I-Optimal Axial Designs for Four Ingredient Concrete Experiment

Njoroge Elizabeth Wambui,Mutiso John,Koske Joseph

doi:10.11648/j.ajtas.20211001.15

Njoroge Elizabeth Wambui, Mutiso John + Show 1 more

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https://doi.org/10.11648/j.ajtas.20211001.15

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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 η2, η3 and η4 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.

Highlights

In the general mixture problem, the measured response is assumed to depend only on the proportions of the ingredients present in the mixture and not on the amount of the mixture according to [2]
The second-degree Kronecker model and its subsystem of interest are given by (1) and (2) respectively. The latter is written in Lexicographic order as suggested by [4]
The model was utilized in obtaining the concrete regression model (18) which was analyzed in this study

Summary

Introduction

In the general mixture problem, the measured response is assumed to depend only on the proportions of the ingredients present in the mixture and not on the amount of the mixture according to [2]. The mixture ingredients , = 1,2, ... The objectives of the analysis of mixture data are to fit a proposed model for describing the shape of the response surface over the simplex factor space, and to determine the roles played by the individual components alluded is that the same analysis may achieve these two objectives at once as said by [2]. The D-optimal designs aims at precise model estimation while the I-optimal designs aims at obtaining precise predictions. The focus is to find certain responses for any given components proportions formulations, with an aim of obtaining the optimal responses from optimal settings with the best precision. Dand G-optimal designs for four ingredient mixture, were evaluated by [9].

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