A Theoretical and Empirical Comparison of Two Mixed-Factor Central-Composite Desicns

1974 ◽  
Vol 18 (4) ◽  
pp. 418-424
Author(s):  
Christine Clark
Keyword(s):  
Human Performance ◽  
Empirical Investigation ◽  
Predictive Accuracy ◽  
Current Paper ◽  
Prediction Equations ◽  
Empirical Comparison ◽  
Central Composite Designs ◽  
Composite Designs ◽  
Performance Research ◽  
Central Composite

This paper provides a brief review of the application of Central-Composite Designs (CCD) in human performance research. Particular mention is made of the mixed-factor CCD, which allows simultaneous consideration of within-subject and between-subjects factors. The current paper details the construction of two alternative versions of such a design. After the two versions have been compared on theoretical grounds, an empirical investigation is proposed to determine the relative predictive accuracy and validity of prediction equations derived from data collected in accordance with each design version.

Response Surface Methodology Central-Composite Design Modifications for Human Performance Research

1973 ◽  
Vol 15 (4) ◽  
pp. 295-310 ◽  
Author(s):  
Christine Clark ◽  
Robert C. Williges
Keyword(s):  
Response Surface Methodology ◽  
Central Composite Design ◽  
Response Surface ◽  
Human Performance ◽  
Experimental Point ◽  
Multiple Observations ◽  
Central Composite Designs ◽  
Composite Designs ◽  
Performance Research ◽  
Central Composite

Selected response surface methodology (RSM) designs that are viable alternatives in human performance research are discussed. Two major RSM designs that are variations of the basic, blocked, central-composite design have been selected for consideration: (1) central-composite designs with multiple observations at only the center point, and (2) central-composite designs with multiple observations at each experimental point. Designs of the latter type are further categorized as: (a) designs which collapse data across all observations at the same experimental point; (b) between-subjects designs in which no subject is observed more than once, and observations at each experimental point may be multiple and unequal or multiple and equal; and (c) within-subject designs in which each subject is observed only once at each experimental point. The ramifications of these designs are discussed in terms of various criteria such as rotatability, orthogonal blocking, and estimates of error.

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 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 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.

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