Classes of Split‐plot Response Surface Designs for Equivalent Estimation
Open accessAbstract
When planning an experimental investigation, we are frequently faced with factors that are difficult or time consuming to manipulate, thereby making complete randomization impractical. A split‐plot structure differentiates between the experimental units associated with these hard‐to‐change factors and those that are relatively easy‐to‐change. Furthermore, it provides an efficient strategy that integrates the restrictions imposed by the experimental apparatus into the design structure. In this paper, several industrial and scientific examples are presented to highlight design considerations when a restriction on randomization is encountered. We propose classes of split‐plot response designs that provide an intuitive and natural extension from the completely randomized context. For these designs, the ordinary least‐squares estimates of the model are equivalent to the generalized least‐squares estimates. This property provides best linear unbiased estimators and simplifies model estimation. The design conditions that provide equivalent estimation are presented and lead to design construction strategies to transform completely randomized Box–Behnken, equiradial and small composite designs into a split‐plot structure. Published in 2006 by John Wiley & Sons, Ltd.
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Those split-plot designs replicate a few treatments many times, mainly center and/or axial points, with much replication inside whole plots.
“These designs involve many replicates of a limited number of treatments (namely, the treatments corresponding to center points and/or axial points).Much of the replication in these designs is within the whole plots.”
From Optimal Blocked and Split-Plot Designs Ensuring Precise Pure-Error Estimation of the Variance Components (2020) · cites this paper as Parker et al. (2006)
Section 5.1 describes adding subplot-center replicates to balance a Box–Behnken design, and Section 5.2 says subplot centers can be added within each whole plot. But Section 5.3 says its base crossed design has no replicates, while Section 6 describes a design without replication. The paper therefore supports within-whole-plot center replication as an option, not the general characterization that these designs contain many replicates concentrated at center and/or axial points. (LLM, conf=0.85)
Experimental — accuracy not yet measuredThe new-criterion designs differ fundamentally from the split-plot designs of Vining et al. (2005), Parker et al. (2006), Kowalski et al. (2002), and Kowalski et al. (2006).
“Consequently, the designs produced by the new criterion are fundamentally dierent from the split-plot designs proposed by Vining et al. (2005), Parker et al. (2006), Kowalski et al. (2002) and Kowalski et al. (2006).”
From Optimal Blocked and Split-Plot Designs Ensuring Precise Pure-Error Estimation of the Variance Components (2020) · cites this paper as Parker et al. (2006)
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Research works printed but not linked: 20
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- Published in 2006 by John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2006; 22:291-305 DOI: 10.1002/qre 10991638, 2006, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.771 by Mount Vernon Nazarene University, Wiley Online Library on [06/09/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License · DOI
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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
- Parker, P. A., Kowalski, S. M., & Vining, G. G.
- Affiliations
- Langley Research Center (US)
- Virginia Tech (US)
- Corresponding author
- Parker, Peter A.
- Venue
- Quality and Reliability Engineering International
- Publisher
- Wiley
- Published
- 2006-04
- Volume
- 22
- Issue
- 3
- Pages
- 291-305
- ISSN
- 0748-8017 (ISSN-L)
- 1099-1638
- OpenAlex
- W2023287634
- Cited by
- 44
- References
- 0
- Citations by year
- 2026: 2 · 2024: 4 · 2023: 1 · 2022: 2 · 2021: 1 · 2019: 2 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 4 · 2014: 2 · 2013: 1 · 2012: 8
- FWCI
- 5.32
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Quality and Reliability Engineering International (publishedVersion, public-domain)
- NASA STI Repository (National Aeronautics and Space Administration) (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- split-plot design, response surface design, generalized least squares, best linear unbiased estimator, Box-Behnken design, design construction, restricted randomization
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