I-Optimal axial designs for four ingredient concrete experimentoptimal axial designs for four ingredient concrete experiment

Abstract

Stakeholders in the construction industry work towards obtaining optimal concrete mixes with an aim of producing structures with the best compressive strength. In many instances, Kenya has witnessed collapse of buildings leading to death and huge financial loses, which has been associated largely to poor concrete mixes. This paper aims at evaluating the I-optimal designs for a concrete mixture experiment for both Equally Weighted Simplex Centroid Axial Design and Unequally Weighted Simplex Centroid Axial Design, based on the second-degree Kronecker model. Optimality tests are performed to locate the optimum values of a design. In various studies, I-optimality has been shown to be among the best criteria in obtaining the most optimal outcomes. In this study, Response Surface Methodology is applied in evaluating I-optimal designs, which are known to minimize average or integrated prediction variance over the experimental region. I-optimality equivalence conditions for the inscribed tetrahedral design and for the concrete experiment model are identical with the boundary points, mid-face points and the centroid, denoted by η 2 , η 3 and η 4 respectively. Equally, Weighted Simplex Centroid Axial Design proved to be a more I-efficient design than the Unequally Weighted Simplex Centroid Axial Design for both the tetrahedral design and the concrete model, with 87.85% and 79.54% respectively. The optimal response surface occurred in the region of the I-optimal designs. The Kronecker model derived from the concrete mixture experiment proved effective and efficient in describing the observed results.