Modified and generalized full cubic polynomial response surface methodology in engineering mixture design

Abstract

This paper presents the modified and generalized full cubic polynomial Response Surface Methodology (RSM) in engineering mixture design. It provided comprehensive parameters definitions that enable development of adequate regression of dependent – independent variables in mixture design with ease. Necessary equations and useful insights were identified and their application outlined. Step-by-step and parameters description necessary in statistical model validation and adequacy using the student’s t-test and the fisher test were provided. NULL and ALTERNATE hypotheses based on standard statistical values techniques were also elaborated. These comprehensive principles and applications in mixture design were based on an extensive review of literature. Hence, difficulties usually experienced by numerous researchers in mixture models development to third degree would be overcome, while model validations and adequacy techniques are made handy. It is believed that this study would motivate vigorous research on the applications of non-conventional materials such as vegetable fibers, soil, wastes from industry, mining and agriculture, alongside the traditional materials, such as: cement, lime, earth, stone, sand and water for engineering applications.

Keywords: Mixture Design, Simplex Lattice, Cubic Polynomials, Scheffe’s Model, Adequacy Tests