Factorial designs applications response

Application of factorial design and response surface methodology to the analysis of caseins by CE using a... 

Application of Factorial Design and Response Surface Methodology to the Analysis of Caseins by CE using a Neutral Capillary... 

Curved one-factor response surface showing (a) the limitation of a 2 factorial design for modeling second-order effects and (b) the application of a 3 factorial design for modeling second-order effects. 

TJ apid entrainment carbonization of powdered coal under pressure in a partial hydrogen atmosphere was investigated as a means of producing low sulfur char for use as a power plant fuel. Specific objectives of the research were to determine if an acceptable product could be made and to establish the relationship between yields and chemical properties of the char, with special emphasis on type and amount of sulfur compound in the product. The experiments were conducted with a 4-inch diameter by 18-inch high carbonizer according to a composite factorial design (1, 2). Results of the experiments are expressed by empirical mathematical models and are illustrated by the application of response surface analysis. 

Stewart, W.H. Application of response surface methodology and factorial designs for drug combination development. Journal of Biopharmaceutical Statistics 1996 6 219-231. 

Note Optimization = 2 factor, 2 and 3-level full factorial design—12 compounds and experiments. Responses (properties) to be measured Static ozone resistance dynamic ozone resistance flex-fatigue resistance extrusion processing high temperature, pressure pulse simulated application test of hose sample. 

Note Optimization = 3 factor, 2,2 and 2-level fiill factorial design—8 compounds and experiments. Responses (properties) to be measured ASTM reference oil resistance, 70 h at 150°C hexane resistance to simulate light hydrocaibons, 70 h at room temperature O-Ring compression set, 1008 h at 150°C pressure extrusion test in simulated application gland. 

The mixture experiment counterpart to conventional screening/fractional factorial experimentation also is possible. So-called axial designs have been developed for the purpose of providing screening-type mixture data for use in rough evaluation of the relative effects of a large number of mixture components on a response variable. The same kind of sequential experimental strategy illustrated in the process improvement example is applicable in mixture contexts as well as contexts free of a constraint such as (5-15). 

Industrial applications of the divided-wall (Petlyuk) column have expanded, so a new chapter has been added that covers both the design and the control of these more complex coupled columns. The use of dynamic simulations to quantitatively explore the safety issues of rapid transient responses to major process upsets and failures is discussed in a new chapter. A more stmctured approach for selecting an appropriate control structure is outlined to help sort through the overwhelmingly large number of alternative stmctures. A simple distillation column has five factorial (120) alternative structures that need to be trimmed down to a workable number, so that their steady-state and dynamic performances can be compared. 

One class of designs directly applicable to computer experiments is orthogonal designs [17,27,35]. An example of such a design for three independent factorial variables (xi, X2, and X3) is shown in Table 1. Each row of this table represents a computer experiment—the hrst column designates its sequential number (1 through 15), the third to hfth columns, labeled Independent variables, list the factorial variable values held in this experiment, and the last column reports the computed response obtained in this computer run. Several different responses could be obtained in a single computer experiment. 

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