New Univariate Synthetic Double Sampling X And Multivariate Synthetic Double Sampling T2 Control Charts
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Date
2017-02
Authors
Lee, How Chinh
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
This thesis proposes a univariate synthetic double sampling X control chart
to monitor the mean of a univariate process and a multivariate synthetic double
sampling 2 T control chart for monitoring the mean vector of a multivariate process.
The proposed univariate chart integrates the conforming run length (CRL) chart and
the double sampling (DS) X chart, while the proposed multivariate chart combines
the CRL chart and the DS 2 T chart. Both the proposed univariate and multivariate
charts are superior to their basic counterparts, namely the synthetic X and DS X
charts for the univariate case, and the synthetic 2 T and DS 2 T charts for the
multivariate case, in terms of the average run length (ARL) and average number of
observations to signal (ANOS) performance criteria. ANOS is a more meaningful
performance criterion compared to the ARL for the variable sample size charts, such
as the proposed charts and the DS chart. This is because ANOS measures the actual
number of observations required before an out-of-control signal is issued by the chart.
Interpretation of a chart's performance based on ARL is complicated when a decision
about a chart's performance is made based on either the first sample only or both the
first and second samples. The proposed synthetic DS X chart is shown to
outperform its basic counterparts, i.e. the synthetic X and DS X charts. By
comparing the synthetic DS X chart with the exponentially weighted moving
average (EWMA) chart, the former provides a better performance than the latter, for
a larger range of mean shift sizes, compared with the synthetic X and DS X charts.
The synthetic DS X chart has a better performance than the EWMA chart for
detecting moderate and large mean shifts, while the latter overtakes the former for
detecting small shifts.
Description
Keywords
New univariate synthetic double sampling x , multivariate synthetic double sampling T2 control charts