Sains Malaysiana 53(4)(2024): 921-934

http://doi.org/10.17576/jsm-2024-5304-15

Dual Response Surface Optimization Based on Skill Scores

(Pengoptimuman Permukaan Tindak Balas Dwi Berdasarkan Skor Kemahiran)

AGAH KOZAN, MELIS ZEYBEK & ELIF KOZAN*

Department of Statistics, Faculty of Science, Ege University, Turkey

Received: 12 April 2023/Accepted: 14 March 2024

Abstract

The popular formulations of dual-response optimization are constructed on minimizing a function of bias and system variability. This study provides an opportunity to evaluate the dual response surface (DRS) problem from a different perspective by adapting two new terms such that internal and external quality forecasts. The background of the proposed approach focuses on the relationship between internal and external quality forecasts and discusses the DRS problem in regards of skill scores by defining a model quality criterion. Skill is the relative accuracy of the forecast and defines a correspondence between forecast of interest and reference forecasts. The reference forecast does not require any knowledge or modelling; thus, it is an unskilled forecast. In this context, skill score is a measure of this relative improvement and widely used in evaluating the performance of operational and experimental forecasts. An alternative version of mean square error (MSE) which is reconstructed by skill scores and model quality criterion is proposed as an objective function for the DRS problem. Integrating the relationship between internal and external quality forecasts into such a response function can improve the effectiveness and cooperation of the applied technique. The proposed approach has a flexible structure and provides decision makers alternative solutions for different values of the model quality criterion. The proposed procedure is discussed by conducted a simulation study and demonstrated in an engineering process.

Keywords: Dual response optimization; mean square error; model quality criterion; robust parameter design; skill scores

Abstrak

Formulasi popular pengoptimuman gerak balas dual dibina untuk meminimumkan fungsi bias dan kebolehubahan sistem. Kajian ini memberi peluang untuk menilai masalah permukaan gerak balas dual (DRS) dari perspektif yang berbeza dengan menyesuaikan dua istilah baharu seperti ramalan kualiti dalaman dan luaran. Latar belakang pendekatan yang dicadangkan memfokuskan pada hubungan antara ramalan kualiti dalaman dan luaran dan membincangkan masalah DRS dalam hal skor kemahiran dengan mentakrifkan kriteria kualiti model. Kemahiran ialah ketepatan relatif ramalan dan mentakrifkan perpadanan antara ramalan kepentingan dan ramalan rujukan. Ramalan rujukan tidak memerlukan sebarang pengetahuan atau pemodelan; oleh itu, ia adalah ramalan yang tidak mahir. Dalam konteks ini, skor kemahiran adalah ukuran peningkatan relatif ini dan digunakan secara meluas dalam menilai prestasi ramalan operasi dan uji kaji. Versi alternatif bagi ralat min kuasa dua (MSE) yang dibina semula oleh skor kemahiran dan kriteria kualiti model dicadangkan sebagai fungsi objektif untuk masalah DRS. Mengintegrasikan hubungan antara ramalan kualiti dalaman dan luaran ke dalam fungsi tindak balas sedemikian boleh meningkatkan keberkesanan dan kerjasama teknik yang digunakan. Pendekatan yang dicadangkan mempunyai struktur yang fleksibel dan menyediakan penyelesaian alternatif pembuat keputusan untuk nilai yang berbeza bagi kriteria kualiti model. Prosedur yang dicadangkan dibincangkan dengan menjalankan kajian simulasi dan ditunjukkan dalam proses kejuruteraan.

Kata kunci: Kriteria kualiti model; pengoptimuman gerak balas dual; ralat min kuasa dua; reka bentuk parameter teguh; skor kemahiran

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*Corresponding author; email: elif.kozan@ege.edu.tr