Monitoring for a Shift in a Process Covariance Matrix Using the Generalized Variance

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.

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2010

Author dc:creator

• Parham, Kellen M.

Contributors dc:contributor

• Broderick O. Oluyede
• Patricia Humphrey

• ETD
• Average run length
• Cumulative sum charts
• Independent samples
• Integral equations
• Markov chain
• Multivariate normal distribution
• Shewhart charts
• Mathematical statistics
• Graphic methods

Repository record dc:identifier

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

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1663