# D-Optimal Design for Mixture Process Variable with Split-Plot Approach Using a Genetic Algorithm

## Authors

• Dea Handayani Juniar Department of Statistics, IPB University, Bogor, 16680, Indonesia
• Aji Hamim Wigena Department of Statistics, IPB University, Bogor, 16680, Indonesia
• Utami Dyah Syafitri Department of Statistics, IPB University, Bogor, 16680, Indonesia

## Keywords:

D-Optimality criterion, Genetic Algorithm, Mixture Experiment, Process Variable, Split-plot

## Abstract

Mixture-process variables (MPV) is an experiment that responds not only to the proportions of the components but also to the conditions of the process. The impact of MPV is a large number of experimental runs. A large number of experimental runs has a consequence on cost, time, and resource constraints. However, choosing an optimal design with limited runs will ensure efficiency in such cases. In practice, the composition of the mixture experiment will run for each level of the process variables. Therefore, it causes a limitation in randomization. A split-plot approach can be an option to solve the problem, where the whole-plot is the process variables, and the sub-plot is the mixture component. In this research, the authors developed a genetic algorithm (GA) to find the optimal design. The genetic algorithm maintains a population of candidate solutions to a problem. It then selects the candidate point that has the most suitable criteria for solving the problem. The selection criterion used is the D-optimality criterion which is focused on parameter optimization. The case study is an experiment consisting of three ingredients and a process variable with three levels. The result concluded that GA provided an excellent design compared to the coordinate exchange algorithm with the value of D-efficiency for   is 1.195,  is  1.082, and  is 1.078.

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2021-12-08

## How to Cite

Dea Handayani Juniar, Wigena, A. H., & Utami Dyah Syafitri. (2021). D-Optimal Design for Mixture Process Variable with Split-Plot Approach Using a Genetic Algorithm . International Journal of Sciences: Basic and Applied Research (IJSBAR), 60(4), 360–375. Retrieved from https://gssrr.org/index.php/JournalOfBasicAndApplied/article/view/13562

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