Exploring the Impact of Key Factors and their Interactions on Process Outcomes in Experimental Optimization
Nanaka, Samuel Owhorndah *
Department of Mathematics, Rivers State University, Port Harcourt, Nigeria.
Davies Iyai
Department of Mathematics, Rivers State University, Port Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study investigates the identification of key factors and their interactions in process optimization using factorial designs specifically the Face-Centered Central Composite Design (FCCCD) by using a reduced quadratic model developed across different factorial configurations (Full and Fractional Factorial Designs with 1 and 5 center points) which demonstrates the importance of factors B, C, D, and E, as well as their critical interactions in determining process outcomes. The research focuses on evaluating the significance of main factors’ interaction effects, and model adequacy through statistical techniques using Analysis of Variance (ANOVA), model coefficients, and residual analysis. The results reveal that factor D is the most influential, followed by factors C and B, with significant interaction effects such as X3X4 and X2X4 shaping the response. The study also highlights the presence of non-linearity and the need for refined model selection to enhance predictive accuracy. Residual analysis confirms the robustness of the models, although certain anomalies suggest areas for improvement in experimental design and data collection. The findings provide valuable insights into optimizing process performance, with implications for future research in advanced modeling techniques and validation in diverse experimental conditions.
Keywords: Process optimization, experimental design, factorial interaction, response surface methodology, model validation