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Using
Data Mining and Knowledge Discovery With SPC
By Thomas
Pyzdek, author of The
Complete Guide to Six Sigma
Introduction
When we find ourselves
with an out of control process, the logical question is, "why?".
Much of the SPC literature would have us immediately begin to search for
special causes of variation. Indeed, the term "special cause"
is defined as something that manifests itself by out of control points
on a control chart. However, before you rush into the workplace it often
pays to spend a little more time sifting through your data to see if you
can find the reasons for those outliers.
Injection
Molding Example
A company manufactured
ABS plastic parts for an automotive supplier. One of the critical quality
characteristics was the load it took to break the parts by application
of tension. The load was measured in pounds. A control chart of the test
data is shown in Figure 1.
Figure
1: X-bar and Sigma Chart of Pull to Failure
It is clear that this
process is out of control with respect to both averages and standard deviations.
In fact, it is so erratic that one has great difficulty in identifying
where to begin the search for assignable causes. What can be done?
Knowledge
Discovery
At this point it is often
worthwhile to shift gears and change the viewpoint from analysis to knowledge
discovery. In knowledge discovery we let the data talk to us. The idea
is to look at the data in different ways to see if there are any patterns
that can guide us to new understanding of the process. With modern data
warehouses this task is made much easier than it was in the past. Quality
analysts are often able to learn a great deal by mining their company's
information gold mine for ideas and answers.
For the case at hand,
the data warehouse also included information about processes and failure
modes. The analyst first examined the breaking strength by process and
failure mode using a boxplot (Figure 2).
Figure
2: Breaking Strength by Process and Failure Mode
A boxplot, also called
a box and whiskers plot, contains a huge amount of information. It simultaneously
gives a picture of the central tendency (the dark bar in the middle of
the box is the median), the spread (the "whiskers" mark the
largest and smallest non-extreme values), the shape of the distribution
(the distance between the median and the largest or smallest values, the
symmetry of the middle 50% as indicated by the box), and a test for outliers
(indicated with a *) or extreme outliers (indicated with a circle). By
displaying multiple boxplots on a single chart we can easily compare all
of these characteristics for multiple causes. This boxplot shows that
most process have comparable averages, but the variance of some processes
is highly erratic. He decided that Snap-in assemblies were probably a
low priority item for starting process improvement because this process
exhibits relative stability and an acceptably high average. The most promising
candidates for starting process improvement appear to be
- Sonic welding and screwing,
failure mode C6.
- Sonic welding and gluing
with failure mode C1 or C6, or Screwing and Gluing with failure mode
C1.
The analyst should now
place control charts on these four processes and follow them closely.
If time and resources do not permit four control charts, the analyst should
start with Sonic welding and screwing, failure mode C6. A control chart
of existing data (used to create the boxplot) is shown in Figure 3.
Figure
3: X-Bar Chart of Breaking Strength for Sonic Welding and Screwing Process:
Failure Mode C6
An interesting place to
start the investigation would be to identify the possible reasons why
jobs 14-16 were below the lower control limit. Theories could provide
the basis for a statistical design of experiments (DOE).
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