Atta, Abdu Mohammed Ali
(2010)
Univariate And Multivariate Synthetic Control Charts
For Monitoring The Process Mean Of Skewed Distributions.
PhD thesis, Universiti Sains Malaysia.
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 T 2 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 T 2 charts. The univariate syntheticWV X chart is based on the
weighted variance method while the multivariate syntheticWSD 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 T 2 chart outperform their respective
counterparts found in the literature
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