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

Allen, Theodore T.; Tseng, Shih-Hsien

doi:10.1002/qre.1210

Cited by 6 publications

(6 citation statements)

References 18 publications

(28 reference statements)

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“…Examining the effects of quantitative, as well as qualitative variables on a response variable is routinely employed for analyzing data in disciplines such as science, social science and business [32,33]. Developing response models using qualitative and quantitative factors have been reported in several studies [34][35][36]; however, the technique has not been applied extensively in science and engineering applications.…”

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confidence: 99%

Photocatalytic Degradation of Phenol and Phenol Derivatives Using a Nano-TiO2 Catalyst: Integrating Quantitative and Qualitative Factors Using Response Surface Methodology

Choquette-Labbé

Shewa

Lalman

et al. 2014

Water

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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 2 particles. A maximum degradation rate constant of 0.0138 minwas recorded for o-cresol at 37 °C and a TiO 2 particle size of 13 nm at a D-optimality value of approximately 0.98. The response model adequately related the apparent degradation rate constant to the factors within the range of factors under consideration.

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confidence: 99%

Photocatalytic Degradation of Phenol and Phenol Derivatives Using a Nano-TiO2 Catalyst: Integrating Quantitative and Qualitative Factors Using Response Surface Methodology

Choquette-Labbé

Shewa

Lalman

et al. 2014

Water

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“…Once we treated fidelity as a categorical factor and coded it as either 0 or 1, the next step was to generate an experimental design involving both quantitative and qualitative factors, following the approach of Allen and Tseng . In this section, we review the EIMSE criterion and associated assumptions.…”

Section: Optimal Design With Categorical Factorsmentioning

confidence: 99%

“…The objective of this work is to explore the possibility of using the relatively simple experimental planning method of Allen and Tseng and OLS regression for predicting the mean of implied volatility. For cases in which comparatively large numbers of runs are available and/or the surfaces are expected to have multi‐modal, not differentiable, or other types of highly non‐linear features, non‐linear model and adaptive procedures offer important advantages.…”

Section: Introductionmentioning

confidence: 99%

A Simple Approach for Multi‐fidelity Experimentation Applied to Financial Engineering

Tseng

Allen

2014

Appl Stoch Models Bus & Ind

Self Cite

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In practical applications, information about the accuracy or 'fidelity' of alternative surrogate systems may be ambiguous and difficult to determine. To address this problem, we propose to treat surrogate system fidelity level as a categorical factor in optimal response surface design. To design the associated experiments, we apply the Expected Integrated Mean Squared Error optimal design criterion, which takes into account both variance and bias errors. The performance of the proposed design was compared using three test cases to four types of alternatives using the Empirical Integrated Squared Error. Because of its ability to foster relatively accurate predictions, the proposed design is recommended in fidelity experimental design, particularly when the experimenters lack sufficient information about the fidelity levels of surrogate systems. The method was applied to the case of intraday trading optimization in which data were collected from the Taiwan Futures Exchange. We also calculated the implied volatility from the Merton's Jump-diffusion model via the fast Fourier transform algorithm with three different models of varying fidelity levels.

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“…This measure can be calculated by using stochastic patterns of response distribution and their associated acceptance regions . Complex systems especially in service industries have categorical/binary response variables as well as categorical/binary factors . Therefore, some specialized methods are required to analyze these variables through the RSM.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Degree of Conformance in Multiresponse–Multistage Systems with a Simulation‐based Metaheuristic

Hejazi

Seyyed-Esfahani

Mahootchi

2014

Quality & Reliability Eng

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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. IntroductionR esponse surface methodology (RSM) is a widely used approach in offline quality control and is one of the well-grounded techniques associated with the design of experiments (DOE). It statistically estimates the underlying relationships between quality characteristics, also called response variables, and controllable factors, and then, it mathematically tries to find the optimal setting of the factors that leads to the most desirable quality. Recently, RSM has expanded its capabilities as a data mining tool to approximate the function between inputs and outputs in complex systems.Applications of this method include manufacturing processes such as assembly, machining, and welding as well as service operations such as public transportation, banking systems, and any complex service systems simulated as a black box model.The classic RSM considers only one quality characteristic as a dependent variable. But as systems become more complicated, RSM is also extended in several aspects. In this regard, multiple response variables with different priorities, importance degrees, and scales of measurement 1-3 have been recently focused to achieve compromise solutions. Variance of response surfaces as a criterion for robustness has been studied to reduce total loss of quality. 4 Taking existing correlations among response variables into the account 5 would help to reach more accurate estimation as well as more precise calculations of statistical properties of the responses. There are many systems in which covariates affect the response measurements as commitment variables, so including these noise variables would help to reach more accurate and well-fitted models. 6 Degree of conformance is a measure that helps to judge a system by its rejection rate as an economic index. This measure can be calculated by using stochastic pattern...

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

Cited by 6 publications

References 18 publications

Photocatalytic Degradation of Phenol and Phenol Derivatives Using a Nano-TiO2 Catalyst: Integrating Quantitative and Qualitative Factors Using Response Surface Methodology

Photocatalytic Degradation of Phenol and Phenol Derivatives Using a Nano-TiO2 Catalyst: Integrating Quantitative and Qualitative Factors Using Response Surface Methodology

A Simple Approach for Multi‐fidelity Experimentation Applied to Financial Engineering

Optimization of Degree of Conformance in Multiresponse–Multistage Systems with a Simulation‐based Metaheuristic

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