Parallel Program
Bipartisan process improvement in polymer coating:
Combining system dynamics with statistical process control (SPC)
Nicholas C. Georgantzas * Fordham University at Lincoln Center ¢ New York, NY 10023-7471, USA
James S. Fraser ¢ Fordham University at Lincoln Center ¢ New York, NY 10023-7471, USA
Elvan Tugsuz ¢ Fordham University at Lincoln Center ¢ New York, NY 10023-7471, USA
Abstract
A firm’s end-product waste problem motivated us to investigate the structure
underlying a polymer coating process (PCP) by combining system dynamics
simulation modeling with statistical process control (SPC). Our bipartisan approach
proved to be rather powerful: not only it provides insight about the negative
feedback-loop structure between temperature distribution and polymer thickness
but also allows-assessing the potential effects of leverage points on the stability of
the polymer manufacturing process directly from process capability and control
charts. The new knowledge gained yields a dramatic improvement in the firm’s end-
product quality and productivity. Worth noting is our transforming of the heat
control equations—which correspond to the gelling operations of polymer foam and
paste, respectively—into semidifference approximations of heat conduction that can
be solved using standard Runge-Kutta methods. Consequently, our essay illustrates
how to effectively handle parabolic partial differential equations using conventional
system dynamics simulation software.
Introduction
Since the summer of 1994, we have been investigating the polymer coating process
of PCP, a firm competing in the global industry of polymer web processing. With a
workforce of ninety, the firm’s manufacturing facility employs a rather sophisticated
polymer foam and paste coating process. Its polymer leather products are marketed
to manufacturers of a whole range of consumer goods, including apparel and
accessories. Despite the potentially huge global market for artificial leather
products, however, the firm has remained rather small in its fledging industry,
partly because of its far from glamorous performance in end-product quality and
productivity. End-product thickness variation has been causing much waste in
output, ranging from 25 to 30 percent.
The manufacturing manager and engineers who work on the coating line agreed
to participate in a system dynamics modeling project to better understand how the
management system structure of the foam and paste coating process might be
causing the undesirable behavior observed in end-product thickness. Initial
discussions culminated into tangible output: a system dynamics simulation model of
the polymer coating process. The model allows tracking changes in the firm’s
coating line configuration, in terms of
(a) the gelling temperature distribution of foam and paste, and
(b) _ the polymer foam, paste and lining thickness.
The project investigates the firm’s end-product waste problem by combining
system dynamics simulation modeling with statistical process control (SPC) tools.
a a
System Dynamics '95 — Volume II
Fig. 1
Coating line configuration.
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This ‘bipartisan approach’ is powerful for not only it provides insight about the
negative feedback-loop structure between temperature distribution and material
thickness, but also allows assessing the potential effects of leverage points on the
stability of the polymer manufacturing process directly from process capability and
control charts. The new knowledge gained warrants a dramatic improvement in the
firm’s end-product quality and productivity.
Worth noting in this research is the transformation of heat control equations—
which correspond to the gelling processes of foam, and paste, respectively—into
semidifference approximations of heat conduction that can be solved using a
standard Runge-Kutta numerical method. Consequently, the essay illustrates how
to effectively handle parabolic partial differential equations of the form
ak aT (xt) AT (x,t)
Ox Ox Bie Ox
conventional system dynamics simulation. software.
Model Construction
Although improving quality—and thereby productivity (Deming, 1993)—is a
prudent goal for any firm, the true value added of the project lies in the benefit of
personal improvement through system dynamics simulation modeling. The real
model the CPC project participants worked on is the model of themselves. The
modeling process force clear thinking about PCP’s coating line process.
Building a model for PCP’s coating line configuration (Fig. 1) required first of all
a clear definition of every part of the process, which by itself is both useful and
educational. In addition, by repeated simulations, a better understanding of the
process is achieved, greatly improving the insight and developing the engineering
intuition of the project participants. Armed with our system dynamics model, PCP’s
quality and productivity problems are studied, the effect of individual variables
isolated, and sensitivity and stability problems explored. All these are hard, costly,
or virtually impossible to carry out in the real production process.
