scholarly journals A note on Variance-Sum Third Order Slope Rotatable Designs

2021 ◽  
Vol 9 (10) ◽  
pp. 760-766
Author(s):  
R. Md. Mastan Shareef
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Interesting Property ◽  
Response Surfaces ◽  
Statistical Techniques ◽  
Third Order ◽  
Controllable Factors ◽  
Four Levels ◽  
Rotatable Design

Abstract: Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques useful for analyzing experiments where the yield is believed to be influenced by one or more controllable factors. Box and Hunter (1957) introduced rotatable designs in order to explore the response surfaces. The analogue of Box-Hunter rotatability criterion is a requirement that the variance of i yˆ(x)/ x be constant on circles (v=2), spheres (v=3) or hyperspheres (v 4) at the design origin. These estimates of the derivatives would then be equally reliable for all points (x , x ,...,x ) 1 2 v equidistant from the design origin. This property is called as slope rotatability (Hader and Park (1978)).Anjaneyulu et al (1995 &2000) introduced Third Order Slope Rotatable Designs. Anjaneyulu et al(2004) introduced and established that TOSRD(OAD) has the additional interesting property that the sum of the variance of estimates of slopes in all axial directions at any point is a function of the distance of the point from the design origin. In this paper we made an attempt to construct Variance-Sum Third Order Slope Rotatable in four levels. Keywords: Response Surface Methodology. Third Order Slope Rotatable Design; TOSRD (OAD), Variance-Sum Third Order Slope Rotatable Design.

scholarly journals A Sequential Third Order Rotatable Design of Eighty Points in Four Dimensions with an Hypothetical Case Study

2019 ◽  
pp. 1-9
Author(s):  
Nyakundi Omwando Cornelious ◽  
Matunde Nambilo Cruyff
Keyword(s):  
Response Surface ◽  
Continuous Cultivation ◽  
Mineral Elements ◽  
Hypothetical Case ◽  
Third Order ◽  
Four Dimensions ◽  
Design Variables ◽  
Controllable Factors ◽  
Rotatable Design

In research, experiments must be performed at pre determined levels of the controllable factors, meaning that an experimental design must be selected before the experiment takes place. Once an experimenter has chosen a polynomial model of suitable order, the problem arises on how best to choose the settings for the independent variables over which he has control. A particular selection of settings or factor levels at which observations are to be taken is called a design. A design may become inappropriate under special circumstances requiring an increase in factors or levels to make it more desirable. In agriculture for instance, continuous cultivation of crops may exhaust the previously available mineral elements necessitating a sequential appendage of the mineral elements which become deficient in the soil over time. In current study, an eighty  points four  dimensional  third order rotatable design is constructed by combining two, four dimensional second order rotatable  designs and a practical hypothetical case study is given by converting coded levels to natural levels. We present an illustration on how to obtain the mathematical parameters of the coded values and its corresponding natural levels for a third order rotatable design in four dimensions by utilizing response surface methodology to approximate the functional relationship between the performance characteristics and the design variables.  This design permits a response surface to be fitted easily and provides spherical information contours besides the economic use of scarce resources in relevant production processes.

An Investigation Effects of Electrospinning Parameters: Process Optimization by Application of Response Surface Methodology

2014 ◽  
Vol 660 ◽  
pp. 140-144
Author(s):  
A. Mataram ◽  
Ahmad Fauzi Ismail ◽  
A.S. Mohruni ◽  
T. Matsura
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Applied Voltage ◽  
Fiber Diameter ◽  
Solution Concentration ◽  
Response Surfaces ◽  
Nano Scale ◽  
The Mean ◽  
Nanoscale Fibers ◽  
Parameter Interactions

