Dual Response Surface Methodology Research Articles

Penalty Function Optimization in Dual Response Surfaces Based on Decision Maker’s Preference and Its Application to Real Data

The dual response surface methodology is a widely used technique in industrial engineering for simultaneously optimizing both the process mean and process standard deviation functions of the response variables. Many optimization techniques have been proposed to optimize the two fitted response surface functions that include the penalty function method (PM). The PM method has been shown to be more efficient than some existing methods. However, the drawback of the PM method is that it does not have a specific rule for determining the penalty constant; thus, in practice, practitioners will find this method difficult since it depends on subjective judgments. Moreover, in most dual response optimization methods, the sample mean and sample standard deviation of the response often use non-outlier-resistant estimators. The ordinary least squares (OLS) method is also usually used to estimate the parameters of the process mean and process standard deviation functions. Nevertheless, not many statistics practitioners are aware that the OLS procedure and the classical sample mean and sample standard deviation are easily influenced by the presence of outliers. Alternatively, instead of using those classical methods, we propose using a high breakdown and highly efficient robust MM-mean, robust MM-standard deviation, and robust MM regression estimators to overcome these shortcomings. We also propose a new optimization technique that incorporates a systematic method to determine the penalty constant. We call this method the penalty function method based on the decision maker’s (DM) preference structure in obtaining the penalty constant, denoted as PMDM. The performance of our proposed method is investigated by a Monte Carlo simulation study and real examples that employ symmetrical factorial design of experiments (DOE). The results signify that our proposed PMDM method is the most efficient method compared to the other commonly used methods in this study.

Dual response surface optimization using a process “capability” index

Dual Response Surface Methodology is a powerful tool for simultaneously optimizing the mean and the variance of a quality characteristic in the field of quality engineering. The optimization of dual response systems to achieve better quality has played a major role in the design of industrial products and processes. In this paper we suggest using a process capability index - Cpk - as the objective function. We show by ways of multiple examples that this method improves the obtained yield of a process for different response variable types.

Ensemble modeling based on 0–1 programming in micro-manufacturing process

Abstract As to micro-manufacturing processes, constructing accurate models plays an important role in the continuous quality improvement. This paper proposes an ensemble modeling technique based on 0–1 programming, in which the redundant models will be eliminated from a set of candidates and then the selected models are combined to construct the final ensemble model. As an alternative way of using a single modeling technique in dual response surface methodology, it would be beneficial to adopt multiple techniques to construct an ensemble model. A laser beam micro-drilling process and a numerical example are used to demonstrate the effectiveness of the proposed modeling technique. The comparison results illustrate that the technique can not only improve the robustness of the model predictions, but also provide a reliable scheme for optimizing the machining parameters.

Application of Dual-Response Surface Methodology and Radial Basis Function Artificial Neural Network on Surrogate Model of the Groundwater Flow Numerical Simulation

Application of Dual-Response Surface Methodology and Radial Basis Function Artificial Neural Network on Surrogate Model of the Groundwater Flow Numerical Simulation

Using dual response surface methodology as a benchmark to process multi-class imbalanced data

Constructing a classification model for the multi-class data is a critical problem in many areas. In practical applications, data in multiple classes are often imbalanced which might result in a classification model with high overall accuracy rate but with low accuracy rate for the minority class. However, minority class is usually the more important one compared to other classes in practice. This study integrates dual response surface methodology, logistic regression analysis, and desirability function to develop an optimal re-sampling strategy for classifying multi-class imbalanced data to effectively improve the low classification accuracy rate of the minority class(es) while still maintain a certain accuracy rate for the majority class(es). Three data-sets drawn from KEEL Database were used in the numerical experiments. The results showed that the proposed method can effectively improve the low classification accuracy rate of the minority class in contrast to the previous work.

Development of Brönsted acidic ionic liquid based microwave assisted method for simultaneous extraction of pectin and naringin from pomelo peels

Abstract Bronsted acidic ionic liquid was introduced in microwave assisted extraction procedure to simultaneously extract pectin and naringin from the albedo part of pomelo peels. The process for the extraction of pectin and naringin was optimized by a dual response surface methodology. The optimal conditions as follows: [HO 3 S(CH 2 ) 4 mim]HSO 4 concentration of 10 mmol/L, microwave irradiation time of 15 min, liquid–solid ratio of 26 mL/g, and microwave irradiation power of 331 W. Under the optimum conditions, the yields reached to 291.60 ± 7.25 mg/g for pectin and 8.38 ± 0.20 mg/g for naringin. [HO 3 S(CH 2 ) 4 mim]HSO 4 enjoyed excellent solvent effect for the extraction of pectin and naringin in microwave assisted extraction method in comparing with reference solvents. Fourier transform infrared spectroscopy, scanning electron microscope, and atomic force microscope were employed for the characterization analysis of pectin. Interestingly, the pectin extracted with [HO 3 S(CH 2 ) 4 mim]HSO 4 aqueous solution possessed relatively low degree of esterification and rough, hard and network structures which were apparently different with that extracted with hydrochloric acid solution. Additionally, 190.37 ± 3.28 mg naringin with a purity of 95.23% ± 1.3% were gained from 50 g albedo part of pomelo peels and confirmed by nuclear magnetic resonance, Fourier transform infrared spectroscopy, and mass spectroscopy analysis. This study provides a promising paradigm in modern separation science for the extraction of natural products from plant sources.

