DP-Optimality in Terms of Multiple Criteria and Its Application to the Split-Plot Design
Abstract
Recent arguments have been made that optimal design criteria should incorporate pure error degrees of freedom for estimating unknown variance components. In this paper, we incorporate pure error, along with traditional design criteria, using Pareto optimization to identify a collection of optimal designs. This strategy demonstrates the trade-offs between these conflicting objectives without having to resort to weighted combinations of the criteria. The proposed approach also allows extension of the criteria for purposes of selecting optimal split-plot designs based on the D-criterion and pure error degrees of freedom.
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The new method differs from Cao et al. (2017) and Trinca and Gilmour (2017) by adjusting the ordinary D-optimality criterion to ensure that the variance components are well estimated.
“Our new method diers from those of Cao et al. (2017) and Trinca and Gilmour (2017), who build on the ideas in Gilmour and Trinca (2012) for completely randomized designs, in the sense that we adjust the ordinary D-optimality criterion to ensure that the variance components are well estimated.”
From Optimal Blocked and Split-Plot Designs Ensuring Precise Pure-Error Estimation of the Variance Components (2020) · cites this paper as Cao et al. (2017)
The new designs aim to be optimal for all parameters, whereas Cao et al. (2017) and Trinca and Gilmour (2017) aim to be optimal only for fixed effects and only stratum by stratum.
“Our designs aim to be optimal for all parameters, whereas theirs aim to be optimal only for xed eects and only stratum by stratum.”
From Optimal Blocked and Split-Plot Designs Ensuring Precise Pure-Error Estimation of the Variance Components (2020) · cites this paper as Cao et al. (2017)
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Mylona, K., Gilmour, S. G., & Goos, P. (2020) · Technometrics · doi:10.1080/00401706.2019.1595153 · Cited by 13 · see citing works
- Authors
- Cao, Y., Wulff, S. S., & Robinson, T. J.
- Affiliations
- Indiana University of Pennsylvania (US)
- University of Wyoming (US)
- Venue
- Journal of Quality Technology
- Publisher
- Informa UK Limited
- Published
- 2017-01
- Volume
- 49
- Issue
- 1
- Pages
- 27-45
- ISSN
- 0022-4065 (ISSN-L)
- 2575-6230
- OpenAlex
- W2586971991
- Cited by
- 9
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2022: 2 · 2019: 2 · 2018: 1 · 2017: 1
- FWCI
- 0.97
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Quality Technology (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Multi-Objective Optimization Algorithms
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- multi-objective optimization, split-plot design, D-optimal design, variance component estimation, optimal experimental design
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