Effects of material and process parameters on the electrospun polyacrylonitrile fibers were experimentally investigated. Response surface methodology (RSM) was utilized to design the experiments at the setting of solution concentration, voltage and the collector distance. It also imparted the evaluation of the significance of each parameter on pore size, contact angle, modulus young and clean water permeability. Effect of applied voltage in micron-scale fiber diameter was observed to be almost negligible when solution concentration and collector distance were high. However, all three factors were found statistically significant in the production of nano-scale fibers. The response surface predictions revealed the parameter interactions for the resultant fiber diameter, and showed that there is negative correlation between the mean diameter and coefficient of variation for the fiber diameters were in agreement with the experimental results. Response surfaces were constructed to identify the processing window suitable for producing nanoscale fibers. A sub-domain of the parameter space consisting of the solution concentration, applied voltage and collector distance, was suggested for the potential nano scale fiber production.

Process Optimization of Ultrasound-Assisted Extraction of Pectin from Helianthus annuus L. Heads by Response Surface Methodology

2014 ◽  
Vol 955-959 ◽  
pp. 848-854
Author(s):  
Yin Xiang Gao ◽  
Lei Yang ◽  
Yuan Gang Zu ◽  
Li Ping Yao
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Helianthus Annuus ◽  
Response Surfaces ◽  
Quadratic Model ◽  
High Yield ◽  
Extraction Temperature ◽  
Ultrasound Assisted Extraction ◽  
Assisted Extraction ◽  
Ultrasound Assisted

An ultrasound-assisted procedure for the extraction of pectin from heads ofHelianthus annuusL. (sunflower) was established. A Box–Behnken design (BBD) was employed to optimize the extraction temperature (X1: 30–50°C), extraction time (X2: 20–40 min) and pH (X3: 2.5–3.5) to obtain a high yield of pectin with high degree of esterification (DE) from sunflower heads. Analysis of variance showed that the contribution of a quadratic model was significant for the pectin extraction yield and DE. An optimization study using response surface methodology was performed and 3D response surfaces were plotted from the mathematical model. According to the RSM model, the highest pectin yield (23.11 ± 0.08%) and DE (39.85 ± 0.14%) can be achieved when the UAE process is carried out at 50°C for 40min using a hydrochloric acid solution of pH 3.0. These results suggest that ultrasound-assisted extraction could be a good option for the extraction of functional pectin from sunflower heads at industrial level.

A Thermomechanical Preprocessing for Pectin Isolation from Orange Peel with Optimisation by Response Surface Methodology

2008 ◽  
Vol 4 (1) ◽  
Author(s):  
Sid-Ahmed Rezzoug ◽  
Zoulikha Maache-Rezzoug ◽  
Frédéric Sannier ◽  
Karim Allaf
Keyword(s):  
Response Surface Methodology ◽  
Moisture Content ◽  
Response Surface ◽  
Processing Time ◽  
Initial Moisture Content ◽  
Control Sample ◽  
Orange Peel ◽  
Response Surfaces ◽  
Acid Extraction ◽  
Pre Treatment

The instantaneous controlled pressure drop process (or D.I.C process: ``Détente Instantanée Contrôlée") was used as a pre-treatment prior to pectin acid extraction from orange peel. This process involves subjecting the orange peel for a short time to steam pressure varying from 100 to 700 kPa, followed by an instantaneous decompression to vacuum at 5 kPa. Effects of processing pressure, moisture content of peels before the thermomechanical treatment and processing time were examined with response surface methodology. The optimal conditions were determined and the response surfaces were plotted from the mathematical models. The Fisher test and p-value indicated that both processing pressure and moisture content of peels before the pre-treatment had a highly significant effect on the pectin yield. The quadratic effect of processing pressure as well as the interaction effects of the initial moisture content and processing time also had a significant effect on the response. Moreover, the kinetics of pectin extraction showed that after few minutes of hydrolysis, the yields of pectin were systematically higher than that of the control sample and this is important from industrial point of view because the hydrolysis of pectin is generally performed in 10-15 minutes.