Ionic liquid–lithium salt based microwave pretreatment followed by ultrasonic-assisted extraction of syringin and oleuropein from Syringa reticulata var. mandshurica branch bark by a dual response surface methodology

An ionic liquid/lithium salt solvent system was successfully introduced into the separation technique for the preparation of syringin and oleuropein fromSyringa reticulatavar.mandshuricabranch bark.

Design optimization of RF-MEMS switch considering thermally induced residual stress and process uncertainties

This paper presents the Design of Experiments (DOE) based parametric design optimization of the Symmetric Toggle RF-MEMS Switch (STS) for minimizing the actuation voltage considering the fabrication process uncertainties and thermally induced residual stress. Initially, three-dimensional (3D) non-linear Finite Element Method (FEM) models are developed and the formation of residual stress during the plasma etching step of the microfabrication process is explained using the Bauschinger effect. The pull-in voltage values and the switch profiles obtained after the thermal loading–unloading cycle in the FEM models are compared with the experimental values and optical profile measurements which showed a close agreement. A DOE based Dual Response Surface Methodology (DRSM) is implemented to identify the significant design parameters affecting the STS switch pull-in voltage in the presence of thermally induced residual stress. Two separate response surface empirical models are developed; one for the mean pull-in voltage and other for variation in the pull-in voltage due to microfabrication process tolerances. The developed response surface models are optimized simultaneously using the desirability function approach. The optimal levels of the design parameters that result in minimum pull-in voltage with increased insensitivity to process uncertainties are obtained using the direct search algorithm.

Up-Cycling Waste Glass to Minimal Water Adsorption/Absorption Lightweight Aggregate by Rapid Low Temperature Sintering: Optimization by Dual Process-Mixture Response Surface Methodology

Mixed color waste glass extracted from municipal solid waste is either not recycled, in which case it is an environmental and financial liability, or it is used in relatively low value applications such as normal weight aggregate. Here, we report on converting it into a novel glass-ceramic lightweight aggregate (LWA), potentially suitable for high added value applications in structural concrete (upcycling). The artificial LWA particles were formed by rapidly sintering (<10 min) waste glass powder with clay mixes using sodium silicate as binder and borate salt as flux. Composition and processing were optimized using response surface methodology (RSM) modeling, and specifically (i) a combined process-mixture dual RSM, and (ii) multiobjective optimization functions. The optimization considered raw materials and energy costs. Mineralogical and physical transformations occur during sintering and a cellular vesicular glass-ceramic composite microstructure is formed, with strong correlations existing between bloating/shrinkage during sintering, density and water adsorption/absorption. The diametrical expansion could be effectively modeled via the RSM and controlled to meet a wide range of specifications; here we optimized for LWA structural concrete. The optimally designed LWA is sintered in comparatively low temperatures (825-835 °C), thus potentially saving costs and lowering emissions; it had exceptionally low water adsorption/absorption (6.1-7.2% w/wd; optimization target: 1.5-7.5% w/wd); while remaining substantially lightweight (density: 1.24-1.28 g.cm(-3); target: 0.9-1.3 g.cm(-3)). This is a considerable advancement for designing effective environmentally friendly lightweight concrete constructions, and boosting resource efficiency of waste glass flows.

Robust parameter design optimization using Kriging, RBF and RBFNN with gradient-based and evolutionary optimization techniques

The dual response surface methodology is one of the most commonly used approaches in robust parameter design to simultaneously optimize the mean value and keep the variance minimum. The commonly used meta-model is the quadratic polynomial regression. For highly nonlinear input/output relationship, the accuracy of the fitted model is limited. Many researchers recommended to use more complicated surrogate models. In this study, three surrogate models will replace the second order polynomial regression, namely, ordinary Kriging, radial basis function approximation (RBF) and radial basis function artificial neural network (RBFNN). The results show that the three surrogate model present superior accuracy in comparison with the quadratic polynomial regression.The mean squared error (MSE) approach is widely used to link the mean and variance in one cost function. In this study, a new approach has been proposed using multi-objective optimization. The new approach has two main advantages over the classical method. First, the conflicting nature of the two objectives can be efficiently handled. Second, the decision maker will have a set of Pareto-front design points to select from.

