A-Optimal Pada Mixture Amount Design Dengan Modifikasi Rancangan Petak Terbagi Menggunakan Algoritma Point-Exchange
DOI:
https://doi.org/10.24256/jpmipa.v12i2.4072Keywords:
Kriteria A-Optimal, Mixture Amount Experiment , Rancangan Petak TerbagiAbstract
Abstract:
A Mixture Amount Experiment (MAE) is a design that consists of a mixture variable and the total amount variable. In practice, the composition of the mixture is run on each total amount of mixture, which consequently cannot be completely randomized, so that a split-plot design approach is needed. This research aims to develop an algorithm to find a A-Optimal design for a mixture amount experiment with a modified split-plot design. A-Optimal design is seeking a design in which minimizing the covariance of the model parameter. The study case of this research involved three ingredients and two total amounts of mixtures with different constraints. In this research, the whole plot factor is the total amount of mixtures, while the subplot factor is the composition of the mixture. The A-Optimal design was generated based on the Second-Order Scheefe model. To Construct the A-optimal design, we used the point exchange algorithm. The result from this algorithm produced an optimum composition in each total amount of mixture.
Abstrak:
Rancangan Jumlah Campuran (MAE) terdiri dari komponen campuran dan jumlah total. Dalam prakteknya, komposisi campuran dijalankan pada setiap jumlah total campuran, akibatnya tidak dapat diacak sempurna, sehingga diperlukan pendekatan rancangan petak terbagi. Penelitian ini bertujuan untuk mengembangkan suatu algoritma untuk menemukan rancangan dengan kriteria A-Optimal untuk percobaan jumlah campuran dengan menggunakan modifikasi rancangan petak terbagi. Rancangan A-Optimal mencari rancangan yang meminimalkan kovarian parameter model. Studi kasus penelitian ini terdiri dari tiga bahan dan dua jumlah total campuran yang berbeda. Dalam penelitian ini, factor petak utama adalah jumlah total campuran, sedangkan faktor anak petak adalah komposisi campuran. rancangan A-Optimal dihasilkan berdasarkan model Second-Order Scheefe. Untuk Membangun rancangan A-optimal, menggunakan pendekatan algoritma point-exchange. Hasil dari algoritma ini menghasilkan komposisi optimum pada setiap jumlah total campuran.
References
Atkinson A, Donev A, Tobias R. 2007. Optimum experimental designs, with SAS. Volume ke-34. Oxford University Press.
Cornell JA. 2011. Experiments with mixtures: designs, models, and the analysis of mixture data. Volume ke-403. John Wiley & Sons.
Goos P. 2012. The optimal design of blocked and split-plot experiments. Volume ke-164. Springer Science & Business Media.
Goos P, Donev AN. 2007. Tailor-made split-plot designs for mixture and process variables. Journal of Quality Technology. 39(4):326–339.
Goos P, Vanderbroek M. 2003. D-optimal split-plot designs with given numbers and sizes of whole plots. Technometrics. 45(3):235–245.
Hilgers R-D, Bauer P. 1995. Optimal designs for mixture amount experiments. Journal of statistical planning and inference. 48(2):241–246.
Jones B, Goos P. 2007. A candidate-set-free algorithm for generating D-optimal split-plot designs. Journal of the Royal Statistical Society: Series C (Applied Statistics). 56(3):347–364.
Kowalski SM, Cornell JA, Vining GG. 2002. Split-plot designs and estimation methods for mixture experiments with process variables. Technometrics. 44(1):72–79.
Montgomery. 2006. Design and Analysis of Experiments (fifth edition). New York: John Wiley & Sons.
Pal M, Mandal NK. 2012. Optimum designs for estimation of parameters in a quadratic mixture-amount model. Communications in Statistics-Theory and Methods. 41(4):665–673.
Peter Goos, Bradley Jones, Katerine AM. 2020. A-optimal versus D-optimal design of screening experiments. Journal of quality technology 53(4): 369-382. 10.1080/00224065.2020.1757391.
Piepel GF, Cornell JA. 1985. Models for mixture experiments when the response depends on the total amount. Technometrics. 27(3):219–227.
Piepel GF, Cornell JA. 1987. Designs for mixture-amount experiments. Journal of Quality Technology. 19(1):11–28.
Scheffé H. 1958. Experiments with mixtures. Journal of the Royal Statistical Society: Series B (Methodological). 20(2):344–360.
Published
How to Cite
Issue
Section
Citation Check
License
Copyright (c) 2024 Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who wish to publish and disseminate their papers with the Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam, shall agree to the publishing rights set by Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam. Authors understand that they shall assign publication rights as part of the process upon acceptance for publication. The authors agreed that they would transfer certain copyrights to Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam. Consecutively, authors still retain some rights to use and share their own published articles without written permission from Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam.
Authors granted Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam the following rights; (1) the right to publish and provide the manuscripts in all forms and media for publication and dissemination, (2) the authority to enforce the rights in the manuscript, for example in the case of plagiarism or in copyright infringement.
Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam will follow COPE's Code of Conduct and Best Practice Guidelines for Journal Editors to protect the research results and take allegations of any infringements, plagiarisms, ethical issues, and frauds should those issues arise. The manuscript is attributed as the authors' work, and is properly identified.
