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Many food products involve mixtures of ingredients, where the mixtures can be expressed as combinations of ingredient proportions. In many cases, the quality and the consumer preference may also depend on the way in which the mixtures are processed. The processing is generally defined by the settings of one or more process variables. Experimental designs studying the joint impact of the mixture ingredient proportions and the settings of the process variables are called mixture-process variable experiments. In this article, we show how to combine mixture-process variable experiments and discrete choice experiments, to quantify and model consumer preferences for food products that can be viewed as processed mixtures. First, we describe the modeling of data from such combined experiments. Next, we describe how to generate D- and I-optimal designs for choice experiments involving mixtures and process variables, and we compare the two kinds of designs using two examples., Comment: arXiv admin note: text overlap with arXiv:2108.01748

Experiments using multi-step protocols often involve several restrictions on the randomization. For a specific application to in vitro testing on microplates, a design was required with both a split-plot and a strip-plot structure. On top of two-level treatment factors and the factors that define the randomization restrictions, a multi-level fixed blocking factor not involving further restrictions on the randomization had to be added. We develop a step-by-step approach to construct a design for the microplate experiment and analyze a response. To consolidate the approach, we study various alternative scenarios for the experiment., Comment: 31 pages, 13 tables, 4 figures

Designs for screening experiments usually include factors with two levels only. Adding a few four-level factors allows for the inclusion of multi-level categorical factors or quantitative factors with possible quadratic or third-order effects. Three examples motivated us to generate a large catalog of designs with two-level factors as well as four-level factors. To create the catalog, we considered three methods. In the first method, we select designs using a search table, and in the second method, we use a procedure that selects candidate designs based on the properties of their projections into fewer factors. The third method is actually a benchmark method, in which we use a general orthogonal array enumeration algorithm. We compare the efficiencies of the new methods for generating complete sets of non-isomorphic designs. Finally, we use the most efficient method to generate a catalog of designs with up to three four-level factors and up to 20 two-level factors for run sizes 16, 32, 64, and 128. In some cases, a complete enumeration was infeasible. For these cases, we used a bounded enumeration strategy instead. We demonstrate the usefulness of the catalog by revisiting the motivating examples., Comment: 37 pages, 1 figure, 13 tables

Discrete choice experiments are frequently used to quantify consumer preferences by having respondents choose between different alternatives. Choice experiments involving mixtures of ingredients have been largely overlooked in the literature, even though many products and services can be described as mixtures of ingredients. As a consequence, little research has been done on the optimal design of choice experiments involving mixtures. The only existing research has focused on D-optimal designs, which means that an estimation-based approach was adopted. However, in experiments with mixtures, it is crucial to obtain models that yield precise predictions for any combination of ingredient proportions. This is because the goal of mixture experiments generally is to find the mixture that optimizes the respondents' utility. As a result, the I-optimality criterion is more suitable for designing choice experiments with mixtures than the D-optimality criterion because the I-optimality criterion focuses on getting precise predictions with the estimated statistical model. In this paper, we study Bayesian I-optimal designs, compare them with their Bayesian D-optimal counterparts, and show that the former designs perform substantially better than the latter in terms of the variance of the predicted utility., Comment: 19 pages, 7 figures, to be published in Chemometrics and Intelligent Laboratory Systems

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