Six Factors

With six factors we require 2 = 64 runs. In confounding in 2 blocks of 32 we obviously choose the highest order interaction PQRSTU to be confounded. For four blocks of 16 the most satisfactory set for confounding is PQRS, RSTU, PQTU, and for 8 blocks of 8 

In all these cases we avoid losing any st order interaction. To get the 64 runs into 16 blocks of 4, however, losing 3 first order interactions is unavoidable. A typical set of 15 interactions for confounding is 

For allocating the treatments to their appropriate blocks the same method as hitherto can be applied. The first block is 

In a confounded experiment the computation proceeds exactly as though the experiment had not been confounded, with the sole difference that we do not compute those interactions which we have confounded. Instead, we take the block totals, square them, divide by the number of treatments occurring in each block, and subtract the usual correcting factor (grand total squared over grand total number of observations). The degrees of freedom for this sum of squares is of course one less than the number of blocks. We would get an identical result if we calculated the sum of squares for the interactions being confounded, and then pooled them. 

As an example, let us consider an experiment on a process employing a mixed catalyst made up of three components. We wish to vary catalyst component A at 4, levels and components C and D each at 2 levels, and we measure the yield as the dependent variable. A straightforward factorial experiment would require 4 X 2 X 2 = 16 runs. However, it was necessary to confound the experiment in blocks of 4, 4 blocks thus being required. 

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Shordy thereafter, the M-4365 complex of six factors (A —A and G —G ), produced by M. capillata (275,276), was reported. From the izenamicin complex of seven factors produced by a M.icromonospora species, three were new fermentation products (277). Many compounds isolated are identical juvenimicin A, M-4365 A2, and izenamicin A are the same as rosaramicin. Stmctures have been proven by chemical interconversions (261,277,278) and microbial transformations (279). 

ISO EN 7730 standardizes the PMV-PPD index as the method for evaluation of moderate thermal environments. To quantify the degree of comfort, the PMV (predicted mean vote) index gives a value on a 7-point thermal sensation scale -t-3 hot, +2 warm, +1 slightly warm, 0 neutral, -I slightly cool, -2 cool, -3 cold. An equation in the standard calculates the PMV index based on the six factors (clothing, activity, air and mean radiant temperatures, air speed, and humidity). 

Before collecting data, at least two lean/rich cycles of 15-min lean and 5-min rich were completed for the given reaction condition. These cycle times were chosen so as the effluent from all reactors reached steady state. After the initial lean/rich cycles were completed, IR spectra were collected continuously during the switch from fuel rich to fuel lean and then back again to fuel rich. The collection time in the fuel lean and fuel rich phases was maintained at 15 and 5 min, respectively. The catalyst was tested for SNS at all the different reaction conditions and the qualitative discussion of the results can be found in [75], Quantitative analysis of the data required the application of statistical methods to separate the effects of the six factors and their interactions from the inherent noise in the data. Table 11.5 presents the coefficient for all the normalized parameters which were statistically significant. It includes the estimated coefficients for the linear model, similar to Eqn (2), of how SNS is affected by the reaction conditions. 

The rate of a reaction is defined as the change in concentration of any of its reactants or products per unit time. There are six factors that affect the rate of a reaction ... 

TABLE 4 2 Fractional Factorial Design to Examine Six Factors in 16 Experiments (Design... 

At least six factors interplay to determine what fuel is selected ... 

Principal component factor analysis followed by varlmax rotation of six factors was performed on four different subsets of the remaining data (each with different preprocessing) ... 

A Six-factor PLS model was found to be optimal based on the model diagnostic tools. The measures of performance for die final model are as follows (see Table 5.18 for a description of these figures of merit) ... 

Predicted vs. Known Concentration Plot (Model and Sample Diagnostic) The predicted versus known concentrations for MCB using a six-factor model in Figure 5.128. show that the samples are clu.stered about the ideal line and there are no patterns or unusual samples. 

