#### Term of Award

Spring 2010

#### 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 Champ

#### Committee Member 1

Broderick O. Oluyede

#### Committee Member 2

Patricia Humphrey

#### Abstract

The commonly recommended charts for monitoring the mean vector are affected by a shift in the covariance matrix. As in the univariate case, a chart for monitoring for a change in the covariance matrix should be examined first before examining the chart used to monitor for a change in the mean vector. One such chart is the one that plots the generalized sample variance lSl verses the sample number t. We propose to study charts based on the statistics V = l(n - 1) Σ₀-¹ Sl¹/̳p̳ and U = 1n (l (n-1) Σ₀-¹Sl¹/̳p̳), where n is the sample size and Σ₀ is the in-control value of the process covariance matrix Σ. In particular, we will study the Shewhart V and U charts supplemented with runs rules. Also, we examine the methods that are useful in studying the run length properties of the cumulative sum (CUSUM) U charts. Further, we will study the effect that estimating Σ₀ has on the performance of these charts. Guidance will be given for designing the Shewhart charts with runs rules with illustrative examples.

#### Recommended Citation

Parham, Kellen M., "Monitoring for a Shift in a Process Covariance Matrix Using the Generalized Variance" (2010). *Electronic Theses & Dissertations*. 663.

https://digitalcommons.georgiasouthern.edu/etd/663