A proposed variable sampling interval synthetic X control chart
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Date
2014
Authors
Lei Yong, Lee
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Abstract
The usual practice in the use of a control chart to monitor a process is to take
samples from the process with fixed sampling interval (FSI). However, based on
several findings, the variable sampling interval (VSI) control charts are substantially
more efficient than the traditional fixed sampling interval (FSI) control charts. In this
research, a synthetic X control chart with the variable sampling interval (VSI)
feature is proposed for monitoring shifts in the process mean. The VSI synthetic X
chart integrates the VSI X chart and the VSI conforming run length (CRL) chart.
The proposed VSI synthetic X chart is evaluated using the average time to signal
(ATS) criterion. The optimal charting parameters of the proposed chart are obtained
by minimizing the out-of-control ATS for a desired shift size, for sample sizes, n = 3,
5, 7 and 9. A simulation model will be used to verify the results of the VSI synthetic
X chart. Comparisons are made between the VSI synthetic X chart and the
existing X , synthetic X , VSI X and EWMA X charts, in terms of ATS. The
results show that the VSI synthetic X chart outperforms the X , synthetic X and
VSI X charts for almost all sizes of shifts, but all these charts have equal
performances for very large shifts. While the EWMA X chart prevails for small
shifts compared with the other X type charts, the VSI synthetic X chart surpasses
the EWMA X chart for detecting moderate and large shifts. An illustrative example
is presented to explain the application of the VSI synthetic X chart. In addition,
suggestions for further research will be discussed