Affordable experimental design with tens of variables

Abstract

Simulation models have importantly expanded the analysis capabilities in engineering designs. With larger computing power, more variables can be modeled to estimate their effect in ever larger number of performance measures. Statistical experimental designs, however, are still somewhat focused on the variation of less than about a dozen variables. In this work, an effort to identify strategies to deal with tens of variables is undertaken. The aim is to be able to generate designs capable to estimate full quadratic models using simply a personal computer. Quadratic models are interesting because they can support statistical testing, provide competitive approximating models, and make optimization problems tractable. Several strategies are contrasted: (1) generate designs with random numbers, (2) use designs already available in the literature, (3) generate designs under a clustering strategy, and (4) generate designs using random-walk methods. The first strategy is an easy way to generate a design, although the statistical properties cannot be controlled. The second strategy does focus on statistical properties, but some of the designs become rapidly inconvenient to generate when increasing the number of variables. The third and fourth strategies are investigated as novel possibilities to generate designs in a convenient manner.

A Simulation-Optimization strategy to deal simultaneously with tens of decision variables and multiple performance measures in manufacturing

“…It also incorporates the possibility of analyzing tens of variables through an economic experimental design proposed by (Mendez-Vazquez et al 2014a) which ensures the possibility of estimating full quadratic regression models, that is, regression models that include linear, quadratic and second-order interaction terms. A collection of experimental designs with these capabilities was described in and can be found online in:…”

“…The experimental design in this case is for 50 variables at three levels each, and has 1327 runs. The number of runs corresponds to the minimum number of necessary runs to estimate a second order model, as proposed in (Mendez-Vazquez et al 2014a). The natural variables and the simulated values of the PMs are coded using a linear transformation to make them fall in the range of [-1,1] to avoid dimensionality problems.…”