Optimal Prediction Variance Capabilities of Inscribed Central Composite Designs

Nwanya, Julius C.; Dozie, Kelechukwu C. N.

doi:10.9734/ajpas/2020/v8i130194

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…In comparing response surface designs, a design with the smallest optimality criterion value is often desired over those that are not [13][14][15]. The results of the D-, A-and G-optimality criteria obtained when the radius of a sphere is 𝛼 = √𝑘𝑘 are presented in Table 2.…”

Section: Comparison Using D- A-and G-optimality Criteriamentioning

confidence: 99%

“…Yankam and Oladugba [9] constructed third-order orthogonal uniform composite designs (OUCD 4 ) to estimate the third-order model parameters. These designs are commonly selected using the best single-valued criteria, such as D-optimality, which considers the variance and covariances of the model's coefficient estimates, I-optimality, which considers the average variance for a projected value over the region of interest, and G-optimality, which considers the overall variance for a projected value over the region of interest [10][11][12][13][14]. Unfortunately, single-valued criteria frequently fail to reflect the true nature of a design employed to fit the response surface model in terms of prediction properties over a specified region of interest or portion of the design space [12,15].…”

Section: Introductionmentioning

confidence: 99%

“…Take for instance Borkowski [15] studied the scaled prediction variance of central composite designs (CCDs) and Box-Benhken designs (BBDs); Wesley et al [22] studied the prediction variance properties of split-plot designs in both the spherical and cuboidal region; Borkowski [12] studied the prediction variance capabilities of CCDs and BBDs in the spherical region; Chigbu et al [23] studied the prediction variance properties of some composite designs in the spherical region; Onwuamaeze [24] investigated the prediction variance properties of several cuboidal designs. ; Zahran et al [17] used the FDS graphs to assess the prediction capability of some designs; Oyejola and Nwanya [13] studied the prediction capability of inscribed central composite designs, by using FDS graphs; Nwanya and Dozie [14] used FDS graph to assess the prediction capability of some designs. The VDG is obtained by plotting scaled prediction variances against the radius r, of the region of interest while the FDS graph is obtained by plotting the scaled prediction variances against a fraction of space [13,18].…”

Section: Introductionmentioning

confidence: 99%

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Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

Oladugba¹,

Yankam²

2022

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The variance dispersion graphs (VDGs) and the fraction of design space (FDS) graphs are two graphical methods that effectively describe and evaluate the points of best and worst prediction capability of a design using the scaled prediction variance properties. These graphs are often utilized as an alternative to the single-value criteria such as D-and E-when they fail to describe the true nature of designs. In this paper, the VDGs and FDS graphs of third-order orthogonal uniform composite designs (OUCD 4 ) and orthogonal array composite designs (OACD 4 ) using the scaled-prediction variance properties in the spherical region for 2 to 7 factors are studied throughout the design region and over a fraction of space. Single-valued criteria such as D-, A-and G-optimality are also studied. The results obtained show that the OUCD 4 is more optimal than the OACD 4 in terms of D-, A-and G-optimality. The OUCD 4 was shown to possess a more stable and uniform scaled-prediction variance throughout the design region and over a fraction of design space than the OACD 4 although the stability of both designs slightly deteriorated towards the extremes.

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Section: Comparison Using D- A-and G-optimality Criteriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

Oladugba¹,

Yankam²

2022

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“…[13] recommended different number of center point, ranging from 3 to 12 for the Box Behnken Designs. [14], examined the contributions of center points on prediction variance performances on CCDs using the G-optimal, I optimal and FDS plots. It was discovered that the designs perform better with or without replication (center points).…”

Section: Center Pointsmentioning

confidence: 99%

Appropriate Number of Center Points for Response Surface Exploration Using Small Box Behnken Design

Kiwu

Kiwu-Lawrence

Boniface

et al. 2022

ACRI

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Industrial exploration using the Box Behnken Design (BBD) has been faced with a serious setback due to the swift upsurge in the runs size as the number of factors increase. This, therefore, dissuades researchers and affects the application of the design. The Small Box Behnken Designs (SBBD) which achieve the research goal of BBD were proposed to overcome the setback. This paper aimed at recommending an appropriate number of center points suitable for response surface exploration and its applications in industries using the SBBD. The method adopted for assessing the center points is the prediction variance-based G-efficiency optimality criterion. The range of design factors, k, considered is 3 to 11, while comparing the designs at 0 - 5 number of center points. For each of the design factors considered, the result showed that increasing the center point, decreases the G-efficiency value. Hence, increasing the center point does not contribute significantly to the prediction variance capability of the designs considered. However, in other to test the model lack of fit and estimate pure error which are very important in experimental design analysis, this study recommends that at most two runs (center points) be replicated at the center. Since with this number, approximately 90% G-efficiency can be achieved for response surface exploration using the SBBD.

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Design of experiments in the optimization of all-cellulose composites

Victoria,

Hine,

Ward

et al. 2023

Cellulose

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In this work, statistical design of experiments (DoE) was applied to the optimization of all cellulose composites (ACCs) using cotton textile and interleaf films under applied heat and pressure. The effects of dissolution temperature, pressure and time on ACC mechanical properties were explored through a full factorial design (23) and later optimized using Response Surface Methodology. It was found that the experimental design was effective at revealing the underlying relationship between Young’s modulus and processing conditions, identifying optimum temperature and time settings of 101 °C and 96.8 min respectively, to yield a predicted Young’s modulus of 3.3 GPa. This was subsequently validated through the preparation of in-lab test samples which were found to exhibit a very similar Young’s modulus of 3.4 ± 0.2 GPa, confirming the adequacy of the predictive model. Additionally, the optimized samples had an average tensile strength and peel strength of 72 ± 2 MPa and 811 ± 160 N/m respectively, as well as a favorable density resulting from excellent consolidation within the material microstructure. This work highlights the potential of DoE for future ACC process understanding and optimization, helping to bring ACCs to the marketplace as feasible material alternatives.

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Optimal Prediction Variance Capabilities of Inscribed Central Composite Designs

Cited by 4 publications

References 13 publications

Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

Appropriate Number of Center Points for Response Surface Exploration Using Small Box Behnken Design

Design of experiments in the optimization of all-cellulose composites

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