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

Ishaq Baba,Gafurjan Ibragimov,Habshah Midi,Sohel Rana

doi:10.1155/2015/450131

Ishaq Baba, Gafurjan Ibragimov + Show 2 more

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https://doi.org/10.1155/2015/450131

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Abstract

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.

Highlights

Response surface methodology (RSM) is a design of experimental technique which shows relationship between several designs and response variables
In the optimization stage, the interest is on what to optimize and how to optimize, in this paper, we propose a new optimization technique in dual response surface methodology based on the penalty function method for simultaneously optimizing both the location and scale functions
We present a new optimization technique for dual response surface methodology based on the penalty function method

Summary

Introduction

Response surface methodology (RSM) is a design of experimental technique which shows relationship between several designs and response variables. Myers and Carter [4] suggested the need for developing statistical methodology known as dual response surface methodology, which can simultaneously optimize the mean and the variance function as to achieve the desired target while keeping the variance small. They defined the two responses as primary and secondary. In the optimization stage, the interest is on what to optimize (i.e., determination of the objective function) and how to optimize (the optimization algorithm), in this paper, we propose a new optimization technique in dual response surface methodology based on the penalty function method for simultaneously optimizing both the location and scale functions.

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