A note on Variance-Sum Third Order Slope Rotatable Designs

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.

Effect of Flaxseed Oil Inclusion and Extrusion Cooking Parameters on Extruded Snack-food Physical and Functional Properties

Aims: Attempts were made to study flaxseed oil incorporated extruded snack by adopting response surface methodology (RSM) approach. Study Design: Central Composite Rotatable Design (CCRD). Place and Duration of Study: Department of Food Processing Technology, A.D. Patel Institute of Technology, Po Box 52, New Vallabh Vidya Nagar, Anand. Methodology: Feed moisture (12 -16%, wb), flaxseed oil (3-7%), extruder barrel temperature (115-145⁰C and screw speed (345 – 375 rpm) were selected as independent variable at three levels. The Central Composite Rotatable Design (CCRD) was employed to study linear, interactive and quadratic effect of selected independent variables on measured responses (expansion ratio ER, breaking strength BS, overall acceptability score OAA, starch-lipid complexing index CI). Results: The physical properties of extrudate (ER at 0.05 and BS at 0.10 level) and functional properties (OAA at 0.05 and CI at 0.01 level) were significantly influenced by flaxseed oil inclusion level. The quadratic effect of feed moisture and barrel temperature were found to be significant on each response (p<0.01). After numerical optimization, flaxseed oil of 6%, feed moisture content of 14.5% (wb), barrel temperature of 1300C and screw speed of 355 rpm were optimized.

Guazuma ulmifolia: an environmentally friendly coagulant aid for water treatment

In the present work the use of a promising novel coagulant aid, Guazuma ulmifolia, was optimized to treat synthetic water using central composite being highly efficient at rotatable design (CCRD). The factors evaluated for the coagulation-flocculation process were coagulants dosages and pH. A model to describe the coagulation-flocculation process was successfully obtained. The model was validated using 5 mg L−1 aluminum sulfate, 2.5 mg L−1G. ulmifolia and pH 9, achieving excellent agreement with observed values.

Construction of twenty-six points specific optimum second order rotatable designs in three dimensions with a practical example

This quadratic response surface methodology focuses on finding the levels of some (coded) predictor variables x = (x1u, x2u, x3u)' that optimize the expected value of a response variable yu from natural levels. The experiment starts from some best guess or “control” combination of the predictor variables (usually coded to x = 0 for this case x1u=30, x2u=25 and x3u =40) and experiment is performed varying them in a region around this center point.We go further to construct a specific optimum second order rotatable design of three factors in twenty-six points. The achievement of this is done with estimation of the free parameters using calculus in an existing second order rotatable design of twenty-six points. Such a design permits a response surface to be fitted easily and provides spherical information contours besides the realizations of optimum combination of ingredients in Agriculture, horticulture and allied sciences which results in economic use of scarce resources in relevant production processes. The expected second order rotatable design model in three dimensions is available where the responses would then facilitate the estimation of the linear and quadratic coefficients. An example involving Phosphate (x1u), Nitrogen (x2u) and Potassium (x3u) is used to represent the three factors in the coded level and converted into natural levels.