Apr-Jun.12 - the Nitie

The presence of autocorrelation in the processes gives
a profound effect on control charts developed for i.i.d
observations. When such an autocorrelation exists,
standard control charts may exhibit an increase in
the frequency of false alarms. There is an increased
likelihood that the data will exhibit autocorrelation in
systems where the process time is longer than the time
between samples collected.
Several researchers have examined control chart
behavior in the presence of autocorrelation. If process
measurements are autocorrelated, then standard
constructions of control charts will violate the
assumption that samples are independent. In-control
ARL is reduced due to the autocorrelation in the data;
moreover it also affects the behavior of the Shewhart
control chart at various shifts. A quality engineer
will search the assignable causes behind the more
number of the false alarms at different shifts but will
found nothing. This is how the autocorrelation in the
measured data affects the performance of the control
chart. The type 1 error rate for control charts is sensitive
to autocorrelated data; that is, control charts are subject
to increased false alarms and, hence, shorter Average
Run Lengths (ARLs). Even at low levels of correlation,
dramatic disturbances can occur in the chart properties.
In the industry, if there is autocorrelation, then the
autocorrelated data is normally distributed. The
autocorrelated data can be generated from a set of
uniformally distributed data with mean of 0 and
standard deviation of 1 with the help of the MATLAB.
The autocorrelated data is generated from the normally
distributed data. Figure 3 clearly shows that the 10,000
correlated numbers are distributed normally.
Figure 3 Distributions of 10,000 positively
autocorrelated numbers
When the successive observations are uncorrelated,
there is no memory in the data: previous observations do
randomly around the mean. In most of the applications
of control charts, it is assumed that the data exhibits this
kind of behavior. However, in actual practice, most data
sets show some form of serial correlation. In Figure 4,
successive negatively correlated data points are shown.
In negative correlation, the observation below the mean
tends to be followed by an observation that is larger
than the mean value, and vice versa. Thus the sequence
of observations exhibits alternating behavior.
Figure 2 shows the distribution of the 10,000
independent and identically distributed (i.i.d) random
numbers following the normal distribution.
Figure 4 Negatively correlated data
Figure 2 Distribution of the 10,000 i.i.d data
The data shown in Figure 5 is positively correlated.
In positive correlation, if the current observation is on
one side of the mean, the next observation will most
Vol. 36, No. 2, April-June, 2012
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