scholarly journals An approach to measuring rotatability in central composite designs

2015 ◽  
Vol 3 (2) ◽  
pp. 126
Author(s):  
Emmanuel Ohaegbulem ◽  
Polycarp Chigbu
Keyword(s):  
New Approach ◽  
Measure Design ◽  
Central Composite Designs ◽  
Composite Designs ◽  
Central Composite

<p>An approach to measure design rotatability and a measure, that quantifies the percentage of rotatability (from 0 to 100) in the central composite designs are introduced. This new approach is quite different from the ones provided by previous authors which assessed design rotatability by the viewing of tediously obtained contour diagrams. This new approach has not practical limitations, and the measure is very easy to compute. Some examples were used to express this approach.</p>

scholarly journals Construction of Modified Central Composite Designs for Non-standard Models

2018 ◽  
Vol 7 (5) ◽  
pp. 95
Author(s):  
Iwundu, M. P.
Keyword(s):  
Loss Function ◽  
Information Matrix ◽  
Missing Observations ◽  
Design Efficiency ◽  
Central Composite Designs ◽  
Standard Models ◽  
Alternative Designs ◽  
Composite Designs ◽  
Hat Matrix ◽  
Central Composite

The use of loss function in studying the reduction in determinant of information matrix due to missing observations has effectively produced designs that are robust to missing observations. Modified central composite designs are constructed for non-standard models using principles of the loss function or equivalently first compound of (I ) matrix associated with hat matrix . Although central composite designs (CCDs) are reasonably robust to model mis-specifications, efficient designs with fewer design points are more economical. By classifying the losses due to missing design points in the CCD portions, where there are multiple losses associated with specified CCD portions, the design points having less influence may be deleted from the full CCD. This leads to a possible increase in design efficiency and offers alternative designs, similar in the structure of CCDs, for non-standard models.

scholarly journals Optimal Prediction Variance Capabilities of Inscribed Central Composite Designs

2020 ◽  
pp. 1-8
Author(s):  
Julius C. Nwanya ◽  
Kelechukwu C. N. Dozie
Keyword(s):  
Central Composite Design ◽  
Design Space ◽  
Optimal Prediction ◽  
Prediction Variance ◽  
Central Composite Designs ◽  
Scaled Prediction Variance ◽  
Composite Designs ◽  
Central Composite

This study looks at the effects of replication on prediction variance performances of inscribe central composite design especially those without replication on the factorial and axial portion (ICCD1), inscribe central composite design with replicated axial portion (ICCD2) and inscribe central composite design whose factorial portion is replicated (ICCD3). The G-optimal, I-optimal and FDS plots were used to examine these designs. Inscribe central composite design without replicated factorial and axial portion (ICCD1) has a better maximum scaled prediction variance (SPV) at factors k = 2 to 4 while inscribe central composite design with replicated factorial portion (ICCD3) has a better maximum and average SPV at 5 and 6 factor levels. The fraction of design space (FDS) plots show that the inscribe central composite design is superior to ICCD3 and inscribe central composite design with replicated axial portion (ICCD2) from 0.0 to 0.5 of the design space while inscribe central composite design with replicated factorial portion (ICCD3) is superior to ICCD1 and ICCD2 from 0.6 to 1.0 of the design space for factors k = 2 to 4.

Slope-Rotatable Central Composite Designs

Technometrics ◽  
1978 ◽  
Vol 20 (4) ◽  
pp. 413-417 ◽  
Author(s):  
R. J. Hader ◽  
Sung H. Park
Keyword(s):  
Central Composite Designs ◽  
Composite Designs ◽  
Central Composite

Research Note: Modified Orthogonal Central-Composite Designs

1976 ◽  
Vol 18 (1) ◽  
pp. 95-98 ◽  
Author(s):  
Robert C. Williges
Keyword(s):  
Central Composite Design ◽  
Second Order ◽  
Research Note ◽  
Design Parameters ◽  
Orthogonal Designs ◽  
Central Composite Designs ◽  
Data Points ◽  
Composite Designs ◽  
Central Composite

Simplified formulae for determining the coded value of α are presentedfor rotatable, blocked orthogonal second–order designs in which all data points are replicated an equal number of times. These three central–composite design parameters are compared, and the advantages and limitations of orthogonal designs are presented.

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