Bayesian analysis for weighted mean-squared error in dual response surface optimization

2009 ◽  
Vol 26 (5) ◽  
pp. 417-430 ◽  
Author(s):  
In-Jun Jeong ◽  
Kwang-Jae Kim ◽  
Dennis K. J. Lin
Keyword(s):  
Bayesian Analysis ◽  
Response Surface ◽  
Mean Squared Error ◽  
Weighted Mean ◽  
Response Surface Optimization ◽  
Squared Error ◽  
Dual Response ◽  
Surface Optimization

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

2012 ◽  
Author(s):  
Chuan Kim Ch’ng ◽  
Boon Chong Michael Khoo
Keyword(s):  
Standard Deviation ◽  
Response Surface ◽  
Mean Squared Error ◽  
Extreme Points ◽  
Robust Estimator ◽  
Sample Standard Deviation ◽  
Response Surface Optimization ◽  
Squared Error ◽  
Dual Response ◽  
Surface Optimization

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

scholarly journals An Alternative Approach of Dual Response Surface Optimization Based on Penalty Function Method

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Ishaq Baba ◽  
Habshah Midi ◽  
Sohel Rana ◽  
Gafurjan Ibragimov
Keyword(s):  
Response Surface ◽  
Mean Squared Error ◽  
Penalty Function Method ◽  
Optimization Approach ◽  
Response Surface Optimization ◽  
Dual Response ◽  
Optimization Function ◽  
Mean And Variance ◽  
Surface Optimization ◽  
Original Objective

The dual response surface for simultaneously optimizing the mean and variance models as separate functions suffers some deficiencies in handling the tradeoffs between bias and variance components of mean squared error (MSE). In this paper, the accuracy of the predicted response is given a serious attention in the determination of the optimum setting conditions. We consider four different objective functions for the dual response surface optimization approach. The essence of the proposed method is to reduce the influence of variance of the predicted response by minimizing the variability relative to the quality characteristics of interest and at the same time achieving the specific target output. The basic idea is to convert the constraint optimization function into an unconstraint problem by adding the constraint to the original objective function. Numerical examples and simulations study are carried out to compare performance of the proposed method with some existing procedures. Numerical results show that the performance of the proposed method is encouraging and has exhibited clear improvement over the existing approaches.

Sign in / Sign up

Export Citation Format

Share Document