The objective of the quality and productivity improvement project is to reduce
the end-product waste of PCP. During the investigation, PCP’s president and CEO,
as well as the production manager, engineers and supervisory personnel of PCP
were invited to participate in the modeling process, and to contribute their own
understanding of how the coating line configuration actually works. This gave them
the opportunity to challenge their engineering intuition about quality improvement
options.
To achieve these objectives, the project incorporated a mix of
(a) prebuilt system dynamics models;
(b) deterministic and stochastic simulation experiments, in order to
-- capture participant knowledge about PCP’s coating line,
-- stimulate critical thinking among participants, and
- invite project and model ownership by participants; and
(c) statistical process control (SPC) charts.
Combining system dynamics simulation models with statistical process control
(SPC) tools helped the participants gain more knowledge about PCP’s sophisticated
coating process. The insight gained from the project warrants the desired
(Nakamura, 1991; Tadmor & Gogos, 1979) using
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System Dynamics '95 — Volume II
sd
Fig. 2
Tracking end-product thickness
through the coating line
configuration.
Initial y1_—yt
Hot y1
end-product thickness
y1 = foam thickness
y2 = foam + paste thickness
y3 = foam + paste + lining thickness
‘gain
OO
creep effect
Q coating [nitial y1_ scraping yl to oven 1}] Hot yi _ to press to rollers
(— ss Pressed y1 Cooling] Rollers
Q ) ®Msd
knife 1 hight Q
embossing
excess foam
pressure 23 3
knife step lining sd paste coating
oN
Cylinders fe cylinders Hot y3 to oven 2 Pressed y3_to press® y3 scraping to| paste
Ont
loss&
vm
creep effect gain
end product
knife 2 hight
laminating pressure
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excess paste
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C) knife step
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Fig. 3
The semidifference approximation for the space- and time-dependent
thermal conductivity exploits the negative feedback loop
between thickness and temperature.
(a) Foam temperature
" Tl I’ 2 13 3 ™4 1%
cyclePoint TO re) 4+ tt
Hot y1 k\cp
cycle dy
control volumes room T°C creep coefficient
creep effect
(b) Paste and foam temperature
T18" TR T2R" T2R 138" T3R T4R" T48
cyclePoint& TOR QB. ¢
Hot y3 k\cp8
cycle dy2
control volumes
\ o
J creep coefficient
oc i
room T°C LS
creep effect
(¢) Relationship between thickness and temperature
temperature thickness
System Dynamics '95 — Volume II
improvement of PCP’s end-product quality and productivity. The more PCP
participants felt that they own the model and the simulation results, the more eager
they became to implement the changes recommended by the model and the
simulation results. Alternatively put, PCP’s end-product waste is reduced, and its
production quality and productivity improve, only because the project participants
are now convinced that their intuition about improvement options is compatible
with the changes recommended by the model and the simulation results.
Model Structure
A fundamental difference between simulation modeling and other problem solving
methods lies in the source of the data. In simulation models, data are gathered from
a computer model as opposed to being gathered in the real world. The simulation
modeling project described here emphasized parameter estimation and simulation
of modified models which begun as simple open-loop models and increased in
complexityas-new feedback~loups’ were added ‘to represent the real production
constraints of PCP’ polymer coating line (Fig. 1).
Figure 2 and Fig. 3 show the system dynamics model which the PCP project
participants helped to build. The model tracks the polymer foam and paste
thickness throughout PCP’s actual coating line of Fig. 1. As originally anticipated,
the project run for a period of seven months, with two model revisions before a final
report was submitted to PCP with definite recommendations for quality and
productivity improvements.
The lower part of Fig. 2 details all the changes that occur in the material from
the initial polymer foam coating and scraping to polymer paste coating and lining to
the cooling cylinders and end-product output and inspection. The small diagram on
the top of Fig. 2 allows tracking the end-product thickness—the major quality
management concern and metric during this project.
Figure 3a and Fig. 3b detail the semidifference approximation used for the
space- and time-dependent thermal conductivity of the polymer foam and paste,
respectively, which exploits the negative feedback loop between polymer thickness
and temperature of Fig. 3c. The higher the polymer temperature, the thicker the
foam and paste will gradually become but, the rate of change in their temperature
distribution will also be gradually annihilated by their thickness.
