Chaughule, Thorat - Statistical Analysis/Design of Experiments
increase at the same rate as the number of polynomial coefficients. For three factors, for
example, the design can be constructed as three blocks of four experiments consisting of
a full two-factor factorial design with the level of the third factor set at zero. The number
of experimental points (N) is defined by the expression N = 2k (k - 1) + C 0 , where k is the
number of variables and C 0 is the number of center points.
Advantage of the BBD is that it does not contain combinations for which all factors
are simultaneously at their highest or lowest levels. So these designs are useful in avoid-
ing experiments performed under extreme conditions, for which unsatisfactory results
might occur. Conversely, they are not to be used for situations in which the aim is to
know the responses at the extremes, that is, at the vertices of the cube. BBD for four and
five factors can be arranged in orthogonal blocks. Because of block orthogonality, the
second-order model can be augmented to include block effects without affecting the pa-
rameter estimates, that is, the effects themselves are orthogonal to the block effects. This
orthogonal blocking is a desirable property when the experiments have to be arranged
in blocks and the block effects are likely to be large (Box and Behnken, 1960).
The Box-Behnken is a good design for response surface methodology because it
permits:
- Estimation of the parameters of the quadratic model;
- Building of sequential designs;
- Detection of lack of fit of the model; and
- Use of blocks.
8.6.6. Evolutionary operation Approach
Evolutionary operation approach (EVOP) is used as an experimental strategy when
only two or three factors can be varied at a time, and only small changes in the factor
levels can be tolerated. As such, EVOP is a hybrid of on-line and off-line quality im-
provement techniques. Two-level factorial experiments around a center point are typi-
cally used. As operating conditions that lead to improved process characteristics are
identified, the experimental region is moved to explore around this new set of condi-
tions. This procedure is repeated until no further improvement is obtained (Mason,
2003 ).
However, certain risks are inherent due to exploring a limited experimental region
and a small number of factors. A consequence of the EVOP approach for process im-
provement is that many repeat test runs are needed at each set of factor–level combina-
tions. This large number of repeat tests is needed because factor levels can only be
changed by small amounts so that existing quality levels will not be seriously degraded
at some of the factor–level settings. Because of this requirement, there is a weak “signal”
(change in the response) relative to the “noise” (experimental error or process varia-
tion). This usually results in the need to collect many observations so that the standard
deviations of the statistics used to measure the effects are sufficiently small and statisti-
cally significant effects can be detected (Antony, 2003 & Montgomery, 2003).
8.6.7. Plackett-Burman design
Plackett-Burman design is used to determine the most influential factors on the
process and their levels. Plackett-Burman orthogonal designs (Plakett and Burman,