Term of Award

Summer 2014

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Charles W. Champ

Committee Member 1

Broderick O. Oluyede

Committee Member 2

Daniel Linder

Abstract

The exponentially weighted moving average chart based on the sample generalized variance is studied under the independent multivariate normal model for the vector of quality measurements. The performance of the chart is based on an analysis of the chart's initial and steady-state run length distributions. The three methods that are commonly used to determinate run length distribution, simulation, the integral equation method, and the Markov chain approximation are discussed. The integral equation and Markov chain approaches are analytical methods that require a nu- merical method for determining the probability density and cumulative distribution functions describing the distribution of the sample generalized variance. Two meth- ods for determining numerically these functions are discussed. The equivalence of the integral equation and Markov chain methods is shown resulting in a new method for obtaining a Markov chain approximation of the chart. Some examples of the implementation of these methods are given using MATLAB.

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