (OLH) which preserves the orthogonality among columns is constructed. The estimates of linear effects of all factors are not only uncorrelated with each other, but also uncorrelated with the estimates of all quadratic effects and bi-linear interactions. First, it retains the orthogonality of traditional experimental designs. Applying an Orthogonal Latin Hypercube design in a computer experiment benefits the data analysis in two ways. The Latin HyperCube method uses a constrained or stratified sampling scheme. AbstractA class of Orthogonal Latin Hypercubes (OLH) which preserves the orthogonality among columns is constructed. An approach which can yield precise estimates of output statistics with a lesser number of samples than simple random sampling.
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