Slope-Rotatable Central Composite Designs

Hader, R. J.; Park, Sung H.

doi:10.1080/00401706.1978.10489695

Cited by 69 publications

(40 citation statements)

References 5 publications

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“…Park and Kim [34] defined a measure ( ) k Q D to quantify the degree of slope rotatability over axial directions [18] for secondorder models. It takes the value zero if and only if the design is slope rotatable.…”

Section: Measuring Slope Rotatabilitymentioning

confidence: 99%

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A General Overview of Response Surface Methodology

Khuri¹

2017

BBIJ

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See also the article by Steinberg and Hunter [5]. RSM Books include1. Myers and Montgomery [6] 2. Khuri and Cornell [7] 3. Box and Draper [8] The present article provides a general overview of response surface methodology (RSM). Notation Response Surface MethodologyResponse surface methodology (RSM) is a collection of statistical and mathematical techniques used for the purpose of I. Setting up a series of experiments (design) for adequate predictions of a response y.

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Section: Measuring Slope Rotatabilitymentioning

confidence: 99%

“…Some relevant articles are: [13][14][15][16]. Hader and Park [18] introduced the concept of design rotatability for second-order models. Under this design criterion,…”

Section: Design Robustnessmentioning

confidence: 99%

A General Overview of Response Surface Methodology

Khuri¹

2017

BBIJ

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“…Thus it is important to know if a particular design is rotatable or, if it is not, to know how rotatable it is. Analogous to rotatability, the concept of slope-rotatability has been advanced by Hader and Park (1978) and Park (1987). In this concept, the variance of O~l(x)/Oxi ({ = 1,..., k) are equal for all x equidistant from the design origin.…”

Section: Introductionmentioning

confidence: 99%

A measure of rotatability for second order response surface designs

1993

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Abstract. The concept of rotatability introduced by Box and Hunter (1957, Ann. Math. Statist., 28, 195-241) is an important design criterion for response surface design. Recently, a few measures of rotatability that enable us to assess the degree of rotatability for a given response surface design have been introduced. In this paper, a new measure of rotatability for second order response surface designs is suggested, and illustrated for 3 k factorial design and central composite design. Also a short comparison is made between the proposed measure with the previously suggested measures.

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“…In many applications of response surface methodology, good estimation of the derivatives of the response function is as important as estimation of the mean response. From the work of Hader and Park (1978), Huda and Al-Siha (1999) and Huda (2006), it is clear that most of the work has been done on central composite designs hence there was a need to extend the concept of slope to mixture experiments third degree Kronecker, this method was therefore used for proper identification of the ingredients ratio that leads to an optimal response.…”

Section: Introductionmentioning

confidence: 99%

Slope Optimal Designs for Third Degree Kronecker Model Mixture Experiments

Kipkoech¹

2017

AJTAS

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Abstract:Mixture experiments are special type of response surface designs where the factors under study are proportions of the ingredients of a mixture. In response surface designs the main interest of the experimenter may not always be in the response at individual locations, but the differences between the responses at various locations is of great interest. Most of the studies on estimation of slope (rate of change) have concentrated in Central Composite Designs (CCD) yet mixture experiments are intended to show the response for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients at different locations. Slope optimal mixture designs for third degree Kronecker model were studied in order to obtained optimal formulations for all possible ingredients in simplex centroid. Weighted Simplex Centroid Designs (WSCD) and Uniformly Weighted Simplex Centroid Designs (UWSCD) mixture experiments were obtained in order to identify optimal proportions for each of the ingredients formulation. Derivatives of the Kronecker model mixture experiment were used to obtain Slope Information Matrices (SIM) for four ingredients. Maximal parameters of interest for third degree Kronecker model were considered. D-, E-, A-, and T-optimal criteria and their efficiencies for both WSCD and UWSCD third degree Kronecker model were obtained. UWSCD was found to be more efficient than WSCD for almost all the points in the simplex designs, therefore recommended for more optimal results in mixture experiments.

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Slope-Rotatable Central Composite Designs

Cited by 69 publications

References 5 publications

A General Overview of Response Surface Methodology

A General Overview of Response Surface Methodology

A measure of rotatability for second order response surface designs

Slope Optimal Designs for Third Degree Kronecker Model Mixture Experiments

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