The Use of Downton’s Estimator in Dual Response Surface Optimization

Abstract

Kaedah sambutan dual terdiri daripada dua sambutan bagi suatu cirian kualiti. Dua sambutan tersebut ialah sambutan min dan sambutan sisihan piawai (varians) yang dianggarkan daripada reka bentuk eksperimen selepas penyuaian model dijalankan. Sambutan sisihan piawai biasanya dianggar daripada sisihan piawai sampel. Kelemahan utama penganggar yang berdasarkan sisihan piawai sampel adalah ia mudah dipengaruhi oleh titik ekstrim. Bagi kes sedemikian, model yang tersuai berdasarkan sisihan piawai sampel adalah mungkin tidak jitu. Oleh itu, penggunaan pendekatan ini mungkin tidak dapat memberi titik kompromi yang betul. Dalam kertas kerja ini, suatu anggaran sisihan piawai berdasarkan penganggar Downton dicadangkan dalam pengoptimuman kaedah sambutan dual. Penganggar teguh kurang dipengaruhi oleh titik ekstrim berbanding dengan sisihan piawai sampel. Dalam hal ini, suatu model tersuai yang berdasarkan penganggar teguh akan memberikan keputusan yang lebih baik. Suatu contoh digunakan untuk mengilustrasikan kecekapan cadangan kami dalam pengoptimuman. Dalam contoh ini ralat kuasadua min (MSE) akan digunakan sebagai ciri pengoptimuman. Kata kunci: Penganggar Downton, pengoptimuman sambutan dual, ralat min kuasa dua, pengoptimuman, titik kompromi A dual response surface approach consists of two responses of a quality characteristic. These two responses are the mean response and the standard deviation (variance) response, which are estimated from an experimental design after performing a model fitting. The standard deviation response is usually estimated using the sample standard deviation. The main drawback of this estimator by means of sample standard deviation is that it is easily influenced by extreme points. For this case, the fitted model based on the sample standard deviation may not be accurate. Thus, the use of this approach may not produce the correct compromised setting. In this paper, an estimation of the standard deviation based on Downton’s estimator in a dual response surface optimization is proposed. A Downton estimator is a robust estimator of standard deviation. A robust estimator is less affected by extreme points compared to the sample standard deviation. Here, a model based on a robust estimator will give better results. An example is used to illustrate the effectiveness of our proposal in optimization. In this example, mean squared error (MSE) will be used as the optimization criterion. Key words: Downton’s estimator, dual response surface optimization, mean squared error, optimization, compromise setting