Ensemble of Surrogates for Dual Response Surface Modeling in Robust Parameter Design

The robust parameter design of industrial processes and products on the basis of the concept of building quality into a design has attracted much attention from researchers and practitioners for many years, and several methods have been studied in the research community. Dual response surface methodology is one of the most commonly used approaches for simultaneously optimizing the mean and the variance of response in quality engineering. Nevertheless, when the relationship between influential input factors and output quality characteristics of a process is very complex (e.g. highly nonlinear and noisy), traditional approaches have their limitations. In this article, we introduced support vector regression, kriging model, and radial basis function, which are commonly used in computer experiments, into robust parameter design, and especially introduced a new strategy that builds the dual response surface using the ensemble of surrogates, which can provide a more robust approximation model. We demonstrated the advantages of kriging, support vector regression, radial basis function, and the ensemble of surrogates by reinvestigating the dual response approach on the basis of parametric, nonparametric, and semiparametric approaches, and a simulation experiment is studied. The results show that our presented models can achieve more desirable results than parametric, nonparametric, and semiparametric approaches in terms of fitting and predictive accuracy, and the optimal operating conditions recommended by our presented models are similar to those recommended in literature, which indicates the validation of our presented models. Copyright © 2012 John Wiley &amp; Sons, Ltd.

A Bayesian hierarchical approach to dual response surface modelling

In modern quality engineering, dual response surface methodology is a powerful tool to model an industrial process by using both the mean and the standard deviation of the measurements as the responses. The least squares method in regression is often used to estimate the coefficients in the mean and standard deviation models, and various decision criteria are proposed by researchers to find the optimal conditions. Based on the inherent hierarchical structure of the dual response problems, we propose a Bayesian hierarchical approach to model dual response surfaces. Such an approach is compared with two frequentist least squares methods by using two real data sets and simulated data.

Analysis strategies for multiple responses in quality improvement experiments

Quality improvement experiments often aim to find operating condition that achieves the target value for the mean of a process characteristic, and simultaneously minimises the process variability. For this purpose, Taguchi's techniques of analysis based on signal-to-noise ratios and dual response surface methodology are commonly used to achieve this goal. This paper shows how the generalised linear models approach of modelling the 'mean function' and 'variance function' jointly can be used to achieve the goal. Two examples illustrate differences among three approaches.

Bayesian Hierarchical Modelling on Dual Response Surfaces in Partially Replicated Designs

In dual response surface methodology both the mean and variance functions are estimated to monitor an industrial process. Statisticians have discovered that often the variance function follows a lower order model than the mean function which requires only a portion of the design to be replicated. In this paper we will discuss the application of the Bayesian hierarchical model on dual response surfaces to partially replicated designs. Partially replicated data from a well-known experiment are used for illustration and the performance of the Bayesian model is compared with least-squares methods by using simulated data under various mean-and variance-models. Apart from the optimal point selected based on the point estimates of the model parameters, the point with the largest probability of falling inside a certain tolerance region is located to incorporate the uncertainty of the model parameters.

OS4-8-5 Optimization of Brazed Joint Parameters Using Dual Response Surface Methodology

Brazing is a method of permanently joining a wide range of materials and has a wide application in fabricating components of commercial value. It is distinguished from welding in that the process takes at temperatures below the melting points of the materials to be joined and from soldering in that the temperature of processing is above 450℃. This method is commonly used in electronics or refrigerating machines due to its advantage of diminution of heat influence and easy manufacturing. Unfortunately, the brazing method for copper alloy used in household air conditioners has some demerits in that the copper alloy is susceptible to heat and the resulting joints may have various flaws. Therefore, deciding on the optimal joint conditions is an effective method to use based on the experimental data. However, using a trial-and-error method from the beginning in such a wide area in order to decide on the optimal conditions requires too much experience to overcome these problems and to decide on the optimal conditions for a procedure using response surface methodology. A response surface methodology, consisting of experimental design, statistical modeling and optimization is used to decide on the optimal joint parameter with process conditions.

Dual-Response Surface Optimization: A Weighted MSE Approach

Dual-response surface methodology is a powerful tool for simultaneously optimizing the mean and the variance of responses in quality engineering. In this article, we suggest a weighted mean squared error (MSE) approach to improve the optimization procedure. In addition, we propose a data-driven approach to determine the weights when the prior information is vague. This is based on the idea of an “efficient curve.” Examples are given to illustrate the superiority of the proposed method, as compared with other existing procedures.

Dual Response Surface Optimization: A Fuzzy Modeling Approach

In modern quality engineering, dual response surface methodology is a powerful tool. In this paper, we introduce a fuzzy modeling approach to optimize the dual response system. We demonstrate our approach in two examples and show the advantages of our method by comparing it with existing methods.