Univariate and multivariate synthetic control charts for monitoring the process mean of skewed distributions
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Date
2010
Authors
Ali Atta, Abdu Mohammed
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Abstract
The most powerful tool in Statistical Quality Control (SQC) is the control chart.
Control charts are now widely accepted and used in industries. One of the recent
enhancements on the univariate Shewhart X and multivariate T2 charts is the
extension of these charts to their respective synthetic chart counterparts by
combining each of these charts with the conforming run length (CRL) chart. These
univariate X and multivariate T 2 synthetic charts assume that the underlying
process follows a normal distribution. However, in many real situations the normality
assumption may not hold. This thesis proposes two new synthetic control charts for
skewed populations, which are the univariate synthetic WV -X and the multivariate
synthetic WSD-T2 charts. The univariate synthetic WV-X chart is based on the
weighted variance method while the multivariate synthetic WSD-T 2 chart employs
the weighted standard deviation approach. These two new proposed synthetic charts
reduce to the univariate X and multivariate T 2 synthetic charts, when the underlying
distributions are univariate and multivariate normal, respectively. To compare the
performances of the two new proposed charts with all the existing charts for skewed
distributions, the false alarm and mean shift detection rates are computed. Overall,
the simulation results show that the proposed univariate synthetic WV -X chart and
multivariate synthetic WSD-T2 chart outperform their respective counterparts
found in the literature.