Utami Dyah Syafitri

I-Optimal Design of Mixture Experiments

ABSTRACT In mixture experiments, the factors under study are proportions of the ingredients of a mixture. The special nature of the factors necessitates specific types of regression models, and specific types of experimental designs. Although mixture experiments usually are intended to predict the response(s) for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients, little research has been done concerning their I-optimal design. This is surprising given that I-optimal designs minimize the average variance of prediction and, therefore, seem more appropriate for mixture experiments than the commonly used D-optimal designs, which focus on a precise model estimation rather than precise predictions. In this article, we provide the first detailed overview of the literature on the I-optimal design of mixture experiments and identify several contradictions. For the second-order and the special cubic model, we present continuous I-optimal designs and contrast them with the published results. We also study exact I-optimal designs, and compare them in detail to continuous I-optimal designs and to D-optimal designs. One striking result of our work is that the performance of D-optimal designs in terms of the I-optimality criterion very strongly depends on which of the D-optimal designs is considered. Supplemental materials for this article are available online.

Fourier transform infrared spectroscopy combined with chemometrics for discrimination of Curcuma longa, Curcuma xanthorrhiza and Zingiber cassumunar

Turmeric (Curcuma longa), java turmeric (Curcuma xanthorrhiza) and cassumunar ginger (Zingiber cassumunar) are widely used in traditional Indonesian medicines (jamu). They have similar color for their rhizome and possess some similar uses, so it is possible to substitute one for the other. The identification and discrimination of these closely-related plants is a crucial task to ensure the quality of the raw materials. Therefore, an analytical method which is rapid, simple and accurate for discriminating these species using Fourier transform infrared spectroscopy (FTIR) combined with some chemometrics methods was developed. FTIR spectra were acquired in the mid-IR region (4000-400 cm(-1)). Standard normal variate, first and second order derivative spectra were compared for the spectral data. Principal component analysis (PCA) and canonical variate analysis (CVA) were used for the classification of the three species. Samples could be discriminated by visual analysis of the FTIR spectra by using their marker bands. Discrimination of the three species was also possible through the combination of the pre-processed FTIR spectra with PCA and CVA, in which CVA gave clearer discrimination. Subsequently, the developed method could be used for the identification and discrimination of the three closely-related plant species.

I-Optimal Design of Mixture Experiments in the Presence of Ingredient Availability Constraints

Mixture experiments usually involve various constraints on the proportions of the ingredients of the mixture under study. In this paper, inspired by the fact that the available stock of certain ingredients is often limited, we focus on a new type of constraint, which we refer to as an ingredient availability constraint. This type of constraint substantially complicates the search for optimal designs for mixture experiments. One difficulty, for instance, is that the optimal number of experimental runs is not known a priori. To deal with this complication, we propose a variable neighborhood search algorithm to find I-optimal designs for mixture experiments in case there is a limited stock of certain ingredients.