• Journal of Korean Society for Quality Management
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• v.27 no.2
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• pp.237-250
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• 1999

Response surface analysis has been a popular tool conducted by engineers in many processes. In this paper, response surface function, named partial least squares response surface function is proposed. Partial least squares response surface function is a function of partial least squares components and the response surface modeling is used in either a first-order or a second-order model. Also, this approach will have the engineers be able to do the response surface modeling and the process optimization even when the number of experimental runs is less than the number of model parameters. This idea is applied to the nondesign data and an application of partial least squares response surface function to the process optimization is considered.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.168-173
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• 2000

Design of experiments is utilized for exploring the design space and for building response surface models in order to facilitate the effective solution of multi-objective optimization problems. Response surface models provide an efficient means to rapidly model the trade-off among many conflicting goals. In robust design, it is important not only to achieve robust design objectives but also to maintain the robustness of design feasibility under the effects of variations, called uncertainties. However, the evaluation of feasibility robustness often needs a computationally intensive process. To reduce the computational burden associated with the probabilistic feasibility evaluation, the first-order Taylor series expansions are used to derive individual mean and variance of constraints. For robust design applications, these constraint response surface models are used efficiently and effectively to calculate variances of constraints due to uncertainties. Robust optimization of automotive seat is used to illustrate the approach.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.595-610
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• 2021

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.203-216
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• 2019

Reliability analysis of composite structures considering random variation of involved parameters is quite important as composite materials revealed large statistical variations in their mechanical properties. The reliability analysis of such structures by the first order reliability method (FORM) and Monte Carlo Simulation (MCS) based approach involves repetitive evaluations of performance function. The response surface method (RSM) based metamodeling technique has emerged as an effective solution to such problems. In the application of metamodeling for uncertainty quantification and reliability analysis of composite structures; the finite element model is usually formulated by either classical laminate theory or first order shear deformation theory. But such theories show significant error in calculating the structural responses of composite structures. The present study attempted to apply the RSM based MCS for reliability analysis of composite shell structures where the surrogate model is constructed using higher order shear deformation theory (HSDT) of composite structures considering the uncertainties in the material properties, load, ply thickness and radius of curvature of the shell structure. The sensitivity of responses of the shell is also obtained by RSM and finite element method based direct approach to elucidate the advantages of RSM for response sensitivity analysis. The reliability results obtained by the proposed RSM based MCS and FORM are compared with the accurate reliability analysis results obtained by the direct MCS by considering two numerical examples.

• Design & Manufacturing
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• v.2 no.6
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• pp.11-16
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• 2008

In order to satisfy the customer's variant needs for a product quality in recent years, a demand for developing higher precision machining technologies in a lot of application areas such as automobile, cellular phone and semiconductor has been increased more and more. Micro-magnetic induced polishing(${\mu}-MIP$) process is one of these precision technologies. In this study, to verify the parameters' effect of the ${\mu}-MIP$ process on the surface roughness improvement of the inclined workpiece, well planned experiment which was called the design of experiments was carried out. Considered parameters were spindle speed, inductor current, abrasive configuration and working gap between the workpiece and the solid tool. As a result, it was seen that the inductor current and the working gap greatly affected the surface roughness improvement. And to predict the surface roughness of the inclined workpiece, S/N ratio and first-order response surface model was developed.

• Computers and Concrete
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• v.28 no.5
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• pp.465-478
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• 2021

On the premise of ensuring that the static performance of the concrete spreader is met, the first-order natural frequency of the concrete spreader is increased, and the weight of the main beam is reduced. ANSYS is used as an analysis tool to perform modal analysis on the concrete spreader. The natural frequency, mode shape and modal test verification will be obtained to ensure the accuracy of finite element model analysis. Using the ANSYS designxplorer module, the size of the main beam is set, and the response surface model between the parameter variables and the optimization objective is established according to the experimental design points. Screening algorithm and MOGA algorithm are used to multi-optimize the stress, first-order natural frequency and girder weight, and the optimal solution is obtained by comparison. The results of modal analysis are consistent with those of the experiment, and a set of optimal solutions is obtained through the optimization algorithm. The optimal solution obtained can meet the purpose of increasing the first-order natural frequency of the concrete spreader and reducing the weight of the main beam under the premise of ensuring the overall dynamic and static performance of the concrete spreader.

