Response Surface Methodology

Abstract

Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. In Social Network Problems usually the underlying mechanism is not fully understood, and the experimenter must approximate the unknown function g with appropriate empirical model,..., , 2 1 ) + ε, where the term ε represents the error in the system.Usually the function f is a first-order or second-order polynomial. This empirical model is called a response surface model.Identifying and fitting from experimental data an appropriate response surface model requires some use of statistical experimental design fundamentals, regression modeling techniques, and optimization methods. All three of these topics are usually combined into Response Surface Methodology (RSM).Also the experimenter may encounter situations where the full model may not be appropriate. Then variable selection or model-building techniques may be used to identify the best subset of regressors to include in a regression model. In our approach we use the simulated annealing method of optimization for searching the best subset of regressors. In some response surface experiments, there can be one or more near-linear dependences among regressor variables in the model. Regression model builders refer to this as multicollinearity among the regressors. Multicollinearity can have serious effects on the estimates of the model parameters and on the general applicability of the final model.The RSM is also extremely useful as an automated tool for model calibration and validation especially for modern computational multi-agent large-scale social-networks systems that are becoming heavily used in modeling and simulation of complex social networks.The RSM can be integrated in many large-scale simulation systems such as BioWar, ORA and is currently integrating in Vista, Construct, and DyNet. This report describes the theoretical approach for solving of these problems and the implementation of chosen methods.

Making Fe0-Based Filters a Universal Solution for Safe Drinking Water Provision

“…This model is flexible and covers all linear, non-linear, and interaction effects between the factors [179]. The quadratic polynomial equation is as follows:…”

Predicting instrumental mass fractionation (IMF) of stable isotope SIMS analyses by response surface methodology (RSM) [Dataset]

“…The selection of the model terms is habitually carried out by a sequential stepwise backward elimination process. 33,35 In each step, the no significant term displaying the highest p-value is eliminated and then the model is refitted again. The procedure sequentially repeats until, ideally most of the remaining model terms display proper levels of significance (p-value ≤ 0.05) and multicollinearity (VIF ≤ 10).…”

“…15,16 Introduced by Box and Wilson, RSM has been applied to build up multivariate statistical models in a wide variety of industrial, engineering and experimental processes. 17 Successful RSM applications can be found in, e.g., Riley [18][19][20][21][22][23][24][25][26][27][28][29][30] In addition, the mathematical and statistical aspects of RSM and related experimental techniques are covered in e.g., Box, Box, and [31][32][33][34][35][36][37] Simultaneously, the statistical prediction models have been recognized as powerful tools for e.g., exploring the underlying causal relationships below the datasets, building and/or assessing new knowledge and improving previous models. 38 While explanatory statistical modelling is based on the causal relationships among previous theoretical constructions, the predictive statistical modelling works on associations of measurable variables.…”

Process Optimization of Effective Partition Constant in Progressive Freeze Concentration of Wastewater

“…The first criteria evaluated to see the model adequacy is by judging the appropriateness of the model from the determination coefficient, the R-squared value, which reveals the total variation of the observed values of activity about its mean [12][13][14][15][16].…”