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Chimica Oggi - Chemistry Today
- vol. 34(2) March/April 2016
of combinations of time and temperature throughout the
experimental space indicated in figure 5 and by statistically
analyzing the resulting data and dependence of yield on
time and temperature we have no gaps in our knowledge.
Analysing the resulting data with multiple regression (2) yields
the 3-d surface and contour plot depicted in figure 5, and with
this knowledge we can see that the best place to operate
is time of 500 minutes and temperature of 550
o
C. Further
improvement is implied if we go to a lower time and a higher
temperature, but an additional cycle of experimentation
would be needed to achieve this gain in a reliable manner.
LEARNING IS INCREMENTAL
Figure 7 illustrates that we typically start with data or a theory
which is analysed to help assess our situation or theory which
typically leads to more questions requiring new data to be
collected to provide answers (3).
If we have a large number of factors and utilize OFAT
approaches we may perform many iterations or cycles of
learning, sometimes a product or process may come back
to us from production for additional cycles of learning to
fix a product or process issue that would not occur if we
were able to develop and transfer products and processes
with a better understanding. Classical DOE methods as
developed by Fisher, refined by Finney and industrialised by
Box will reduce the total number of learning cycles relative
to OFAT, and increase the predictability of R&D. Modern
advances in DOE such as Definitive Screening by Jones and
Nachtsheim (4) may further reduce the number of cycles of
learning.
OFAT approaches frequently lead to sub-optimal solutions. This
is because OFAT assumes the effect of one factor is the same
at each level of the other factors, i.e. that factors do not
interact. Unfortunately, in practice, factors frequently interact,
and the chances of two or more factors interacting increases
the greater the number of factors investigated and the wider
the range over which factors are varied.
The 3-d plot and contour diagram in figure 5 illustrate the
interactive effect of time and temperature on yield with the
ridge effect that runs from time, temperature combinations
of (1200, 528) with a yield of 56% to (900, 536) with a yield
of 61% to (500,550) with a yield of over 65%. The effect
of this interaction (or ridge) is that the best setting for
temperature chosen by OFAT depends upon the value of
time. For example if time is fixed at 1000 the best setting of
temperature is 534 resulting in a yield of slightly more than
60%. Whereas, as we have already seen if time is fixed at 500
the best setting of temperature is 550 resulting in a yield of
slightly more than 65%. In the presence of such interactive
effects of factors on a response, the solution identified by
OFAT depends on your starting point and it is only by chance
that the global optima is determined. In our case OFAT failed
to find the true optima because it assumed the two factors
act independently on yield.
DOE provides the most efficient and effective way of
investigating relationships between factors and responses
when the factors have interactive effects on the responses.
One DOE appropriate for investigating the effects of time
and temperature on yield with which to find the optimum
yield is a 3x3 factorial design given in Figure 6. This is a 3x3
grid of points in time by temperature with three additional
replicates of the centre point to give a baseline for noise
or uncontrolled variation. These twelve rows in the resulting
data table indicated in figure 6 give a balanced distribution
Figure 5.
Relationship between yield, time and temperature.
a.
b.
Figure 6.
DOE in Time and Temperature.
Figure 7.
Learning is Incremental.
1...,22,23,24,25,26,27,28,29,30,31 33,34,35,36,37,38,39,40,41,42,...68
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