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Journal ArticleDOI

Variance plus bias optimal response surface designs with qualitative factors applied to stem choice modeling

01 Dec 2011-Quality and Reliability Engineering International (John Wiley & Sons, Ltd)-Vol. 27, Iss: 8, pp 1199-1210
TL;DR: New designs are proposed specifically to address bias and compared with five types of alternatives ranging from types of composite to D-optimal designs using four criteria including D-efficiency and measured accuracy on test problems.
Abstract: This paper explores the issue of model misspecification, or bias, in the context of response surface design problems involving quantitative and qualitative factors. New designs are proposed specifically to address bias and compared with five types of alternatives ranging from types of composite to D-optimal designs using four criteria including D-efficiency and measured accuracy on test problems. Findings include that certain designs from the literature are expected to cause prediction errors that practitioners would likely find unacceptable. A case study relating to the selection of science, technology, engineering, or mathematics majors by college students confirms that the expected substantial improvements in prediction accuracy using the proposed designs can be realized in relevant situations. Copyright © 2011 John Wiley & Sons, Ltd.
Citations
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Journal ArticleDOI
17 Jun 2014-Water
TL;DR: In this paper, the photocatalytic degradation of phenolic compounds in the presence of titanium dioxide (TiO 2 ) nano-particles and UV light was investigated, where a full factorial design consisting of three factors at three levels was used to examine the effect of particle size, temperature and reactant type on the apparent degradation rate constant.
Abstract: Due to the toxicity effects and endocrine disrupting properties of phenolic compounds, their removal from water and wastewater has gained widespread global attention. In this study, the photocatalytic degradation of phenolic compounds in the presence of titanium dioxide (TiO 2 ) nano-particles and UV light was investigated. A full factorial design consisting of three factors at three levels was used to examine the effect of particle size, temperature and reactant type on the apparent degradation rate constant. The individual effect of TiO 2 particle size (5, 10 and 32 nm), temperature (23, 30 and 37 °C) and reactant type (phenol, o-cresol and m-cresol) on the apparent degradation rate constant was determined. A regression model was developed to relate the apparent degradation constant to the various factors. The largest photocatalytic activity was observed at an optimum TiO 2 particle size of 10 nm for all reactants. The apparent degradation rate constant trend was as follows: o-cresol > m-cresol > phenol. The ANOVA data indicated no significant interaction between the experimental factors. The lowest activation energy was observed for o-cresol degradation using 5-nm TiO

75 citations


Cites methods from "Variance plus bias optimal response..."

  • ...Developing response models using qualitative and quantitative factors have been reported in several studies [34–36]; however, the technique has not been applied extensively in science and engineering applications....

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Journal ArticleDOI
TL;DR: A new mathematical program to simultaneously optimize multiple quality characteristics in multiple stage systems using Multivariate form response surface methodology with iterative seemingly unrelated regression as the estimation method to extract the relationships between the outputs and inputs in each stage.
Abstract: In today's manufacturing and service systems, entities are progressed across the several stages of operations wherein one or more quality characteristic may be formed. The quality of final system outputs depends on the quality of intermediate characteristics as well as design parameters in each stage. This paper presents a new mathematical program to simultaneously optimize multiple quality characteristics in multiple stage systems. Multivariate form response surface methodology is applied with iterative seemingly unrelated regression as the estimation method to extract the relationships between the outputs and inputs in each stage. Because the intermediate response variables may act as covariates in the next stages, the probabilistic patterns of the response surfaces are considered by association with the quality of the previous stages. The objective function in the proposed model is the acceptance probability of the outputs based on predefined specification limits. A combination of Monte Carlo simulation and the genetic algorithm is also proposed to solve the final stochastic optimization model. At the end, the applicability of the proposed approach is illustrated by a numerical example. Copyright © 2014 John Wiley & Sons, Ltd.

24 citations

Journal ArticleDOI
TL;DR: Optimal experimental designs are effective offline quality improvement techniques used to enhance existing products and develop new products for a constrained design region.
Abstract: Optimal experimental designs are effective offline quality improvement techniques used to enhance existing products and develop new products for a constrained design region. For some practical situ...

10 citations

Journal ArticleDOI
TL;DR: The algorithmic foundations for the proposed D - and I -optimality criteria embedded mixed integer linear programming models are laid out in order to obtain optimal operating conditions using the first-order response functions.
Abstract: Computer-aided optimal experimental designs are an effective quality improvement tool that provides insights of information under various quality engineering problems. In the literature, considerable attention has been focused on maximizing the determinant of the information matrix in order to generate optimal design points. However, minimizing the average prediction based on the I -optimality criterion is more useful than commonly used D -optimality criterion for a number of situations. In this paper, special experimental design situations are explored where both qualitative and quantitative input variables are considered for an irregular design space with the pre-specified number of design points and the first-order polynomial model. In addition, this paper lays out the algorithmic foundations for the proposed D - and I -optimality criteria embedded mixed integer linear programming models in order to obtain optimal operating conditions using the first-order response functions. Comparative studies are also conducted. Finally, the proposed models are superior to the traditional counterparts.

3 citations


Cites background from "Variance plus bias optimal response..."

  • ...Draper (1982), Borkowski (2003) and Allen and Tseng (2011) conducted the further studies in the context of the I-optimality criterion....

