Generating blocked fractional factorial split-plot designs using integer programming

Capehart, Shay R.; Keha, Ahmet B.; Külahçı, Murat; Montgomery, Douglas C.

doi:10.1504/ijedpo.2012.049297

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Vivacqua and Bisgaard 30 presented novel arrangements for strip‐block designs that reduce the experimental effort. Woods and van de Ven 31 provided blocked designs for experiments with a correlated non‐normal response and Capehart et al 32 generated blocked fractional factorial split‐plot designs using integer programming.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

A sequential experimentation method to separate interaction effects from block effects

Ríos

Murillo

Pantoja

et al. 2020

Engineering Reports

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Blocking is a basic experimentation principle that separates the variability caused by noise factors. Unless the experiment is replicated, blocking produces loss of information, particularly two‐factor interactions (2FIs) are commonly lost to blocks. Additionally, the ANOVA table does not show to what extent each blocked noise factor affects the response variable. Individual contributing percentages for noise factors can be useful to make process improvements and to understand which noise factors are most influential. This research proposes a sequential experimentation method to separate 2FIs from blocks and assign contributing percentages to each blocked noise factor. The method is evaluated and compared to foldover, semifold, and D‐optimal augmentation.

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Section: Theoretical Frameworkmentioning

confidence: 99%

A sequential experimentation method to separate interaction effects from block effects

Ríos

Murillo

Pantoja

et al. 2020

Engineering Reports

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show abstract

“…Capehart et al (2011) uses integer programming to design regular fractional factorial split-plot experiments, while Sartono et al (2015b) use integer programming to block given regular and nonregular orthogonal designs. Capehart et al (2012) and Sartono et al (2015a) use integer programming to construct blocked fractional factorial split-plot designs and general orthogonal fractional factorial split-plot designs, respectively.…”

Section: Time Trends and Optimal Design Of Experimentsmentioning

confidence: 99%

An integer linear programing approach to find trend-robust run orders of experimental designs

Ares

Goos

2019

Journal of Quality Technology

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When a multi-factor experiment is carried out over a period of time, the responses may depend on a time trend. Unless the tests of the experiment are conducted in a proper order, the time trend has a negative impact on the precision of the estimates of the main effects, the interaction effects and the quadratic effects. A proper run order, called a trend-robust run order, minimizes the confounding between the effects' contrast vectors and the time trend's linear, quadratic and cubic components. Finding a trend-robust run order is essentially a permutation problem. We develop a multistage approach based on integer programming to find a trend-robust run order for any given design. The multistage nature of our algorithm allows us to prioritize the trend robustness of the main-effect estimates. In the literature, most of the methods used are tailored to specific designs, and are not applicable to an arbitrary design.Additionally, little attention has been paid to trend-robust run orders of response surface designs, such as central composite designs, Box-Behnken designs and definitive screening designs. Our algorithm succeeds in identifying trend-robust run orders for arbitrary factorial designs and response surface designs with two up to six factors.

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“…Arnouts et al (2010Arnouts et al ( , 2013 present an alternative construction based on optimal experimental design methodology. The combination of split-plot designs and blocking has been discussed in Capehart et al (2012), while staggeredlevel designs have been proposed by Goos (2012, 2015) as an alternative to split-plot designs when there are multiple so-called hard-to-change factors.…”

Section: Follow-up Workmentioning

confidence: 99%

Discussion on “Søren Bisgaard's contributions to Quality Engineering: Design of experiments”

Goos

Schoen

2019

Quality Engineering

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Generating blocked fractional factorial split-plot designs using integer programming

Cited by 3 publications

References 25 publications

A sequential experimentation method to separate interaction effects from block effects

A sequential experimentation method to separate interaction effects from block effects

An integer linear programing approach to find trend-robust run orders of experimental designs

Discussion on “Søren Bisgaard's contributions to Quality Engineering: Design of experiments”

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