Optimal Third Order Rotatable Designs Constructed from Balanced Incomplete Block Design (BIBD)

Rotich, Jeremy; Kosgei, Mathew; Kerich, Gregory

doi:10.9734/cjast/2017/34937

Cited by 2 publications

(3 citation statements)

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“…The same trend was observed on the other optimality criteria. It is important to note that for a given number of factors, the design with a relatively lower number of points was more optimal than its counterpart of more points as confirmed in [15].…”

Section: Resultsmentioning

confidence: 78%

“…the designs considered in this paper were A-optimal. In a similar study by [15], all their designs were found to be E-Optimal. This implies that the TORDs are uniquely optimal.…”

Section: Resultsmentioning

confidence: 86%

“…If the first order model is found to be adequate, as the representation of the unknown function by noting the evidence of the goodness of fit, the experiment may be terminated at this stage [12, 14 & 15]. However, if the first model is found to be inadequate, the trials of the second order are run and ultimately, proceed to fit a third order if a second order model is also found to be inadequate [15]. According to Draper [7], third order rotatable designs can be constructed by combining the existing second order rotatable designs in three dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Sequential Third Order Rotatable Designs in Three, Four and Five Dimensions

Cornelious¹,

Kilonzo²

2021

IJSSAM

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Response surface methodology (RSM) is a statistical technique used to evaluate the relationship between multiple input variables and one or more response variables with the aim of optimizing the response variables. Sequential experiments are very economical and useful in practice. Therefore, rotatable designs such as the third order rotatable design (TORD) may be run sequentially in three stages with three or four blocks depending on the model adequacy. Normally, the first section consisting of first order is run and the response function is approximated using a first order model. If the first order model is found to be adequate, as the representation of the unknown function by noting the evidence of the goodness of fit, the experiment may be stopped at this stage. However, if the first model is found to be unfit, the trials of the second order are run and ultimately, proceed to fit a third order if a second order model is also found to be inadequate. In this paper, two sets of second order rotatable designs are combined to form sequential third order rotatable designs (TORD) in three, four and five dimensions. The TORDs are then evaluated on their alphabetic optimality criteria with the aim of reducing the costs of experimentation. The classical optimality criteria includes; D-criterion, A-criterion, T-criterion and E-criterion.

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Section: Resultsmentioning

confidence: 78%

“…the designs considered in this paper were A-optimal. In a similar study by [15], all their designs were found to be E-Optimal. This implies that the TORDs are uniquely optimal.…”

Section: Resultsmentioning

confidence: 86%