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  • ...On the contrary, Box and Draper (1959) was offered the I-optimality criterion. This criterion focuses on the integrated variance function over a studied design region. Draper (1982), Borkowski (2003) and Allen and Tseng (2011) conducted the further studies in the context of the I-optimality criterion....

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  • ...Draper (1982), Borkowski (2003) and Allen and Tseng (2011) conducted the further studies in the context of the I-optimality criterion. Furthermore, Toro Diaz et al. (2012) and Myers et al. (2016) reviewed the existing studies and provided theoretical aspects of computer-aided optimal experimental designs....

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  • ...Draper (1982), Borkowski (2003) and Allen and Tseng (2011) conducted the further studies in the context of the I-optimality criterion. Furthermore, Toro Diaz et al. (2012) and Myers et al....

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  • ...On the contrary, Box and Draper (1959) was offered the I-optimality criterion....

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01 Jan 2017

3 citations


Cites background from "Variance plus bias optimal response..."

  • ...Allen and Tseng (2011) conducted the further research study in the field of optimal experimental designs and developed variance plus bias optimal experimental designs for stem choice modelling....

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References
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Book
05 Dec 2012
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and expensive process of manually cataloging samples and generating random numbers.
Abstract: Introduction.- Estimating Volume and Count.- Generating Samples.- Increasing Efficiency.- Random Tours.- Designing and Analyzing Sample Paths.- Generating Pseudorandom Numbers.

2,215 citations

Journal ArticleDOI

1,306 citations


"Variance plus bias optimal response..." refers background in this paper

  • ...The IMSE criterion in Equation (10) is difficult to apply since it requires the assumption that 2 is known....

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Journal ArticleDOI
TL;DR: In this paper, the problem of choosing a design such that the polynomial f(ξ) = f (ξ1, ξ2, · · ·, ξ k ) fitted by the method of least squares most closely represents the true function over some region of interest R in the ξ space, no restrictions being introduced that the experimental points should necessarily lie inside R, is considered.
Abstract: The general problem is considered of choosing a design such that (a) the polynomial f(ξ) = f(ξ1, ξ2, · · ·, ξ k ) in the k continuous variables ξ' = (ξ1, ξ2, · · ·, ξ k ) fitted by the method of least squares most closely represents the true function g(ξ1, ξ2, · · ·, ξ k ) over some “region of interest” R in the ξ space, no restrictions being introduced that the experimental points should necessarily lie inside R; and (b) subject to satisfaction of (a), there is a high chance that inadequacy of f(ξ) to represent g(ξ) will be detected. When the observations are subject to error, discrepancies between the fitted polynomial and the true function occur: i. due to sampling error (called here “variance error”), and ii. due to the inadequacy of the polynomial f(ξ) exactly to represent g(ξ) (called here “bias error”). To meet requirement (a) the design is selected so as to minimize J, the expected mean square error averaged over the region R. J contains two components, one associated entirely with varian...

697 citations


"Variance plus bias optimal response..." refers background in this paper

  • ...It is easy to show that the expected bias, Tr[K2 ], in Equation (8) is proportional to 2 and, therefore, as the degree of model misspecification increases, so will any gaps in EIMSE values between the various designs....

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Journal ArticleDOI
TL;DR: The package rsm was designed to provide R support for standard response-surface methods and implements a coded-data structure to aid in this essential aspect of the methodology.
Abstract: This introduction to the R package rsm is a modied version of Lenth (2009), published in the Journal of Statistical Software. The package rsm was designed to provide R support for standard response-surface methods. Functions are provided to generate central-composite and Box-Behnken designs. For analysis of the resulting data, the package provides for estimating the response surface, testing its lack of t, displaying an ensemble of contour plots of the tted surface, and doing follow-up analyses such as steepest ascent, canonical analysis, and ridge analysis. It also implements a coded-data structure to aid in this essential aspect of the methodology. The functions are designed in hopes of providing an intuitive and eective user interface. Potential exists for expanding the package in a variety of ways.

521 citations


"Variance plus bias optimal response..." refers background in this paper

  • ...In all other cases the fitted models of the model form in Equation (4)....

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  • ...For example, consider a hypothetical situation in which commercial constraints forced the team to focus on a fitted model similar to Equation (4), but with fewer terms....

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Journal ArticleDOI
TL;DR: Extensive computational tests for dual degenerate problem instances show that suboptimal solutions can be obtained with the genetic algorithm within running times that are shorter than those of the OSL optimization routine.
Abstract: We present a genetic algorithm for the multiple-choice integer program that finds an optimal solution with probability one though it is typically used as a heuristic. General constraints are relaxed by a nonlinear penalty function for which the corresponding dual problem has weak and strong duality. The relaxed problem is attacked by a genetic algorithm with solution representation special to the multiple-choice structure. Nontraditional reproduction, crossover and mutation operations are employed. Extensive computational tests for dual degenerate problem instances show that suboptimal solutions can be obtained with the genetic algorithm within running times that are shorter than those of the OSL optimization routine.

241 citations


"Variance plus bias optimal response..." refers background or methods in this paper

  • ...Then, the four rounds were simulated using Equation (17) for each student....

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  • ...the impact model in Equation (17) is designed to emulate peer pressure....

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  • ...375 k i∈Qk,i =j[Si / (di −dj)(2)] for k =1, 2 and l =1, 2 (17)...

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