Bayesian Networks
for the Injection Molding Industry
Introduction
Thank you for taking a moment to learn about this
project. As part of my doctoral work at
Shear Splay
It appears shear splay is a molding defect that is difficult
to accurately diagnose and quickly solve.
There are many factors that have complex relationships with one another
that make predicting shear splay even tougher.
Figure 1 shows a predictive, shear splay model with 38 variables. They are color coded by where they fall in
product development and by the type of information they provide. Although some variables may not be included
in this model, it does capture of a majority of the critical factors related to
shear splay. This problem serves as
starting point from which other injection molding defects can be modeled. With a few modifications this predictive
model can be used as a diagnostic or monitoring tool.
Example
To avoid biasing participants of this project, an example
[not related to shear splay] will be used to illustrate the potential of a
Bayesian network. Consider the simple
model in Figure 2 as a stripped-down version of a scenario in product
development. Imagine the manager of a
program is deciding how to handle a variety of newly awarded work, so that the
deadline is met. Two causes that influence
the ability to meet the deadline are the number of engineering changes (ECs)
and the level of experience of the designer.
Generally, as the number of engineering changes increases and the
experience of a designer decreases, the probability of meeting a deadline
diminishes. In turn, one measure the
manager uses as an indicator for the expected number of engineering changes is
the familiarity of the product.
Typically, unfamiliar designs (and materials) mean more engineering
changes. Product familiarity also
influences the manager’s assignment of certain products to certain
designers. Experienced designers are
usually best suited to handle those never-been-seen-before products.
In most cases, a good manager understands these
relationships and handles the situation appropriately. But what if all experienced designers are already
being utilized or they are on vacation and several unfamiliar designs arrive
that demand a very short launch (a not too unlikely scenario)? More importantly, the work is from a
customer that your company has been courting for some time. Knowing the likelihood of being on-time is
of utmost importance. A Bayesian
network supports the decisions of the manager by providing quantitative
knowledge in a series of what-if scenarios.
Consider scenario A in Figure 2 as the normal operating
conditions of a company. For example,
50% of the products handled by the company are familiar, while an average of
81% of the deadlines are on-time. Consider
scenario B as the situation described earlier.
An unfamiliar product in the hands of a novice designer increases the
number of engineering changes and decreases the ability to meet the deadline by
13%. However, if the manager can free
up an experienced designer, the timing returns to near normal operating
conditions as shown in scenario C. The
best-case scenario shown in scenario D raises the likelihood of being on-time
to 93%. Here, the Bayesian network
relieves the manager’s uncertainty by confirming his/her belief and supports
his/her decision.
Expertise Needed
You may be wondering where the probabilities in a Bayesian
network are acquired or how they are calculated. Although the answer is simple, it is quite difficult to
achieve. Data often come from two
sources 1) literature, such as historical records, equations and guidelines and
2) experts (i.e. interviews, surveys, monitoring). The data are obtained according to tables that make up all
combinations of every possible scenario.
As shown in Figure 4, the previous simple example required 24
probabilities. For example, the 0.85
probability within the table for # of ECs is an average response to the
following question: “Given that the product is familiar, what is the likelihood
that there are zero engineering changes?” (P(x) is the probability of being in state
X).
It is easy to recognize that as the number of variables is
increased and/or the number of categories of a variable is increased, the size
of the probability table grows rapidly.
In the case of the shear splay model, special attention has been paid to
balance precision and accuracy with the time required to gather the
probabilities. However, it still
requires approximately 872 probabilities, of which 284 are needed from
experts. The remaining probabilities
will be collected through flow simulation software and interpolation. In an effort to speed up the collection of the
284 probabilities, an interactive software program was created. Should you choose to participate, the
electronic survey should take between 45 and 100 minutes, depending upon the
breadth of your expertise.
Incentive
A predictive model for shear splay strives to capture a high
level of human reasoning and incorporate technical relationships that can only
be attained with your help. As I stated
earlier, the greater the expertise, the more powerful the results become. I wish I could afford to pay you for your
time. Unfortunately, the best thing I
can offer is a copy of this work when it is completed. As you can imagine, the applications are
numerous and the potential is great. In
fact, you may already be thinking of a situation at your company right
now. Hopefully, this work when
completed can arm you with the information you need to build a network specific
to your company’s situation.
Even if you are unable to complete the survey or can only
answer portions of it, your knowledge will be greatly appreciated. I thank you for your time and look forward
to your input.
Sincerely,
Jason S. Trahan
Cell: 269.760.9335
Fax: 269.276.3353
E-mail: jason.trahan@wmich.edu