Download Recognition of Control Chart Patterns Using Self Organization Models

Journ al of Scientific & Industrial Research
Vol . 60, November 200 I , pp 860-862
Recognition of Control Chart Patterns Using Self Organization Models
J Srini vas •• M Ananda Rao and G Rambabu
Deparment of Mechanical Engineering, Andhra University, Yisakhapatnam 530 003
Received: 08 May 2001; accepted: 20 August 2001
The study proposes the use of self organizing neural networks for accurate and speedy detection of control chart pattern s in
order to achieve tight control of the process and ensuring good product qu ality. Control charts used in statisti ca l process control
can exhibit six principal types of patterns. Apart from the normal patterns , all other patterns indicate abnormalit ies in th e process.
which mu st be corrected to bring the process under control. Hence, accurate identification of control chart pattern is essential in
modern industry. Unlike conventional tool s that require a prior knowledge of the problem, the network class ifies in a pure
intuitive manner. Further the network is noise-tolerant. The training and classificatio n results of the neiwork are presented.
Introduction
Present strategy of recognition of patterns in signal
identification and image processing requires knowledgebased software. One of such pattern recognition problem
is the identification of industrial control charts, where it
is frequently necessary to monitor the process within the
control limits . Statistical Process Control (SPC) makes
use of control charts to access whether a particular
process is functioning correctly. In 1924, Walte r
Shewhart designed the first control chart and gave a
rationale for its use in process monitoring and control.
Critical process variables are to be periodically sa mpled
and average values of each sample is plotted on a mean
control chart. Abnormaliti es in the process can be
identified as unu sual developments in the control charts.
Based on the nature of the variation in the control chart,
basically six main types of patterns have been identifi ed.
These are normal , upward sh ift, downward shift ,
increasing trend, decreasing trend and cyclic. Correct
identification of these patterns is important to achieve
earl y detection of potential problems and maintaining
the quality of the process under observation .
Wh en a process is operatin g normally i.e., its
co ntrol chart shows a normal patte rn , its variables
fl uctuate within a range. All other pattern s indicate th at
the process is abnormal. There are numerous sc hemes
in the identification of control chart patterns, which can
be divided broadly into two types:
*Author for correspondence
( i)
By the use of statistical classification and
heuristic methods 1 and
(ii)
By the use of neural network s.
For automatic identification o f control c hart
patterns, many neural network s 2· 4 were e mplo yed.
Supervised neura l network s can be succ essfu ll y
employed but these ty pes of network s cannot be easily
retrained to identify new pattern s. T he network has to
be trained again from starting with both original trainin g
data and new-patterns to be identified. This class ical
stability-plasti city dilemma can be overcome by usin g
self-organi sing neural networks havin g an expandab le
layer of class neurons 5 . After training, if additional new
input patterns are required to be learned, they will , first
of all, be tested against the establi shed class neurons. If
they can be acco mm odated in th e e neurons with out
degrading the information already encoded in them, then
they will be learn ed by the neurons. Ot herwi se, new class
of neurons will be created to cater for th ese addit ional
new input vectors, so that th ey can be a part of th e
kn owledge encoded in the neural network, whil e not
affecting the already stored class ifi cation inform ati on.
This capability of incre mental learn ing is a desirabl e
feature of an on-line classifier required for rapid detect ion
of abnormal process behaviour.
In thi s paper, a competiti ve lea rning algorithm 6 is
used for learn ing th e netwo rk. wh ich is app li ed to
process-control problem.
X61
SRINIVAS et al.: RECOGNITION OF CONTROL CHART PAlTERNS
Outputs (pattern classes)
-Normal
-~==~~====~~~~
O~.
0.6
Cydic
0.-4
0.2
°f---~--~--~--~Ar~
-0.2
-0.04
---.J
-0.6 ~---------
(a)
--Increaoing
trend
'--Decreasing
trend
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Inputs I, ( Process mean)
Figure I-Present
Kohonen's
neural network topology
Network
o t----r---~.L--
Sketch of the present network is presented in the
Figure 1. The network consists of two layers, the input
layer and the output layer. The neurons of the two layers
are fully connected. In addition, each neuron of the output
layer is connected laterally to indicate lateral inhibition.
Input pattern (l) is processed through neurons of
input layer after normalization.
The connection weights
must also be normalized. The products of input vector
and the weights of an output node give the output of that
node. Output is calculated for all the nodes of output
layer. The output having the highest value is the winner.
Training
is based on a 'winner
take all' strategy.
Therefore, weights corresponding
to the output node Wi;
with maximum output (0) are updated according to the
J
Eq.(l).
wnew.] . = W0 ld -I . + at]
- W0 ld ,j .) ,
... (I)
where a is learning rate, which varies from 0 to I and
controls the rate of learning. An a== I means that it learns
a new example as soon as it is presented. It, however,
forgets all previous examples of that class. Similarly, a==0
means that the network does not learn at all and it
classifies new examples based on previous experiences
only. The number of input units depends on required
resolution of the input patterns. Output units are equal
to the desired number of classes. The network can be
initialized to any value of weights and an initial value of
a is kept close to I. It can be reduced gradually as the
network
learning
progresses.
