25 2 quarter-fraction

As an example, a seven factor quarter fraction factorial design would be written as seen in equation below... 

Now let us try to generate a quarter-fraction factorial design for 6 factors. In this design one fourth of the experiments of a fiill factorial design are... 

The design is called a 2 design. In the same way quarter-fraction factorial designs N — eighth-fraction factorial designs N — 2 ),... can be derived, which... 

For the determination of antimony, the digestion efficiency of particulate matter, collected on Whatman 41 cellulose filters, was evaluated by means of radiotracer experiments [6], A quantitative recovery was obtained using 8 ml sulfuric acid and 4 ml hydrogen peroxide, when applied to a quarter fraction of the filter. For the dissolution of residual silicates 0.5 to 4 ml of hydrofluoric acid were added, which were later on evaporated. After digestion the solution was filtered if needed and diluted appropriately. 

We take the full factorial design with the number of variables required and select half the experiments. Each half fraction can in turn be divided into quarter fractions. Whereas for a given number of variables at 2 levels there is only one possible full factorial design, there can be many possible fractional factorial designs and they are not at all equivalent to one another. We saw in paragraph II.C.3 that the 2 design consists of 16 experiments representing all possible combinations of... 

If the design is a quarter fraction (2 ) there is no simple method for choosing the two independent generators, as one must consider also the length of the product of the 2 generators. 

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. ... 

The resolution of an experiment shows the maimer in which the confounding in a given experiment occurs. The resolution is denoted using a subscripted Roman numeral, for example, 2fy is a quarter fraction of a 2 -factorial experiment with a resolution of IV. There are three common resolutions ... 

Example 4.6 Confounding Pattern for a Quarter-Fractional Factorial Example... 

Determine the confounding pattern for a quarter-fractional factorial experiment, where 1 = 2, p = 2, and k = 5. Select a suitable set of generators. 

Quarter of reactor Fractional conversion of A leaving quarter Fraction of total heat removed in quarter... 

It was decided that four parameters or factors would cover the range of service conditions. Upper dwell time and temperatures were tested at three different values, lower dwell time at two different values and with two different environments. The number of combinations of conditions is therefore 36. A quarter fractional nine trial design necessarily has some confounding and loss of information compared to a full factorial design, but retains the analysis of main effects and some synergies or interactions between factors. 

Ore samples are analyzed for %w/w Ni. A jaw crusher is used to break the original ore sample into smaller pieces that are then sieved into 5 size fractions. A portion of each fraction is reduced in size using a disk mill and samples taken for analysis by coning and quartering. The effect of particle size on the determination of %w/w Ni is evaluated. 

The desugarization by-product is normally sold as a low value molasses. Pulse method systems also produce a relatively high value betaine-rich (at least 50% on soHds) fraction. The concentrated betaine-rich by-product is used as a custom animal feed, whose European markets are well estabUshed and may provide a future opportunity in the U.S. feed industry. Beet sugar molasses contains from 3 to 6% betaine, by weight, about three-quarters of which may be recoverable as a potential by-product ( 40 50% purity). 

Epichlorohydrin [106-89-8] M 92.5, b 115.5 , n 1.438, d 1.180. Distd at atmospheric pressure, heated on a steam bath with one-quarter its weight of CaO, then decanted and fractionally distd. 

Since the early 1990s the United States has imported more oil than it has produced for its own use. And, as the nuclear option became frozen, coal has become the chief source for gcirerating electricity, which itself accounts for about 35 percent of the energy sector. In 1997, 52 percent of electricity produced in the United States was generated from coal and in other recent years the fraction has approached 56 percent. Since the United States accounts for one—quarter of total world energy usage, the increase in coal use in the United States alone has a significant... 

---