Model Behavior
Once several prebuilt system dynamics models were revised, and the participants’
input captured and mapped, a set of simulation experiments followed, like those in
Fig. 4 and Fig. 5. The objective of each experiment was to challenge intuition about
quality and productivity improvement options at PCP’s polymer coating process.
The project also. incorporated SPC control charts (Fig. 6). Statistical process
control can assess whether or not quality problems exist in production. Control
charts either suggest that corrective action is needed to improve quality or give
assurance that a process is producing satisfactory quality. Using data from the
computer model, the control charts of Fig. 6 were constructed for (a) the range and
(b) the mean of end-product thickness. Ten samples of size n=10 were gathered from
the model of Fig. 2 and Fig. 3, with random variation (sd = standard deviation) on in
coating thickness as well as in raw material (RM). The range and mean values that
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(a) variability sources lining *, J paste coating
Fig. 4
The effect of variability (sd)
on the gelling temperature (T°C)
distribution of foam and paste.
*. pressure
200
TC 100
(b) without variability
thickness (mm)
200
TC 100
(¢) with variability
1.0 foam
thickness (mm) 0.5 300
0.0
t (sec)
EN
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(a) variability sources ining *. " paste coating
Fig. 5 :
The effect of variability (sd)
on end-product thickness,
foam density ..............00 foam coating
paste density > *, pressure
(b) 2.204 end-product thickness sum Without variability
—__— with variability
1.255
(c¢) 1.354 end-product thickness umn Without variability
with variability
-- Specification UL = 1.3 mm-f- Sore ae) Boon ccc
1.255
4 Specification LL = 1.2 mm--#--
t (sec)
1.15
0.00 75.00
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Fig. 6
Statistical process control (SPC) charts
given the end-product specifications
(10 samples of size n = 10).
(a)
(>)
Control chart for range (3-sigma limits)
| | | |
0 2.0 alo 6.0 8.0 10.0
Sample
Control chart for mean (3-sigma limits)
| | | | |
0 2.0 4.0 6.0 8.0 10.0
Sample
gin
UCL=1.27
Center=1.25
LCL=1.23
System Dynamics '95 — Volume II
fall above the upper control limit (UCL) or below the lower control limit (LCL) show
how PCP’s polymer coating process gets out of control. Therefore, corrective action
was required to reduce the variability that produced these values.
This recommendation, which is consistent with the process capability chart of
Fig. 5c, shows the type of recommendation that should be anticipated throughout a
bipartisan process improvement that combines system dynamics with statistical
process control (SPC). Upon completion of the project, a final report was submitted
to document the investigation, with specific and concrete action recommendations
for quality and productivity improvement in PCP’s coating line.
Conclusion
In the last thirty years, the computer evolution has turn simulation modeling into a
prelude to organizational learning. Engaging in simulation modeling for learning
now helps PCP compete by creating new knowledge about the system structure of
its production-process. Creating-this new knowledge will require capturing aspects
of this structure that may be neither easy to observe nor easy to measure. The
proposed project will use the system dynamics methodology to simulation modeling
because of the broad yet coherent structure for modeling this methodology provides
(Forrester, 1961).
The more PCP participants felt that they own the model and the simulation
results, the more eager they became to implement the changes recommended by the
model and the simulation results. Alternatively put, PCP’s end-product waste is
reduced, and its production quality and productivity improve, only because the
project participants are now convinced that their intuition about improvement
options is compatible with the changes recommended by the model and the
simulation results.
Together, the project team and the PCP participants bring together a unique
combination of skills and knowledge that is a prerequisite for effective modeling. On
the one hand, the PCP participants have already shown that they can provide a
solid base of operating knowledge, including factory knowledge of PCP’s
manufacturing process, and industry knowledge of the technology used in PCP’s
production. The system dynamics model of Fig. 2 and Fig. 3, as well as the attached
simulation results, could not have been created without their timely and effective
cooperation.
References
Deming, W.E. (1993). The New Economics. Cambridge, MA: MIT/CAES.
Forrester, J.W. (1961). Industrial Dynamics. Cambridge, MA: MIT Press.
Nakamura, S. (1991). Applied Numerical Methods with Software. Englewood Cliffs,
NJ: Prentice Hall.
Tadmor, Z. & Gogos, C.G. (1979). Principles of Polymer Processing. New York, NY:
Wiley.
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