DoE / Taguchi





Interactions - a surface plot view

The effect of an interaction can be clearly seen by plotting the model equation on a 3D surface plot.  If we have a model of the type:

                                                            y = K + a1C + a2T

- i.e. no interaction term - then the resulting surface plot would be of the following form:


Here, y is the yield, C is the % concentration and T is the temperature.  We can see that, as we increase both C and T, the yield also increases.  We can also see that the increase in the yield for a given increase in T is independent of the value of C.  This gives the parallel straight lines on the surface which describe yield vs. temperature (T).  The practical outcome of this is that we would be correct to choose the high values of both C and T to obtain the maximum yield.

If, however, we have a model equation of the type:

                                                                     y = K + a1C + a2T + a3CT

- i.e. there is an interaction term (CT) - then the surface plot could look completely different, depending on the size of the interaction.  From a practical perspective, the worst case would be where the interaction is large and negative, which would give a surface plot of the following form:


Here we can see that the expected yield has been significantly reduced at the high values of C and T.  If the interaction is large enough then the yield could actually be pushed lower. 

From the above plot we can see that the optimum operating point is actually where T is high, but C is low.

Detecting the presence of such an interaction is difficult enough with 2 factors: as the number of factors increases it becomes impossible without the use of DoE methods.