FIGURE 5.129. Concentration residual (known-predicted) versus predicted concentration for MCB using a six-factor PLS model. 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) The RMSEP versus number of factors plot in Figure 5.113 shows a break at three factors and a leveling off after six factors. Tlie RMSEP value with six factors (0,04) is comparable to the estimated error in the reported concentrations (0.033), indicating the model is predicting well At this point we tentatively choose a rank six model. The rank three model shows an RMSEP of 0.07 and may well have been considered to be an adequate model, depending on how well the reference values are known. 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) The RMSEP plot for the MCB model is shown in Figure 5.127. Although the shape of this RMSEP plot is not ideal, it does not exhibit erratic behavior. Tlie first minimum in this plot is at four factors with a lower minimum at six factors. In Section 5.2.1.2, nonlinear behavior was suspected as the root cause of the failure of the DCLS method. Tlicreforc, it is reasonable that a PLS model re-... 

Concentration Residual vs. Predicted Concentration Plot (Model and Sample Diagnostic) Figure 5-129 displays the MCB concentration residuals versus the predicted concentration for the six-factor PLS model. The prediction for sample I is slightly worse than the re.st of the samples. However, sample 1 has tlie highest MCB concentration (it is pure MCB). When using Icave-one-out cross- -alidation, the model is required to extrapolate in order to predict this sample and, therefore, this elevated prediction error is not unusual. 

StiKkntizcd Concentration Residual vs. Sample Leverage Plot (Sample Diagnostic) Figure 5.131 displays the studentized concentration residual versus sample leverage for the validation samples using a six-factor PLS model. Samples 1 and 3 are pure-component spectra and, therefore, it is reasonable tliat... 

Hopke, et al. (4) and Gaarenstroom, Perone, and Moyers (7) used the common factor analysis approach in their analyses of the Boston and Tucson area aerosol composition, respectively. In the Boston data, for 90 samples at a variety of sites, six common factors were identified that were interpreted as soil, sea salt, oil-fired power plants, motor vehicles, refuse incineration and an unknown manganese-selenium source. The six factors accounted for about 78 of the system variance. There was also a high unique factor for bromine that was interpreted to be fresh automobile exhaust. Large unique factors for antimony and selenium were found. These factors may possibly represent emission of volatile species whose concentrations do not oovary with other elements emitted by the same source. 

The difference can be seen from the following example. If there are six factors, one can perform a Plackett-Burman design with 8 experiments, containing six real and one dummy factor. Another possibility would be to perform the twelve experiment design that would contain five dummies. 

The decision to select a larger design with more experiments could depend on the statistical interpretation one would like to apply (see Section 3.4.7). If the same six factors are examined in a fractional factorial design,... 

As the number of factors increases, the economies of fractional replication become more evident. With six factors, a l/4 replicate of the 64 possible combinations is not unusual and a l/8 replicate of the 256 run eight-factor factorial is fairly common, Cochran and Cox [3] give a very extensive list of fractional factorial designs, including some in which factors are at three and four levels. 

A system consisting of a column and a cooler, produces a material characterized by density as a system response. The density of the observed product is affected by six factors X chlorine consumption X2 water consumption in the column X3 phleg-matizer consumption X4 temperature in column X5 level of liquid in column and X6 water consumption in cooler. The opinions of four researchers are given in Table 2.13. Check the concordance of the researchers opinions. 

The rank histogram shows that the sum of ranks does not change evenly, so that we can accept the solution to include the following four factors into the basic design of experiment X3, X1 X2, and X5. A more cautious approach to drawing conclusions suggests a more detailed check of all six factors in an active experiment for screening factors such as, the method of random balance. 

Which six factors characterize the operational risk associated with information technology and automation in pharmacies ... 

Table 1 tabulates literature values for acidity constants of seven amine-Ptn complexes with notations on the temperature, ionic strength, total Ptn concentration, method employed, conditions and other remarks, and the reference number. At least six factors enter into comparing determinations of a single complex. First is the purity of the complex under investigation. Because they rely on chemical shifts of an individual species, NMR methods are less dependent on purity than potentiometric titrations, which are interpreted on the basis of equivalents of added base. Rarely is the raw titration data published, but in one case it is evident from a plot of the data that the titration curve reveals up to about 10% impurity [7], Without knowing whether the impurities are acidic, basic, inert, or even forming during... 

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