After satisfactory
classification
a value of a=O can be set.
Identification
of Patterns
The network is presented with the control chart
patterns of a process and is expected to organize itself to
.0.1
-02
.0.3
~~~r---\-1
(b)
--
Upward sI>ft
--
Downward
shift
0.8
0.6
0.4
0.2
0f---~---r----r--~~~
-0.2
-04
j
.0.6
...J
'------------
( C)
Figure 2-
Six basic control chart patterns
classify the input patterns according to their trends. Using
appropriate
mathematical
equations I, analytically
generates
the six-basic
control chart patterns.
The
parameters like process mean, standard deviation are
predefined.
The classification
is carried out purely
intuitively by the network without any prior knowledge
of attributes like number of zero crossings. Three sets of
each type of control-chart
are generated with a simple
program and all these values are normalized
with
corresponding
Euclidian norm. The normalized
mean
values as a function of sample size are plotted randomly
and are shown for all the six basic patterns in Figure 2.
Present network has ten input nodes to accept the
sampled data for ten different samples. The initial value
of learning rate has been set to 0.9. The network
converged to six control chart patterns as soon as at least
one example
from each representative
group was
presented. The corresponding connection weights of the
network after learning are shown in Figure 3.
From Figure 3, it can be noticed that weight vectors
are following inputs very accurately. Several trials have
J SCI IND RES VOL 60 NOVEMBER 2001
862
--cyclic
-+-lncreasm.. trend
- - Upshift
-downshift
Table 2-Ability of the network to identify new patterns
Sl No.
l_ _ _ _
-0.4
-0.6
.L__ _ _ _ _ _ _ __ _ __..J
2
Experiment
number
Pattern
Output
winning
node
3
Cyclic
2
2
Upw ard shift
5
______.
Figure 3- Patterns captured in.connection weights
Table !-Output of the network for new problem
Normalized output
Output No.
0.6400
0.9990
0.0360
0.4830
0.2887
Pattern 3
(Increasi ng
trend)
0.2348
0.0370
0.8859
0.5527
0.6459
Pattern 4
(decreasing
trend)
0.6043
0.4830
0.5500
1.070
0. 5480
Pattern 5
( pward
shift)
0.0504
0.0442
0.8859
0.5214
1.0000
Pattern 6
{down wa rd
shift)
1.000
0.6404
0.0671
0.6043
0.8353
0.4467
0.3368
0.566
0.3773
0.258
Pattern I
(Normal)
Pattern 2
(Cycli c)
5
0.2580
0.4467
0.3736
0.5662
0.1634
6
1.0000
I
2
3
4
been conducted to test the robustness of the network for
convergence. The network classified the sample values
of new problems, i.e., sample values at different location s
of time (in control chart equations) accurately. Table I
shows normalized output of network for different patterns
for a definite sample value set. As evident from Table I,
appropriate output nodes are noticed to be c lear winners
for all the patterns. Network performed similarly for other
examples presented to it.
To test whether the present network has an ability
to di scover a new pattern the pre-calculated sampled
values are presented at two different times. Results of
the identification of new patterns are shown in the
Table 2. Two of the basic control charts viz., up-shift
and cyclic patterns are presented as new patterns and
the network has classified them appropriately.
The training and classification are found to be stabl e
even when the data contains di sturbances (noi se). The
sample values measured at manufacturing sites, contain
inaccuracies . Network is able to di stingui sh between
noi se and a new pattern and diagnose correctly the data
with noi se as the new pattern . Significant limitation of
the present network is that the number of output nodes
determines the maximum number of clas e . Network is
not able to create a new class on its o wn, wh en all
available class ifications are occupied by previous input
patterns.
Conclusions
For control chart pattern classification, se lforganising neural network model has been utilized. Based
on the Euclidian di stance-firin g ru le, the netw o rk
classified the patterns very accurate ly. Th is network is
highly noise-tol erant. Thi s is very desirab le property
when plant-data is available.
References
2
3
4
5
6
Evans J R & Lindsay W M, Computlnd Eng, 14( 1988) 335.
Guo Y & Dooley K J, lnt 1 Prod Res, 30( 1992) 1655 .
Guh R S & Hsieh Y C, Comput lnd Eng, 36( 1999) 97.
Chang S I & Aw C I, lnt 1 Prod Res, 34 ( 1996) 2265 .
Mukherj ee A, 1 Com put Civil Eng, ASCE, 14 ( 1997) 74.
Ko ho ne n J, Self organizing associative memory (SpringerVerlag, New York) 1988.