Extraction of Flavonoids from Clovers

2012 ◽  
Vol 195-196 ◽  
pp. 360-363
Author(s):  
Chun Gang Chen ◽  
Fen Xia Han ◽  
Yuan Zhang ◽  
Yu Zhong Shi
Keyword(s):  
Response Surface Methodology ◽  
Optimum Condition ◽  
Central Composite Design ◽  
Response Surface ◽  
Ethanol Concentration ◽  
Response Surfaces ◽  
Second Order ◽  
Order Model ◽  
Solid Ratio ◽  
Central Composite

The extraction of flavonoids from clovers was optimized to maximize flavonoid yield Y in this study. A central composite design of response surface methodology involving extracting time, liquid-solid ratio, extracting temperature and ethanol concentration was used, and second-order model for Y was employed to generate the response surfaces. The optimum condition for Y was determined as follows: extracting time 24min, liquid-solid ratio 20, extracting temperature 80°C, and ethanol concentration 72%. Under the optimum condition, the flavonoid yield was 2.49%.

A novel robust multivariate regression approach to optimize multiple surfaces

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1233-1243
Author(s):  
Amir Moslemi ◽  
Mirmehdi Seyyed-Esfahani
Keyword(s):  
Response Surface ◽  
Multivariate Regression ◽  
Ordinary Least Squares ◽  
Response Surfaces ◽  
Response Models ◽  
New Approach ◽  
Global Criterion ◽  
Global Criterion Method ◽  
Controllable Factors ◽  
Criterion Method

Response surface methodology involves relationships between different variables, specifically experimental inputs as controllable factors, and a response or responses by incorporating uncontrollable factors named nuisance. In order to optimize these response surfaces, we should have accurate response models. A common approach to estimate a response surface is the ordinary least squares (OLS) method. Since OLS is very sensitive to outliers, some robust approaches have been discussed in the literature. Most problems face with more than one response which are mostly correlated, that are called multi-response problem. This paper presents a new approach which takes the benefits of robust multivariate regression to cope with the mentioned difficulties. After estimating accurate response surfaces, optimization phase should be applied in order to have proper combination of variables and optimum solutions. Global criterion method of multi-objective optimization has also been used to reach a compromise solution which improves all response variables simultaneously. Finally, the proposed approach is described analytically by a numerical example.

Process Parameters Optimization for Thin-walled Tube Push-bending Using Response Surface Methodology

2021 ◽  
Author(s):  
Wenlong Xie ◽  
Weihao Jiang ◽  
Yunfeng Wu ◽  
Hongwu Song ◽  
Siying Deng ◽  
...  
Keyword(s):  
Response Surface Methodology ◽  
Friction Coefficient ◽  
Response Surface ◽  
Process Parameters ◽  
Relative Length ◽  
Response Surfaces ◽  
Parameters Optimization ◽  
Process Window ◽  
Thin Walled Tube ◽  
Thin Walled

Abstract In this paper, the response surface methodology (RSM) and finite element (FE) simulation were applied to optimize the push-bending process parameters of the thin-walled tube with polyurethane mandrel. The objective of the present work is to predict the optimal set of process parameters including the relative length of the mandrel (L/D), the friction coefficient between die and tube (μ1), the friction coefficient between polyurethane and tube (μ2) and Poisson’s ratio of polyurethane (υ) to obtain qualified bent tubes. Three empirical models were developed to describe the relationship between process parameters and quality parameters of the bent tubes. In addition, the significant factors affecting the forming quality were analyzed using analysis of variance (ANOVA) of each model. Response surfaces were constructed to study the effect of each process parameter on the quality of the bent tubes. Finally, the process optimization window with the maximum thinning rate (ϑ) less than 20%, the maximum thickening rate (ψ) less than 17%, and the maximum cross-section ovality (ξ) less than 5% of the bent tube was established. Qualified bent tubes with diameter of 144 mm, wall thickness of 2 mm, and bending radius of 280 mm were formed experimentally by following the established process window.

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