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17- (سيترجمها محمد)
Two-Level Fractional Factorial Designs
The number of experiments needed to study five or
more factors in a full factorial design is large, and to
determine the main effects and their interactions, a
fraction of the full design is often sufficient. These
are 2kr fractional factorial designs, where r ¼ 1,
2, . . . for the half, quarter, etc. fractions. An example
of a half-factorial design for five factors (251) is given
in Table 2 (the entire table). Note that the first four
columns are the same as the four factor, full-factorial
design, and the column for the fifth factor is constructed
by multiplying the first four columns together.
Methods for constructing such designs and their limitations
are described in many textbooks.[5–7]
18- (سيترجمها محمد)
Evidently, for the 251 design, the 16 triple and
higher interactions are not determined. In fact, they
are confounded with the calculated effects. Thus, the
estimate of the interaction between factors one and
two includes the triple interaction between the other
three factors. Because the latter is assumed negligible,
this does not usually matter.
(ستترجمها نسرين) 19 -
Menon et al. studied the formation of pellets by
fluid-bed granulation using this design.[8] The five factors
investigated were (X1), the binder concentration;
(X2), the method of introducing it (dry or solution);
(X3), the atomization pressure; (X4), the spray rate;
and (X5), the inlet temperature. Particle sizes of the
resulting particles are shown in Table 3.
20-
The coefficients of the model are calculated by linear
regression (the logarithm of the particle size was
used here) and then plotted as a cumulative distribution
of a normal plot (Fig. 2). The important coefficients
are those that are strongly positive or negative,
for example, the spray rate b4 and the interaction
between atomization pressure and inlet temperature b35.
Others not identified on the diagram are not considered
significant and could well be representative
mainly of experimental error. The equation can thus
be simplified to include only the important terms.
However, if interactions are included, their main
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