| To date, a significant amount of work for process control has focused on the analysis of continuous data for process monitoring and control. Many of the methods have been developed for determining changes in performance, and establishing limits on achievable control. In some processes, we want to analyze integer data such as the situation indicators. So far, little work has been done on establishing descriptive and quantitative tools for displaying or analyzing time series count data in the chemical process industries.; Time series count data is prevalent in political science and economics, but it can also be collected from process monitoring studies. For example, if we want to control the defect number occurring in paper production line, we will use time series count data. In Model Predictive Control (MPC) applications, we have m unconstrained manipulated variables and n controlled variables. Defining Degrees Of Freedom as m-n, we can monitor the process performance by analyzing this discrete valued quantity.; The purpose of this thesis is to develop and apply statistical methods for analyzing time series count data that arise in process monitoring. We will use Poisson autoregressive (PAR) models to deal with time series count data with non-negative value outputs, and Markov Chain model for time series count data with finite states. The Poisson conditional maximum likelihood estimation is used when regressors are determined. We also use the maximum likelihood estimation to estimate the probability transition matrix of a Markov Chain model, and provide the hypothesis tests to determine whether the DOF data are from a certain Markov Chain model. The models and estimators are applied to data on control loop status and Degrees Of Freedom data for Poisson regression model and Markov Chain model respectively. |
