Three-level orthogonal design

A policy of a three level safety design was also adopted. This includes the use of utilities and safety devices. An orthogonal design was used such that interruption of any part of these services would not affect the remaining sections. Manual bypasses were also provided in order to permit operator intervention at any point in the process. Finally, any releases of material from any of the relief devices were directed into secondary holding vessels in order to prevent releases into the atmosphere. 

The large number and variety of factors on which SFE performance relies makes optimizing it rather a difficult task. Multivariate optimization approaches have been used from the beginning of this technique to both minimize the processing time and increase the extraction efficiency [18,19]. Simplex models [20] were the first to be used to examine the influence of interdependent variables. Two- and three-level orthogonal factor designs were developed to optimize up to nine extraction variables (viz. CO, flow-rate, fluid... 

For this study, the control factors, that is, the most influential parameters affecting the electrical resistivity of GO during the process of chemical reduction were identified to be the type of acid used for reduction, the extent of exfoliation, and the period of reaction. Thus, the three factors are the ultrasonication time, the reducing agent, and the reaction time. Three-level experimental design was selected over two levels to understand the nonlinearity in the factor—response relationship (Jones and Nachtsheim, 2011). The Lg orthogonal array for a three-level system (3") was selected to obtain the combination of factors and their respective levels for each of the standard trial order as presented in Table 8.12. The arrangement in statistical terms is presented here as Tables 8.11 and 8.12. 

Lyophilized powder (0.2 g) was put in eontaet with 10 mL of 5 mol-L lactic acid at controlled temperature. After eell disruption, the mixture was centrifuged and the liquid phase removed. Then the fraetion of disrupted eells was extracted with 15 mL of organic solvent at room temperature. The proeess parameters were optimized to estimate the best conditions for the extraction yield of astaxanthin and for that, a four-factor three-level orthogonal array design was used. The factors and levels were the following disrupting temperature (35, 50, and 65°C), disrupting time (10, 60, and 110 min), type of solvent (ethyl lactate and ethyl lactate + ethanol in 1/1 and 3/1 ratios) and extraction time (10, 30, and 50 min). 

The design factors require 12 df so an Lig orthogonal array (with 15df) was selected. Hence we can study a factor at two levels and seven factors at three levels each. The matrix is adapted to our needs by discarding column 1 (designed for a variable with two levels) and column 7 (not needed in this example). This yields 3 df to calculate the residuals. Hence the experimental matrix is as presented in Table 2.14. 

Considering the practice and simulation design possible, each factor takes three levels. Test two indicators are (1) the main roof produce the plastic damage position (2) the main roof maximum shear stress position Seven factors and three levels Choose L9 (37) design orthogonal table as shown in Table 2. 

Based on single-factor experiment of enzymolysis extraction, the yield was used as index, three factors and three levels L9 (33) were designed (Zhu et al., 2006). Hydrolysis time. Hydrolysis temperature and Mass ratio of trypsin and cellulose were studied in the orthogonal experiment. 

Now, consider the case of determining the orthogonal basis for the factorial design with three levels. The three equispaced coded treatment points are —1, 0, and 8i= ). Ignoring the zero-power basis function, there will be two additional basis functions of general form ... 

The more than three-dimensional designs are referred to as hyper-Graeco-Latin squares, or a complete set of mutually orthogonal Latin squares. In Example 2, the use of four factors at three levels adds the prefix hyper. ... 

Design an orthogonal array to investigate the effects of the pressure, temperature, cosolvent level (methanol), and extraction time on the yield of raw material. The orthogonal matrix contains four factors, and each factor includes three levels. As a rule, the flow rate of SCFs is 25 kg/h see Notes 8-11) (Table 1). Keep other independent variables (e.g., sample size and solvent flow rate) constant during the above experiments. 

Table 1 displays an orthogonal array of strength three because it contains each of the 23 = 8 level combinations of any set of three factors exactly twice. In other words, its projection onto any set of three factors consists of two replicates of the complete 23 factorial design. 

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