Split-Plot Designs and Estimation Methods for Mixture Experiments With Process Variables
Abstract
In mixture experiments with process variables, the response depends not only on the proportions of the mixture components, but also on the effects of the process variables. In many such mixture-process variable experiments, constraints such as time or cost prohibit the selection of treatments completely at random. In these situations, restrictions on the randomization force the level combinations of one group of factors to be fixed and the combinations of the other group of factors are run. Then a new level of the first factor group is fixed and combinations of the other group of factors are run. Earlier work referred to this restriction on randomization as a split-plot approach where several factor-level combinations among one or more groups of process variables defined the whole-plot treatments while a group of mixture blends defined the subplot treatments. New split-plot designs are presented for mixture experiments with process variables while considering a new model form. Three methods of estimation are considered for the terms in the model.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
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 Kowalski et al. (2002)
The 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 Kowalski et al. (2002)
Cited by
Sorted by citations
Analysis of Data from Non-Orthogonal Multistratum Designs in Industrial Experiments
Gilmour, S. G., & Goos, P. (2009) · Journal of the Royal Statistical Society Series C: Applied Statistics · doi:10.1111/j.1467-9876.2009.00662.x · Cited by 31 · see citing works
Mylona, K., Gilmour, S. G., & Goos, P. (2020) · Technometrics · doi:10.1080/00401706.2019.1595153 · Cited by 13 · see citing works
- Authors
- Kowalski, S. M., Cornell, J. A., & Vining, G. G.
- Affiliations
- University of Florida (US)
- Virginia Tech (US)
- ORCID
- Vining, G. Geoffrey
- Venue
- Technometrics
- Publisher
- Informa UK Limited
- Published
- 2002-02
- Volume
- 44
- Issue
- 1
- Pages
- 72-79
- ISSN
- 0040-1706 (ISSN-L)
- 1537-2723
- OpenAlex
- W1996507898
- Cited by
- 112
- References
- 0
- Citations by year
- 2026: 2 · 2025: 3 · 2023: 2 · 2022: 6 · 2021: 3 · 2020: 1 · 2019: 3 · 2018: 1 · 2017: 4 · 2016: 3 · 2015: 3 · 2014: 2 · 2013: 5 · 2012: 4
- FWCI
- 9.88
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Technometrics (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Keywords
- mixture experiments, process parameters, split-plot design, estimation methods, mixture models
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
