A control chart pattern recognition system using a statistical ...

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J.-H. Yang, M.-S. Yang / Computers & Industrial Engineering 48 (2005) 205–221
Fig. 7. Diagram of the correlation coefficient recognition system.
On the other hand, unnatural patterns, such as upward (downward) shift and upward (downward)
trend, etc. may incur out-of-control signals during the pattern length nZ30. We can see this
phenomenon from the ARL values shown in Table 1 of Section 1. The ARL values will drop down from
370 to 6 when the mean m increases from 0 to 2. We know that the smaller ARL exhibits out-of-control
signal more often, and Fig. 6 is created with x(t)Zn(t)Cdt of Eq. (5) where d is selected from 0.05 to
0.12. According to ARL shown in Table 1, it is quite possible for Shewhart control chart to have out-ofcontrol
signals for upward shift and trend patterns. These out-of-control signals are actually occurred at
nZ46, 48 and 49 in Fig. 6. In fact, some out-of-control signals will be also occurred in Fig. 8. Of course,
if an out-of-control signal is issued in Shewhart control chart, we stop the process and check the causes
and then remove them. If an unnatural cause can be detected and removed, such as upward shift or trend,
the model will become x(t)Zn(t), i.e. a normal pattern. However, it may be difficult for detecting such
unnatural patterns using the Shewhart control chart because ARL will decrease when a mean m increases.
This is the point that a control chart pattern recogniser is useful for recognizing unnatural patterns in
control charts. Thus, the main idea of the proposed correlation coefficient method is that, if we do not
have enough evidence to classify an input pattern as an unnatural pattern, even though it has a maximum
correlation coefficient value to reference patterns, we still wait and take it as a normal pattern. The
diagram of our recognition system is shown in Fig. 7.
Because the statistical correlation coefficient r has a constraint with the range in the closed interval
[K1,1], the threshold h can be used as a criterion what the similarity degree is enough for the recognition
of an unnatural pattern. The pattern length for generating an unnatural control chart pattern and sample
numbers in our simulations are chosen with nZ30 and NZ200. The moving window for the recognition
of control charts uses a window size 30. For the normal control chart pattern, we take the sample number
with NZ1000. Based on a threshold h, unless there exists sufficiently unnatural pattern evidence,
we regard it as a normal and wait for more pattern information. According to the recommendation in
Section 2, we choose hZ0.5 in our simulations. We implement 1000 runs for each pattern and then
calculate its average accuracy as shown in Table 2.
We mention that these testing samples are also simulated using the inner-product technique proposed
by Al-Ghanim and Ludeman (1997). There are almost the same average accuracy as our approach when
hZ0.4 in Table 2 for recognizing upward trend, downward trend, cyclic and systematic patterns.
However, if we add upward shift and downward shift patterns, then their recognition average accuracy