• Journal of the Korean Statistical Society
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• v.9 no.1
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• pp.61-77
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• 1980

In response surface experiments, a polynomial model is often used to fit the response surface by the method of least squares. However, if the vectors of predictor variables are multicollinear, least squares estimates of the regression parameters have a high probability of being unsatisfactory. Hoerland Kennard have demonstrated that these undesirable effects of multicollinearity can be reduced by using "ridge" estimates in place of the least squares estimates. Ridge regrssion theory in literature has been mainly concerned with selection of k for the first order polynomial regression model and the precision of $\hat{\beta}(k)$, the ridge estimator of regression parameters. The problem considered in this paper is that of selecting k of ridge regression for a given polynomial regression model with an arbitrary order. A criterion is proposed for selection of k in the context of integrated mean square error of fitted responses, and illustrated with an example. Also, a type of admissibility condition is established and proved for the propose criterion.criterion.

• Elastomers and Composites
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• v.58 no.4
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• pp.191-200
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• 2023

In this study, MoS₂ nanoparticles were synthesized and analyzed through powder X-ray diffraction, Raman, ultraviolet-visible, and X-ray photoelectron spectroscopies. The surface morphologies of the as-synthesized MoS₂ nanoparticles were investigated through scanning and transmission electron microscopies. The sonocatalytic activity of the MoS₂ nanoparticles toward Orange II removal was evaluated by utilizing a Box-Behnken design for response surface methodology in the experimental design. The sonocatalyst dosage, Orange II dye concentration, and ultrasound treatment time were optimized to be 0.49 g/L, 5 mg/L, and 150 min, respectively. The maximum efficiency of Orange II degradation on MoS₂ nanoparticles was achieved, with a final average value of 82.93%. Further, the results of a kinetics study on sonocatalytic Orange II degradation demonstrated that the process fits well with a pseudo-first-order kinetic model.

• Journal of Animal Science and Technology
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• v.63 no.3
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• pp.603-613
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• 2021

This research improved the growth potential of Bifidobacterium animalis subsp lactis strain JNU306, a commercial medium that is appropriate for large-scale production, in yeast extract, soy peptone, glucose, L-cysteine, and ferrous sulfate. Response surface methodology (RSM) was used to optimize the components of this medium, using a central composite design and subsequent analyses. A second-order polynomial regression model, which was fitted to the data at first, significantly lacked fitness. Thus, through further analyses, the model with linear and quadratic terms plus two-way, three-way, and four-way interactions was selected as the final model. Through this model, the optimized medium composition was found as 2.8791% yeast extract, 2.8030% peptone soy, 0.6196% glucose, 0.2823% L-cysteine, and 0.0055% ferrous sulfate, w/v. This optimized medium ensured that the maximum biomass was no lower than the biomass from the commonly used blood-liver (BL) medium. The application of RSM improved the biomass production of this strain in a more cost-effective way by creating an optimum medium. This result shows that B. animalis subsp lactis JNU306 may be used as a commercial starter culture in manufacturing probiotics, including dairy products.

• Journal of Korean Society for Quality Management
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• v.23 no.3
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• pp.102-112
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• 1995

Estimation of each of mean response, difference between mean responses and derivatives of the response function is a possible objective of a response surface design. These objectives are to be achieved simultaneously when an experiment is designed to improve mean response. For the situations where departure from the assumed model is suspected, first and second order designs for improving mean response are obtained by combining minimum bias designs for the individual design objectives. D- and A-optimalities are used for selecting specific second order designs. The results are applied to central composite designs.