Feng Yang

Bio: Feng Yang is an academic researcher from Sichuan Normal University. The author has contributed to research in topics: Optimal design & Design of experiments. The author has an hindex of 2, co-authored 6 publications receiving 23 citations. Previous affiliations of Feng Yang include Sichuan University.

Orthogonal-array composite design for the third-order models

Abstract: In many industrial trials, the second-order models may not be enough to fit the non linearity of the underlying model, and the third-order models may be considered. In this article, the orthogonal-...

Mixed-Level Column Augmented Uniform Designs

Abstract: Follow-up experimental designs are popularly used in industry. In many follow-up designs, some additional factors with two or three levels may be added in the follow-up stage since they are quite important but may be neglected in the first stage. Such follow-up designs are called mixed-level column augmented designs. In this paper, based on the initial designs, mixed-level column augmented uniform designs are proposed by using the uniformity criterion, wrap-around $L_2$-discrepancy (WD). The multi-stage augmented procedure which adds the additional design points stage by stage is also investigated. We present the analytical expressions and the corresponding lower bounds of the WD of the column augmented designs. It is shown that the column augmented uniform designs are also the optimal designs under the non-orthogonality criterion, $E(f_{NOD})$. Furthermore, a construction algorithm for the column augmented uniform design is provided. Some examples show that the lower bounds are tight and the construction algorithm is effective.

Uniformity criterion for designs with both qualitative and quantitative factors

Abstract: Experiments with both qualitative and quantitative factors occur frequently in practical applications. Many construction methods for this kind of designs, such as marginally coupled designs, were p...

Small response-surface designs

Abstract: Standard composite designs for fitting second-order response surfaces typically have a fairly large number of points, especially when k is large. In some circumstances, it is desirable to reduce the number of runs as much as possible while maintaining the ability to estimate all of the terms in the model. We first review prior work on small composite designs and then suggest some alternatives for k ≤ 10 factors. In some cases, even minimal-point designs are possible.

Multiple doubling: a simple effective construction technique for optimal two-level experimental designs

Abstract: Design of experiment is an efficient statistical methodology of establishing which input variables are important (have significant effects) in an experiment (process) and the conditions under which these inputs should work to optimize the outputs of that process. Two-level designs are widely used in high-tech industries and manufacturing for productivity and quality improvement experiments. The construction of (nearly) optimal two-level designs for real-life experiments with large number of input variables can be quite challenging. The practice demonstrated that the existing techniques are complex, highly time-consuming, produce limited types of designs, and likely to fail in large experiments (i.e., optimal results are not expected). To overcome these significant problems, this article gives a simple and effective technique for constructing large two-level designs with good statistical properties. To meet practical needs in different fields, the statistical properties of the generated designs by the new technique are investigated from four basic perspectives: minimizing the similarity among the experimental runs, minimizing the aliasing among the input variables, maximizing the resolution, and filling the experimental domain as uniformly as possible. New recommended saturated orthogonal main effect plans and uniform orthogonal arrays of strength three with thousands or even millions of runs and factors are generated via the new technique without recourse to optimization software.

Cross-Entropy Loss for Recommending Efficient Fold-Over Technique

Abstract: Due to the limited resources and budgets in many real-life projects, it is unaffordable to use full factorial experimental designs and thus fractional factorial (FF) designs are used instead. The aliasing of factorial effects is the price we pay for using FF designs and thus some significant effects cannot be estimated. Therefore, some additional observations (runs) are needed to break the linages among the factorial effects. Folding over the initial FF designs is one of the significant approaches for selecting the additional runs. This paper gives an in-depth look at fold-over techniques via the following four significant contributions. The first contribution is on discussing the adjusted switching levels fold-over technique to overcome the limitation of the classical one. The second contribution is on presenting a comparison study among the widely used fold-over techniques to help experimenters to recommend a suitable fold-over technique for their experiments by answering the following two fundamental questions: Do these techniques dramatically lessen the confounding of the initial designs, and do the resulting combined designs (combining initial design with its fold-over) via these techniques have considerable difference from the optimality point of view considering the markedly different searching domains in each technique? The optimality criteria are the aberration, confounding, Hamming distance and uniformity. Many of these criteria are given in sequences (patterns) form, which are inconvenient and costly to represent and compare, especially when the designs have many factors. The third innovation is on developing a new criterion (dictionary cross-entropy loss) to simplify the existing criteria from sequence to scalar. The new criterion leads to a more straightforward and easy comparison study. The final contribution is on establishing a general framework for the connections between initial designs and combined designs based on any fold-over technique.