Strategy


Since predictive capability of 83% for "Breaking Strength" and of 89% for "Elongation at Break" of such Linear Predictive Models have been considered as sufficient, we have defined the "Strategy" for the purpose of the study:

Increase of parameter "Breaking Strength" of the product, keeping parameter "Elongation at Break" constant, if possible.

To find out these conditions we have calculated the Response Surfaces of the two PLS1 models obtained.
In the Figures 11, 12 and 13, below, we included the response surfaces of the two models, which have been obtained by keeping the two Viscose variables
(NH4CL and Temp Visc.) constant - as they are more complex to modify in the practice - and by modifying the four bath variables - easier to set.

Fig 11 - 2D Response Surface Plot of the Models "Breaking Strength" and
"Elongation at Break" Variables (H2SO41BDF, ZnSO41BDF)
Fig 12 - 2D Response Surface Plot of the Models "Breaking Strength" and
"Elongation at Break" Variabili (H2SO41BDF, H2SO42BDF)
Fig 13 - 2D Response Surface Plot of the Models "Breaking Strength" and
"Elongation at Break" Variables (H2SO41BDF, Densità1BDF)

In all Figures 11, 12 and 13 the coloured upper bar displays the range of the Values of "Breaking Strength" (in the upper part of the figure) and of "Elongation at Break" (in the lower part).
The coloured lines in the diagram represent constant value lines of the two parameters (i.e. Breaking Strength and Elongation at Break).
These diagrams have enabled us to define the corrective actions on the process settings, in order to keep the "Breaking Strength" of the Product at the max values of its standard field, without modifying the parameter "Elongation at Break".
In particular:

1 - Fig. 11 shows that the simultaneous increase of ZnSO41BDF and
H2SO41BDF (working point which moves along the diagonal of
the diagram) results in the increase of the "Breaking Strength", while
the "Elongation at Break" practically does not vary (constant value
lines of this parameter along the diagonals).
2 - Fig. 12 shows that the increase of H2SO41BDF, with
H2SO42BDF on a constant value (working point which moves
along a line parallel to X axis of the diagram), in practice affects the
"Breaking Strength" very little (nearly horizontal constant value
lines) while the "Elongation at Break" tends to increase.
3 - Fig. 13 shows that simultaneous increase of 1BDFDensity and
H2SO41BDF (working point which moves along the diagonal of
the diagram) in practice affects the "Breaking Strength" and the
"Elongation at Break" very little (constant value lines of the two
parameters along the diagonals).


Therefore, in order to have Breaking Strength at a high value, you must modify ZnSO41BDF and H2SO41BDF simultaneously (increasing them) and you should act as follows:

a
- On the diagram H2SO42BDF and H2SO41BDF of
Elongation at Break (Fig. 12) select the value of H2SO41BDF,
which guarantees an acceptable elongation, moving along a horizontal
line of working of variable H2SO42BDF (e.g. 0,99 in diagrams in
Fig. 12).
b
- On the basis of the value of H2SO41BDF found, select, on
diagrams ZnSO41BDF and H2SO41BDF (Fig. 11), the value
of ZnSO41BDF to obtain the max Breaking Strength.
c
- In this way also the Density of the First Spinning Bath will tend to
increase, though without any consequence; in fact, on the diagrams
"Density and H2SO41BDF" (Fig. 13) the density does not
affect either Breaking Strength or Elongation at Break.


In terms of "Measurement" of parameter "Breaking Strength" of the Product we have employed the Linear Predictive Model PLS1 obtained, which leaves us uncertain in only 17% of cases, and we have postponed the development - using the variables already found - of a Neural Net which might further improve the prediction degree by detecting the possible non-linearities of the process.