Asian Journal of Probability and Statistics

The Laboratory experiments were conducted using a second order rotatable design in four dimensions constructed using balanced incomplete block designs. Obtained data was applied in developing a semi-empirical model based on a second degree polynomial for predicting bioethanol yield. The model testing using ANOVA in R resulted in a correlation coefficient of 0.95 and an adjusted R-squared value of 0.911 for the E-optimal design, which indicates a good model fit. The model was used to generate contour plots and response surface for bioethanol yield. A maximum yield of 12.35 g/L of ethanol was realized at factor settings of 54.35 h, 4.96 level of pH, 34.67 ⁰C temperature and 28.03 g/L of substrate concentration using the E-optimal design which was found to be the most efficient design relative to the general design which had an optimal yield of 12.39 g/L at factor settings of 56.45 h, 4.95 pH level, 34.59 ⁰C level of temperature and 28.30 g/l of substrate concentrations. A yield of 12.35 g/L of ethanol for a substrate concentration of 28.03 g/L. translates to 0.441 g of ethanol per gram of substrate comparing well with many other findings in literature from similar studies which is roughly 86% of the theoretical yield (0.511 g/g of substrate). A second order rotatable design in four dimensions constructed using balanced incomplete block designs when the number of replications (r) are less than three the number of times (\(\lambda\)) pairs of treatments occur together ( r<\(\lambda\)) in the design was applied and found reliable in modeling, optimizing and studying the effects of the four factors and their interaction to the processes of fermentation of pineapples peels as substrate for ethanol production using Saccharomyces cerevisiae.