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-array composite design (OACD), combined with two-level OA and four-level OA and denoted by OACD₄, is proposed to estimate the second-order and third-order models. It is shown that OACD₄ has good properties and has higher efficiency than other types of designs for the third-order models, and OACD₄ can perform multiple analysis for cross-validation. The usefulness of OACD₄ is also shown by a case study for polymer synthesis experiment.

KEYWORDS:

• Central composite design
• D-efficiency
• Orthogonal-array composite design
• Third-order model
• Uniform design

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K15

Funding

This work was supported by CEMEE State Key Laboratory fund project (CEMEE2015Z0301A1), National Natural Science Foundation of China (11471229), and Fundamental Research Funds for the Central Universities (2013SCU04A43).