Abstract
Follow-up experiments are used extensively to provide precious information about the relationships between inputs and outputs to gain a better understanding of a process or system under study. This article gives a new look at designing optimal follow-up experiments that involve any number of factors with any number of different levels in light of the uniformity behaviour of the corresponding two stage sequential experiments, which are composed of initial experiments and follow-up experiments. Novel analytical expressions and lower bounds of the wrap-around \(L_2\)-discrepancy, as a uniformity measure, for sequential experimental designs are proposed for evaluating the optimality of the follow-up experimental designs. Finding equivalent follow-up experimental designs is investigated, which can be used to reduce the computational complexity. Our results show that two stage sequential experimental designs give greater precision than single stage experimental designs with the same size.
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Acknowledgements
The authors greatly appreciate helpful suggestions of the two referees that significantly improved the paper. This work was partially supported by the UIC Grants (Nos. R201409 and R201712) and the Zhuhai Premier Discipline Grant.
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Elsawah, A.M., Fang, KT. New foundations for designing U-optimal follow-up experiments with flexible levels. Stat Papers 61, 823–849 (2020). https://doi.org/10.1007/s00362-017-0963-z
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DOI: https://doi.org/10.1007/s00362-017-0963-z
Keywords
- Indicator function
- Follow-up experiment
- Follow-up map
- Sequential experiment
- Equivalent design
- Optimal sequential experiment