Setting Up the Design

Elements of a central composite design, each axis representing one factor 

111 this section we analyse in detail the features of such designs. In most cases, however many factors are used, only two factor interactions are computed so higher order interactions are ignored, although, of course, provided that sufficient degrees of freedom are available to estimate the lack-of-fit, higher interactions are conceivable. 

Degrees of freedom for central composite design of Table 2.31 

Note that the number of degrees of freedom for the lack-of-fit equals that for replication in this case, suggesting quite a good design. 

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In setting up the design, we decide the range over which we would like to study the variables and then set the levels for each experimental condition to conform with the design. For example, if Xx = temperature, Xz — pressure, and Xz = catalyst concentration, we might assign the following experimental levels. 

For a 2 f fractional factorial, first set up the design consisting of 2k f experiments for the first k — f factors, i.e. for a quarter (/ = 2) of a five (=k) factorial experiment, set up a design consisting of eight experiments for the first three factors. 

A 10 parameter model is to be fitted to the data, consisting of the intercept, all single factor linear and quadratic terms and all two factor interaction terms. Set up the design matrix, and by using the pseudo-inverse, calculate the coefficients of the model using coded values. 

For die model in question 3, set up the design matrix, calculate the new coefficients and show how diese relate to die coefficients calculated in question 1 using the relationship obtained in question 3. 

MINITAB is used to set up the design matrix. The matrix showing the 16 experiments to be run is shown in Table 1. The column labeled Run Order is used to... 

And, as we have already seen a number of times, the experimenter does not know what will be the best model. He therefore has the following dilemma to set up the design he must postulate a model, but if he makes the wrong choice of model, the design loses much of its interest. 

Figure 3 Schematic illustration of the complete mold, vacuum, and resin inlet set-up. The design of the resin inlet is enlarged.

To set up the Design SpecA ary function, click on Design Spec under the Cl block in the Data Browser window. The window shown in Figure 3.37a opens up. Clicking the New button opens the window shown in Figure 3.37b. Click OK and another window... 

Figure 3.37 (a) Setting up the Design Spec, (b) Set Design Spec number. 

In a combination oil-water quench tower, the hot cracked gas is first contacted with cool oil which reduces the gas temperature to a point slightly above the water dew point of the gas and at the same time condensing out the heavy portion of the PO. The gas then passes to the water section where it is cooled by direct water washing. The dilution steam and some additional lighter PO are condensed. The general points to be considered in setting up the design are as follows. 

For all the probes we design a specific and simple measurement set-up. The figure 2 illustrates the three different targets we made for the illustrated probes, following the rules ... 

Two major sources of ultrasound are employed, namely ultrasonic baths and ultrasonic immersion hom probes [79, 71]- The fonuer consists of fixed-frequency transducers beneath the exterior of the bath unit filled with water in which the electrochemical cell is then fixed. Alternatively, the metal bath is coated and directly employed as electrochemical cell, but m both cases the results strongly depend on the position and design of the set-up. The ultrasonic horn transducer, on the other hand, is a transducer provided with an electrically conducting tip (often Ti6A14V), which is inuuersed in a three-electrode thenuostatted cell to a depth of 1-2 cm directly facing the electrode surface. 

AC Good, R Lewis. New methodology for profiling combinatorial libraries and screening sets Cleaning up the design process with HARPick. I Med Chem 40 3926-3936, 1997. 

It is important to note, however, that all this is not free. The designer must invest the time to set up the cases and evaluate the results. Only the designer can make the final decision as to whether the cases and the comparisons are valid (a true representation of the plant). The computer printout is simply the results of matrix manipulation and should be considered suspect until given the designer s stamp of approval. 

In December 1998 I was fortunate to be invited to participate in the development of the ISO/TS 16949 certification scheme and later to represent the UK Society of Motor Manufacturers and Traders (SMMT) on the lATF Training Council, set up to design the auditor qualification program. I would therefore like to acknowledge Bob Lawrie and Robert Coles of the SMMT for providing the opportunities in which I was able to learn about the lATF and ISO/TS 16949. 

In a typical chapter, you will find ten or more Examples, each designed to illustrate a particular principle. These have answers, screened in colon Most of them contain a Strategy statement, which describes the reasoning behind the Solution. You should find it helpful to get into the habit of working all problems this way. First, spend a few moments deciding how the problem should be solved. Then, and only then, set up the mathematics to solve it... 

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