IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 11 NO. 1 2025
DOI: 10.56201/ijasmt.vol.11.no1.2025.pg117.131

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Performance Evaluation of a Five-Variable Face-Centered Central Composite Design with Full and Fractional Factorial Points in Process Optimization

Samuel Owhorndah Nanaka, Issac Didi Essi, Iyai Davies, Nkuturum Christy

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Abstract

Experimental design techniques play a crucial role in optimizing processes, particularly in resource-constrained environments. The Face-Centered Central Composite Design (FCCCD) is widely used for response surface modeling, but its performance when combining full and fractional portions remains underexplored. This study evaluates the performance of a Five-Variable Face- Centered Central Composite Design (FCCCD) with full and fractional factorial points in process optimization. The objective is to compare the design efficiency, predictive accuracy, and reliability of both design types under varying experimental conditions. The study assesses design parameters, fit statistics, and optimality criteria using statistical metrics such as A-efficiency, D-efficiency, and G-efficiency. Model validation is performed to show if the model fits the data, and adequacy precision through residual versus predicted plots. The performance of FCCCD is analyzed in terms of model adequacy, predictive capability, and practical feasibility. The impact of center points on model fit is also investigated. The findings provide that the fractional factorial design demonstrates significant advantages in efficiency, achieving higher A-efficiency (25.20% versus 18.55%) and D-efficiency (32.13% versus 12.06%) compared to the full factorial design. This makes it ideal for studies constrained by time, budget, or experimental resources. Despite its efficiency, it shows mild heteroscedasticity and non-linearity at the extremes of the response range, suggesting potential for further refinement. On the other hand, the full factorial design achieves superior G-efficiency (94.66% versus 80.59%), making it better suited for applications requiring extensive exploration of variable interactions and robust predictions. The fit statistics for FCCCD indicate strong model performance. The full factorial designs with 5 center points shows a moderate coefficient of variation o

keywords:

Face-Centered Central Composite Design, Process Optimization, Full Factorial,

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