Computer-aided robust design of mixture experiments based on Bayesian D-optimality.

摘要

Three and four component mixture experiments are very common in practice. The special nature of the experiment frequently requires additional constraints which transform the factor space into a convex (q{dollar}-{dollar}1)-dimensional polyhedron. In this situation an algorithmic approach to the design selection must be used. One of the computer-generated designs most widely used in practice are D-optimal designs. However, D-optimal designs, like other computer-generated designs, are too dependent on an assumed model. They spend all of the experimental effort to provide the most precise estimation of the assumed model and, therefore, they do not incorporate an explicit mechanism to provide robustness against model inadequacies. DuMouchel and Jones proposed a simple Bayesian modification of D-optimal designs that reduces this dependency and preserves the flexibility and computational convenience of D-optimal designs.; This research studies the performance of the family of Bayesian D-optimal designs defined by the prior variance of the potential term coefficients when it varies from zero (D-optimal design) to a large number (D-optimal design for the potential model when the design size is greater than or equal to the number of terms in the potential model). The performance of the designs over the whole space of response models defined by the prior distribution of coefficients is studied. The designs are evaluated with respect to prediction errors, variance optimality, distribution of information, power to detect lack of fit, and error estimation. The study is centered in three and four components, constrained and unconstrained mixture experiments.; Some designs perform extremely well with respect to all of the characteristics. Compared to D-optimal designs they produce smaller bias errors, increase the power to detect model inadequacies, allow the fitting of a larger number of higher order terms, improve the coverage of the factor space, and still keep very good variance properties. Furthermore, a Bayesian D-optimal is easily generated. A D-optimal augmentation strategy that allows the use of a standard D-optimal search algorithm is introduced in this work. Practical recommendations are given to aid in the selection of a robust design.