scholarly journals Robustness of Central Composite Design and Modified Central Composite Design to a Missing Observation for Non-Standard Models

2021 ◽  
Vol 4 (2) ◽  
pp. 25-40
Author(s):  
Jaja E.I. ◽  
Etuk E.H. ◽  
Iwundu M.P. ◽  
Amos E.
Keyword(s):  
Decision Making ◽  
Standard Model ◽  
Central Composite Design ◽  
Missing Observations ◽  
Efficient Design ◽  
Standard Models ◽  
Hat Matrix ◽  
Central Composite ◽  
Lower Loss ◽  
Missing Observation

Missing observations in an experimental design may lead to ambiguity in decision making thereby bringing an experiment to disrepute. Robustness, therefore, enables a process, not to break down in the presence of missing observations. This work constructed a modified central composite design (MCCD) from a four-variable central composite design (CCD) augmented with four center points using the leverage of a hat-matrix. The robustness of the CCD and MCCD were assessed when a design point is missing at the factorial, axial, and center points of the experiment, for a non-standard model, using the loss criterion, D-optimality, D-efficiency, and relative D-efficiency. When the designs are complete the MCCD shows higher D-efficiency and D-optimality for the non-standard model when compared to the CCD. In the absence of an observation from any of the designs, the CCD is found to be a more robust and efficient design compared to the MCCD as it has overall lower loss values at all the factors levels.

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 The Comparative Study of CCD and MCCD in the Presence of a Missing Design Point

2021 ◽  
Vol 4 (2) ◽  
pp. 10-24
Author(s):  
Jaja E.I. ◽  
Iwundu M.P. ◽  
Etuk E.H.
Keyword(s):  
Comparative Study ◽  
Central Composite Design ◽  
Missing Observations ◽  
Design Point ◽  
The Comparative Study ◽  
Central Composite ◽  
Missing Observation

The work constructed a modified central composite design from a rotatable central composite design augmented with seven center points adapted from the work of Wu and Li (2002). The comparison of the robustness of the CCD and MCCD to missing observation was investigated at various design points of factorial, axial and center points’ when the model is non-standard, using A-efficiency and the Losses associated. The results of the evaluations of the designs to missing observations are presented, and the MCCD is shown to be more A-optimal while the CCD is more robust and relatively A-efficient to a missing observation.

scholarly journals Design Efficiency and Optimal Values of Replicated Central Composite Designs with Full Factorial Portions

2021 ◽  
Vol 4 (3) ◽  
pp. 89-117
Author(s):  
Iwundu M.P. ◽  
Oko E.T.
Keyword(s):  
Central Composite Design ◽  
Optimal Combination ◽  
Efficient Design ◽  
Center Portion ◽  
Design Variables ◽  
Central Composite Designs ◽  
Optimal Values ◽  
Full Factorial ◽  
Composite Designs ◽  
Central Composite

Efficiency and optimal properties of four varieties of Central Composite Design, namely, SCCD, RCCD, OCCD and FCCD and having r_f replicates of the full factorial portion, r_α replicates of the axial portion and r_c replicates of the center portion are studied in four to six design variables. Optimal combination,[r_f: r_α: r_c ] of design points associated with the three portions of each central composite design is presented. For SCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the center portion of the SCCD. However, replicating the center and axial portions allows for G-optimal and efficient designs. For RCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the factorial and center portions of the RCCD. However, replicating the center and axial portions allows for G-optimal and efficient designs. For OCCD, the optimal combinations resulting in A- optimal and efficient designs generally put emphasis on replicating the axial and center portion of the OCCD. The optimal combinations resulting in G- optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the OCCD. To achieve designs that are D-optimal and D-efficient, the optimal combination of design points generally put emphasis on replicating the center portion of the OCCD. For FCCD, the optimal combinations of design points resulting in A-efficient designs put emphasis on replicating the axial portion of the FCCD. The optimal combinations resulting in G- optimal and efficient designs as well as G-optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the FCCD. It is interesting to note that for FCCD in five design variables, any r^th complete replicate of the distinct design points of the combination [r_f: r_α: r_c ] resulted in a D-efficient design. Many super-efficient designs having efficiency values greater than 1.0 emerged under the D-criterion. Unfortunately, these designs did not perform very well under A- and G-criteria, having some efficiency values much below 0.5 or just about 0.6.

Development and optimization of solid lipid nanoparticles of amikacin by central composite design

2009 ◽  
Vol 00 (00) ◽  
pp. 090721051030036-8
Author(s):  
Jaleh Varshosaz ◽  
Solmaz Ghaffari ◽  
Mohammad Reza Khoshayand ◽  
Fatemeh Atyabi ◽  
Shirzad Azarmi ◽  
...  
Keyword(s):  
Central Composite Design ◽  
Solid Lipid Nanoparticles ◽  
Lipid Nanoparticles ◽  
Solid Lipid ◽  
Central Composite

Formulation Design and Optimization of Repaglinide Solid Dispersions by Central Composite Design

2018 ◽  
Vol 11 (6) ◽  
pp. 4337-4348
Author(s):  
Bhikshapathi D. V. R. N. ◽  
Srinivas I
Keyword(s):  
Central Composite Design ◽  
Dissolution Rate ◽  
Solid Dispersion ◽  
Solid Dispersions ◽  
Solvent Evaporation ◽  
Release Mechanism ◽  
Solvent Evaporation Method ◽  
Onset Of Action ◽  
Evaporation Method ◽  
Central Composite

Repaglinide is a pharmaceutical drug used for the treatment of type II diabetes mellitus, it is characterized with poor solubility which limits its absorption and dissolution rate and delays onset of action. In the present study, immediate release solid dispersion of repaglinide was formulated by solvent evaporation technique. Repaglinide solid dispersions were prepared using PEG 8000, Pluronic F 127 and Gelucire 44/14 by solvent evaporation method. A 3-factor, 3-level central composite design employed to study the effect of each independent variable on dependent variables. FTIR studies revealed that no drug excipient interaction takes place. From powder X-ray diffraction (p-XRD) and by scanning electron microscopy (SEM) studies it was evident that polymorphic form of repaglinide has been converted into an amorphous form from crystalline within the solid dispersion formulation. The correlation coefficient showed that the release profile followed Higuchi model anomalous behavior and hence release mechanism was indicative of diffusion. The obtained results suggested that developed solid dispersion by solvent evaporation method might be an efficacious approach for enhancing the solubility and dissolution rate of repaglinide.

Formulation and Optimization of 5-Fluorouracil Loaded Chitosan Nanoparticles Employing Central Composite Design

2012 ◽  
Vol 2 (4) ◽  
pp. 281-289
Author(s):  
Rattan Lal ◽  
Rakesh Kumar Marwaha ◽  
Deepti Pandita ◽  
Harish Dureja
Keyword(s):  
Central Composite Design ◽  
Chitosan Nanoparticles ◽  
Central Composite
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