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302 3:6 Economical Experimentation via ‘Lean Design’
eight-run analysis. It may be noted that to do this, some caution is to be exercised to
avoid any possible block effect associated with the sequential data collection.

19.5 ILLUSTRATIVE EXAMPLE

For an illustration of such an approach, consider the frequently cited filtration plant
6
example on pp. 424--429 of Box et al. In this example, various factors were suggested
for an investigation of the cycle time at a filtration plant: source of water supply (x 1 ),
original of raw material (x 2 ), level of temperature (x 3 ), presence of recycling (x 4 ), rate
of addition of caustic soda (x 5 ), type of filter cloth (x 6 ), and length of hold-up time
(x 7 ). The experimental design used was 2 7−4 , as shown in Table 19.2, in which the
response values are also shown. The results of the analysis are as follows, where l j ,
j = 1, 2,..., 7, are, respectively, values of E j , j = 1, 2,..., 7, each confounded with
interaction effects:

l 1 = E 1 + E 24 + E 35 + E 67 =−10.875,

l 2 = E 2 + E 14 + E 36 + E 57 =−2.775,
l 3 = E 3 + E 15 + E 26 + E 47 =−16.575,
l 4 = E 4 + E 12 + E 37 + E 56 = 3.175,
l 5 = E 5 + E 13 + E 27 + E 46 =−22.825,

l 6 = E 6 + E 17 + E 23 + E 45 =−3.425,
l 7 = E 7 + E 16 + E 25 + E 34 = 0.525.

Based on a Pareto analysis, it was concluded that the important effects were l 5 ,
l 1 and l 3 , and attention was focused on x 5 , x 1 and x 3 as prime candidates for factors
crucial to the filtration time variation. Another 2 7−4 experiment based on the fold-over
technique finally identified x 5 and x 1 as the factors that really mattered.
During the initial phase of the investigation, it was already suspected by the person
responsible that out of the seven factors, perhaps only one or two, at most three, factors
would be found important. That being the case, if there had to be a constraint on the
investigationsuchastime,thenleandesignwouldbeextremelyhelpful.Supposethere
was only time for six experimental runs before the first results of the investigation were
due; the investigator could use his best judgment to name two factors least likely to
be important to the process. These factors would still be included in the experimental
work, but now only six instead of eight observations would need to be taken in the
first instance: in this way a 25% reduction in experimentation time was possible prior
to the first interim report on the investigation.
Consider an L 6 2 7−4 lean design comprising the first six runs listed in Table 19.2;
that is to say two response values, y 7 and y 8 , are absent. Assume that x 6 and x 7 are
considered by the investigator to be least important in the filtration process, so that l 6
and l 7 can be set to zero. Then, using the reasoning explained earlier, y 7 and y 8 can be
estimated by equations (19.5) and (19.6) to be 76.6 and 44.5, respectively. With these
values, the l j values, j = 1, 2,..., 5, can be computed.