Novel techniques for performing successful follow-up experiments based on prior information from initial-stage experiments

ABSTRACT

Performing successful experiments is a crucial topic for scientists. The selection of factors and levels that have significant effects on the outputs is the most hard problem they may face. For a perfect procedure, a small number of runs (trials) are preferred as an initial-stage experiment (ISExp) for gaining prior information about the influence (importance) of the suggested factors and levels. After analysing the ISExp, the following prior information may arise: (i) the number of parameters in the used model is much larger than the expected number of runs and thus more runs need to be added; (ii) some of the ignored or fixed factors may be active and need further investigations; (iii) extending the levels of some active factors is necessary for optimising the outputs; and/or (iv) the impacts of the active factors are not equally important and thus different weights need be assigned to the factors to identify their importance. Therefore, follow-up experiments (FuExps) need to be conducted for adding new active factors, levels, runs, and/or factor-weights to the ISExps. This paper provides novel techniques for designing FuExps to deal with these real-life scenarios for ISExp with a mixture of two-level factors and four-level factors. To clarify the power and efficiency of the proposed techniques, numerical and theoretical justifications are given.

KEYWORDS:

• Follow-up experiments
• augmented experiments
• mixture factor-weight designs
• uniform designs
• aberration
• Hamming distance

MSC:

• 62K05
• 62K15

Acknowledgments

The author thank the two referees, Associate Editor and the Editor in Chief Professor Alexander Meister for constructive comments that lead to significant improvements of this paper. The author also would like to thank Prof. Kai-Tai Fang for his kind support during this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the UIC Research Grants with No. of (UICR201912 and UICR202010); the Curriculum Development and Teaching Enhancement with No. of (UICR0400046-21CTL); the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College with No. of (2022B1212010006); and the Guangdong Higher Education Upgrading Plan (2021-2025) with No. of (UICR0400001-22).