Univariate And Multivariate Synthetic Control Charts For Monitoring The Process Mean Of Skewed Distributions - Atta, Abdu Mohammed Ali (2010)

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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