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Virtual-DOE,
Data Mining and Artificial Neural Networks
By
Thomas
Pyzdek
March 1999
As beneficial and productive
as design of experiments can be, the process of conducting them has its
drawbacks. The workplace, be it a factory, a retail establishment or an
office, is designed around a routine. The routine is the "real work"
that must be done to generate the sales which, in turn, produce the revenues
that keep the enterprise in existence. Experimenting, by its very nature,
means disrupting the routine. Important things are changed to determine
what effect they have on various important metrics. Often, these effects
are unpleasant; that’s why they weren’t changed in the first
place! The routine was often established to steer a comfortable course
that avoids the disruption and waste that results from making changes.
The problem is, unless
we change things we can never improve. Six Sigma generates as much improvement
by changing things as it does by reducing variability. It’s part
of the Six Sigma paradox mentioned in the first chapter.
In this article we present
a way of conducting "virtual" experiments using existing data
and artificial neural network (neural net) software. Neural nets are popular
because they have a proven track record in many data mining and decision-support
applications. Neural nets are a class of very powerful, general purpose
tools readily applied to prediction, classification, and clustering. They
have been applied across a broad range of industries from predicting financial
series to diagnosing medical conditions, from identifying clusters of
valuable customers to identifying fraudulent credit card transactions,
from recognizing numbers written on checks to predicting failure rates
of engines. In this section we explore only the application of neural
nets to design of experiments for Six Sigma, but this merely scratches
the surface of the potential applications of neural nets for quality and
performance improvement.
Neural networks use a
digital computer to model the neural connections in human brains. When
used in well-defined domains, their ability to generalize and learn from
data mimics our ability to learn from experience. However, there is a
drawback. Unlike a well-planned and executed DOE, a neural network does
not provide an explicit mathematical model of the process. It is possible,
however, to include various transformed variables to "help"
the neural net if one has a model in mind. For example, in addition to
feeding the neural net X1 and X2 raw, one could
include transformations, higher-order polynomial and interaction terms,
etc. as inputs to the neural network. Still, for the most part, neural
networks must be approached as black boxes with mysterious internal workings,
much like the mystery of the human mind it is designed to imitate.
BUILDING
A NEURAL NET FOR VIRTUAL-DOE
All companies record important
data, some in well-designed data warehouses, some in file drawers. This
data represents potential value to the Six Sigma team. It contains information
that can be used to evaluate process performance. If the data include
information on process settings, for example, they may be matched up to
identify possible cause-and-effect relationships and point the direction
for improvement. The activity of sifting through a database for useful
information is known as data mining. The process works as follows:
- Create a detailed inventory
of data available throughout the organization. The IS department may
already have compiled this information.
- Determine the variables
which apply to the process being improved and for which historical data
exist.
- Using a subset of the
data which include the most extreme values, train the neural net to
recognize relationships between patterns in the independent variables
and patterns in the dependent variables.
- Validate and test the
neural net’s predictive capacity with the remaining data.
- Perform experimental
designs as you would on a real process. However, instead of making changes
to the actual process, make changes to the "virtual process"
as modeled by the neural net.
- Once the sequential
application of designed experiments has been completed using the neural
net model, use the settings from the neural net as a starting point
for conducting experiments on the actual process. If the results of
experimenting confirm the results from the neural net you can reduce
sample sizes and move quickly along the path discovered by the virtual-DOE
process.
It can be seen that the
entire virtual experimentation process helps answer the question "Where
are we?" It is important to recognize that neural net experiments
are not the same as live experiments, they are only simulations. However,
the cost of doing them is minimal compared with live experiments and the
process of identifying input and output variables, deciding at which levels
to test these variable, etc. will bear fruit when the team moves on to
the real thing. Also, virtual experiments allow a great deal more "what
if?" analysis, which may stimulate creative thinking from team members.
Example
of Building a Neural Net Model
The data in Table 1 are
from the solder process described above. Data were not gathered for a
designed experiment, but were merely collected during the operation of
the process. Variable B represents the circuit board preheat time in seconds.
Variable D represents the distance from the preheat element in centimeters.
The data were used to train and validate a neural net.
Table 1:
Raw Data Used to Build a Neural Net Model
A
simple neural net was built to analyze the above data, as shown in Figure
1.
Figure
1: A Neural Net Model
The neural net was trained
using the above data producing the model shown in Figure 2.
Figure
2: Neural Net Model for Solder Process Data
It is interesting to compare
the neural net model with the response surface model (RSM) produced by
classical DOE methods. The RSM is shown in Figure 3.
Figure
3: Response Surface from Designed Experiment
In the RSM the zero point
for factor B was 45 seconds, zero for factor D was 22.5 cm. You can see
that the surface described by the neural net is somewhat different than
the one modeled earlier using DOE [using response surface methods]. However,
both models direct the B and D settings to similar levels and both make
similar predictions for the defect rate.
Neural net software allows
"what if" analysis, as shown in Figure 4. By using What If?
you can conduct virtual DOE by designing proper experiments just as you
would design real world experiments. The inputs are fed into the neural
net, and the outputs from the neural net are analyzed just as you would
analyze the results of real experiments.
Figure
4: What If? Analysis Using the Neural Net Model
This article is based
on an excerpt from The Complete Guide to Six Sigma, Quality Publishing,
LLC, Scheduled for publication in the Summer, 1999.
Notes:
Berry, Michael J.A. and
Linoff, Gordon, Data Mining Techniques: for marketing, sales, and customer
support, New York: John Wiley & Sons, 1997.
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