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Summary: Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a non‐linear model in these factors. This non‐linear model can be mechanistic, empirical or a hybrid of the two. Motivated by experiments in chemical engineering, we focus on D‐optimal designs for multifactor non‐linear response surfaces in general. To find and study optimal designs, we first implement conventional point and co‐ordinate exchange algorithms. Next, we develop a novel multiphase optimization method to construct D‐optimal designs with improved properties. The benefits of this method are demonstrated by application to two experiments involving non‐linear regression models. The designs obtained are shown to be considerably more informative than designs obtained by using traditional design optimality algorithms. [ABSTRACT FROM AUTHOR]

Many optimal experimental designs depend on one or more unknown model parameters. In such cases, it is common to use Bayesian optimal design procedures to seek designs that perform well over an entire prior distribution of the unknown model parameter(s). Generally, Bayesian optimal design procedures are viewed as computationally intensive. This is because they require numerical integration techniques to approximate the Bayesian optimality criterion at hand. The most common numerical integration technique involves pseudo Monte Carlo draws from the prior distribution(s). For a good approximation of the Bayesian optimality criterion, a large number of pseudo Monte Carlo draws is required. This results in long computation times. As an alternative to the pseudo Monte Carlo approach, we propose using computationally efficient Gaussian quadrature techniques. Since, for normal prior distributions, suitable quadrature techniques have already been used in the context of optimal experimental design, we focus on quadrature techniques for nonnormal prior distributions. Such prior distributions are appropriate for variance components, correlation coefficients, and any other parameters that are strictly positive or have upper and lower bounds. In this article, we demonstrate the added value of the quadrature techniques we advocate by means of the Bayesian D-optimality criterion in the context of split-plot experiments, but we want to stress that the techniques can be applied to other optimality criteria and other types of experimental designs as well. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In many industrial experiments, complete randomization of the runs is impossible as, often, they involve factors whose levels are hard or costly to change. In such cases, the split-plot design is a cost-efficient alternative that reduces the number of independent settings of the hard-to-change factors. In general, the use of generalized least squares is required for model estimation based on data from split-plot designs. However, the ordinary least squares estimator is equivalent to the generalized least squares estimator for some split-plot designs, including some second-order split-plot response surface designs. These designs are calledequivalent-estimation designs. An important consequence of the equivalence is that basic experimental design software can be used for model estimation. This article introduces two new families of equivalent-estimation split-plot designs, one based on subset designs and another based on supplementary difference set designs. The resulting designs complement existing catalogs of equivalent-estimation designs and allow for a more flexible choice of the number of hard-to-change factors, the number of easy-to-change factors, the number and size of whole plots, and the total sample size. It is shown that many of the newly proposed designs possess good predictive properties when compared to D-optimal split-plot designs. [ABSTRACT FROM AUTHOR]