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Bridge Designs for Modeling Systems With Low Noise

Summary: [This abstract is based on the authors' abstract.] For deterministic computer simulations, Gaussian process models are a standard procedure for fitting data. These models can be used only when the study design avoids having replicated points. This characteristic is also desirable for one-dimensional projections of the design, since it may happen that one of the design factors has a strongly nonlinear effect on the response. Latin hypercube designs have uniform one-dimensional projections, but are not efficient for fitting low-order polynomials when there is a small error variance. D-optimal designs are very efficient for polynomial fitting but have substantial replication in projections. This article proposes a new class of designs that bridge the gap between D-optimal designs and D-optimal Latin hypercube designs. These designs guarantee a minimum distance between points in any one-dimensional projection allowing for the fit of either polynomial or Gaussian process models. Subject to this constraint, they are D-optimal for a pre-specified model.

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  • Topics: Statistical Process Control (SPC)
  • Keywords: Gaussian curve, Optimal design, D-optimality, Polynomial model, Simulations, Latin squares, Computer models
  • Author: Jones, Bradley; Silvestrini, Rachel T.; Montgomery, Douglas C.; Steinberg, David M
  • Journal: Technometrics