Control charts are widely used tools of
statistical quality control in industrial environments since its inception by
Shewart in 1920’s. The major function of control charting is to detect the
occurrences of assignable causes so that the necessary corrective action may be
taken before large quantity of non conforming product is manufactured. A survey
conducted by Saniga and Shirland (1977) shows that on continuous measurement
scale the control chart for averages dominates the use of any other control
chart technique. All control charts have a common structure. A plot of the
result of repeated sampling is made on a vertical scale against the number of
samples plotted horizontally. The center line of the chart represents a long
term average of the process statistic or its standard value. The upper control limit
(UCL) and Lower control limit (LCL) represent the boundaries of typical
statistic variation. The process call for adjustment if the points fall outside
the control limits. Departures from expected process behavior within the limits
(non random patterns on the chart) can be detected by using different run tests
for pattern recognition (Nelson (1985)). On using control charts two kinds of
errors may occur: over adjustment and under adjustment. Uncertainty of
inferences based on sampling statistic is the major cause for these errors. The
magnitude of the errors depends on the decision-making method. It is beneficial
that a control chart detect process change quickly so that the causes of any
undesirable changes can be identified and removed. It is also beneficial that
the rate of false alarms generated by the control chart be low in order to
maintain the confidence of process operations in the chart. Sampling cost will
be an issue for most of the applications, thus it is important that a control
chart be able to provide fast detection of process change and a low false alarm
rate with a reasonable rate of sampling. So the statistical performance of a
control chart is often evaluated by considering, for a given false alarm rate
and sampling rate, the expected time required by the chart to detect various
process changes. It has been found in recent years that the statistical
performance of control charts can be improved considerably by changing the rate
of sampling as a function of the data coming from the process. The basic idea
is that whenever there is an indication of a problem with the process the
sampling should be more intensive and less intensive when there is no
indication of a problem. There are many ways in which the sampling rate can be
varied as a function of process data. One of the ways is to vary the sampling interval:
a short sampling interval is used when there is a indication of a problem and a
long sampling interval is used when there is no indication of a problem. The
resulting variable Sampling interval (VSI) control charts have been studied
broadly (see, e.g., Reynolds et al (1988) ; Zee (1990), Runger and Pignatiello
(1991); Baxley (1996); and Reynolds (1996a, 1996b). 

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