D-OPTIMAL DESIGNS FOR SPLIT-PLOT MIXTURE PROCESS VARIABLE DESIGNS OF THE STEEL SLAG EXPERIMENT - Arina, Faula; Wigena, Aji Hamim; Sumertajaya, I Made; Syafitri, Utami (BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2022)
The nature of the steel slag concrete experiment followed a mixture process variable (MPV) design. In this study, the concrete is composed of five mixture components, cement, fine aggregate, coarse aggregate, percentage steel slag replaced the fine aggregate and water, and process variable was the size of steel slag. Due to the constraints of the components, the experimental region was not a simplex. The standard MPV of a quadratic model produces large experimental runs. In this paper, D-optimal design with split- plot MPV approach was proposed. The five mixture components were assigned as the subplot factors and the process variable was assigned as the whole plot factors. The main objective of this information is a modified point exchange algorithm was developed to generate the D-optimal design. In addition, the paper investigates related issue namely, the estimation of the covariant matrix in MPV split-plot design. The final design consisted of 18 whole plots each of size 2 and experiment design with 36 observations