Excel factorial designs

Optimization of a process or catalyst by experimental design such as two-factorial design can lead to significant reduction in time required to achieve the goal. In their excellent work, Mylroie et al. (3) reduced the time required for the optimization of the reductive alkylation process conditions by a factor of 10. Here, we turn our attention to the optimization of the catalyst rather than the process. 

There are innumberable ways by which the settings of experimental variables can be varied to determine their influence on the measured response. To obtain good and reliable estimates the lay-out of the experimental runs in the experimental domain is veiy important. Different designs in that respect will correspond to different dispersion matrices, and hence to the quality of the estimated parameters. It is seen that two-level factorial designs have excellent statistical properties we cannot do better. 

Response surface methodology (RSM) is an optimization technique based on factorial designs introduced by G.E.R Box in the 1950s. Since then, RSM has been used with great success for modeling various industrial processes. In this chapter, we use the concepts introduced in the previous chapters to explain the basic principles of RSM. The interested reader can find more comprehensive treatments in Cornell (1990a), Myers and Montgomery (2002) and in the excellent books and scientific papers of G.E.R Box and his co-workers (Box and Wilson, 1951 Box, 1954 Box and Youle, 1955 Box and Draper, 1987). 

Tables of two-level factorial designs can be found in most textbooks of DOE. A good source is also NIST SEMATECH e-Handbook of Statistical Methods (NIST SEMATCH). Another way to create such tables is to use DOE-software e.g. (JMP, MODDE, MiniTab,...). It is also very easy to create tables of two-level factorial designs in any spreadsheet program. For example in Excel, you can simply enter the somewhat hideous formula...

The solution to this problem using Excel is presented in Sect. 8.7.3 Factorial Design Examples. 

It can be noted that the values are not the same. This is expected since an orthonormal basis was not used. An explanation of how to implement this problem in Excel is presented in Sect. 8.7.3 Factorial Design Examples. 

Goal perform the analysis of a factorial design experiment in Excel in an easy and straightforward manner. 

This section presents three examples that show how to implement various forms of regression analysis in Excel. The topics considered are linear regression, nonlinear regression, and analysis of factorial design. All examples are based on real data obtained from experiments. The procedures use the appropriate templates for... 

This section presents the Excel spreadsheets for analysing some of the factorial design experiments presented in Chap. 4. The examples are all based on the factorial design template. The following examples have a corresponding Excel spreadsheet ... 

The book, Hollow Fibers (Scott, 1981) is an excellent practical source for details about the large-scale manufacture of hollow fibers. The effect of spinning parameters on both the macroscopic dimensions and permeation performance of polysulfone ultrafiltration hollow fibre membranes has been studied by several people (Kim et al., 1995, Liu et al., 1992, McKelvey et al., 1997, and Lee et al., 1995). The latter paper uses a factorial design to study the effects of various spinning parameters, and gives optimal spinning conditions for ultrafiltration performance. 

For this reason, at several S.R. facilities, instruments have been designed which can be used excellently for X-ray scattering experiments with polymers. The most important beamlines exist at the storage ring DORIS at DESY in Hamburg (FRG), at the SRS in Daresbury (GB), at the SSRL in Stanford (USA), at the CHESS in Cornell (USA), at the NSLS in Brookhaven (USA), at L.U.R.E. in Orsay (F), and at the Photon Factory in Tsukuba (JPN). 

The fractional design has an important characteristic. Its contrasts do not miK main effects with interaction effects involving two factors, but with interaction effects involving three factors, which in principle should be less significant. If these interaction effects are really negligible, the contrasts wiU furnish excellent approximations to the main effects calculated from the frill factorial. We should have, for example, I2 =l = 2. In general, we expect that Ij = IJ = J, where J stands for any main effect. 

Four of the runs in Table 4.9 are identical to runs in Table 4.6. The responses for these runs are the same in both tables and represent real values. The other four runs have level combinations for which the experiments had not been performed. Their response values are simulations obtained from the experimental data in Table 4.6. The calculated contrasts are also shown in Table 4.9, where we can observe that their values are in excellent agreement with the estimates of the average and the main effects determined from the 2y design (Table 4.7). Analyzing the results of the 2 quarter-fraction, which would be obtained in the initial stage of the investigation, the research workers could decide if they should perform more runs to arrive at a half-fraction or even the 2 complete factorial, if they should introduce new factors in place of the 1 and 5 variables (which appear to have little influence on the response), or even if they woifld rather change the levels of the variables. ... 

If a reactor is transportable and has a long life, it can be built in a factory and shipped to the site and installed and operated there within a certain period of time without refuelling. After its lifetime is completed it could be shipped back to the factory and replaced with a new reactor. When the vessel of such reactor is designed to be sealed, this reactor may possess excellent proliferation resistance features. 

In addition to the requirement for code and standard compliance, many cleanroom occupancies are insured through carriers, such as Factory Mutual (FM) or Industrial Risk Insurers (IRI)) who have additional design and constmction requirements, in order to reduce the risk of fire and other liabilities. With respect to semiconductor facilities, FM Publication No. 1-56, Cleanrooms, No. 7-7, Semiconductor Fabrication Facilities, and IRI Publication IM. 17.1.1, Guiding Principles for the Protection of Semiconductor Manufacturing Facilities, provide excellent guidelines and should be used as design and operations references. Other IRI or FM guidelines may also apply. 

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