- 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.

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

Relationship between yield, time and temperature.

a.

b.

DOE in Time and Temperature.

Learning is Incremental.

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