Date of Award
Spring 1999
Project Type
Dissertation
Program or Major
Mathematics
Degree Name
Doctor of Philosophy
First Advisor
Kevin M Short
Abstract
Dynamic analysis involves describing how a process changes over time. Applications of this type of analysis can be implemented in industrial settings in order to control manufacturing processes and recognize when they have changed significantly. The primary focus of this work is to construct methods to detect the onset of periodic behavior in a process which is being monitored using a scheme where data is sampled unevenly.
Techniques that can be used to identify statistically significant periodic structure using the periodogram will be reviewed and developed. The statistical properties of the periodogram for unevenly sampled data will be calculated. These statistics reveal that standard methods applied to randomly sampled data give incorrect results, especially for small sample sizes. These standard tests are not designed specifically for data collected at random times. Monte Carlo methods are used to adjust the critical values used for testing the significance of spectral peaks. The effectiveness of the tests for determining periodic behavior are compared using the standard critical values and the adjusted values. The adapted test is then extended into a control chart which will signal when periodic behavior enters into an irregularly sampled process.
The new methods are applied to an industrial example from a silicon wafer coating process. The data was collected irregularly and the underlying dynamics of the process were investigated. Interesting periodic behavior was uncovered in the analysis.
When data has complicated oscillatory behavior, methods of nonlinear dynamic analysis can be used to make predictions. A new toroidal reconstruction technique is developed for data that appears to be driven predominantly by two or three frequencies. Comparisons between the new method and a standard time delay reconstruction utilizing nonlinear dynamic forecasting methods are made using simulated and real-world data collected from a vibrating warehouse air duct.
Recommended Citation
McSweeney, Laura Ann, "Dynamic analysis of unevenly sampled data with applications to statistical process control" (1999). Doctoral Dissertations. 2079.
https://scholars.unh.edu/dissertation/2079