Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

A design optimality criterion, such as D-, A-, I-, and G- optimality criteria, is often used to analyze, evaluate and compare different designs options in mixture modeling test. A mixture test is an experiment where the descriptive variable and response rely only on the mixture's relative ratio in the mix but not its composition. The study geared toward exploring D-, A-, I-, and G- optimality criteria and their efficiency in determining an optimal split-plot design in mixture modeling within the presences of process variables. We evaluated and discussed in detail D-, A-, I-, and G- optimality criteria based on literature review. We also explored and examine why I- and D-optimal criteria are often involved within the formulation of an optimal design in the context of mixture process variable settings. We recommend that optimality criterion must always be used when assessing the various styles of designs so as to search out a desirable design that matches a combination model.

Design Optimality Criteria of Reduced Models for Variations of Central Composite Design

Choosing a response surface design to fit certain kinds of models is a difficult task. This work focuses on the reduced second order models having no quadratic and no interaction terms for five variations of Central Composite Design (SCCD, RCCD, OCCD, Slope-R and FCC) using the D-, G- and A- optimality criteria. Results show that for models having no quadratic terms that G- and A-optimality criteria are equivalent and replication of the axial portion with increase in center points tends to decrease the D-, A- and G-optimality criteria values of the CCDs while for models having no interaction terms, replication of the axial portion with increase in center points increases the D-optimality criterion values of SCCD, RCCD and OCCD in all the factors considered. Finally, the work have shown that replication of the axial portion reduces the performance of the CCDs with models having no quadratic terms and Slope-R is a better design with respect to D- and A-optimality criteria.

Highly D‑efficient Weighing Design and Its Construction

In this paper, some aspects of design optimality on the basis of spring balance weighing designs are considered. The properties of D‑optimal and D‑efficiency designs are studied. The necessary and sufficient conditions determining the mentioned designs and some new construction methods are introduced. The methods of determining designs that have the required properties are based on a set of incidence matrices of balanced incomplete block designs and group divisible designs.

Optimality Criteria for the Design of 2-Color Microarray Studies

We discuss the definition and application of design criteria for evaluating the efficiency of 2-color microarray designs. First, we point out that design optimality criteria are defined differently for the regression and block design settings. This has caused some confusion in the literature and warrants clarification. Linear models for microarray data analysis have equivalent formulations as ANOVA or regression models. However, this equivalence does not extend to design criteria. We discuss optimality criterion, and argue against applying regression-style D-optimality to the microarray design problem. We further disfavor E- and D-optimality (as defined in block design) because they are not attuned to scientific questions of interest.

Cooperative body–brain coevolutionary synthesis of mechatronic systems

To support the concurrent design processes of mechatronic subsystems, unified mechatronics modeling and cooperative body–brain coevolutionary synthesis are developed. In this paper, both body-passive physical systems and brain-active control systems can be represented using the bond graph paradigm. Bond graphs are combined with genetic programming to evolve low-level building blocks into systems with high-level functionalities including both topological configurations and parameter settings. Design spaces of coadapted mechatronic subsystems are automatically explored in parallel for overall design optimality. A quarter-car suspension system case study is provided. Compared with conventional design methods, semiactive suspension designs with more creativity and flexibility are achieved through this approach.