Process monitoring in the chemical and other process industries has been of great practical importance. Early detection of faults is critical in avoiding product quality deterioration, equipment damage, and personal injury. The goal of this dissertation is to develop process monitoring schemes that can be applied to complex process systems. Neural networks have been a popular tool for modeling and pattern classification for monitoring of process systems. However, due to the prohibitive computational cost caused by high dimensionality and frequently changing operating conditions in batch processes, their applications have been difficult. The first part of this work tackles this problem by employing a polynomial-based data preprocessing step that greatly reduces the dimensionality of the neural network process model. The process measurements and manipulated variables go through a polynomial regression step and the polynomial coefficients, which are usually of far lower dimensionality than the original data, are used to build a neural network model to produce residuals for fault classification. Case studies show a significant reduction in neural model construction time and sometimes better classification results as well. The second part of this research investigates classification trees as a promising approach to fault detection and classification. It is found that the underlying principles of classification trees often result in complicated trees even for rather simple problems, and construction time can excessive for high dimensional problems. Fisher Discriminant Analysis (FDA), which features an optimal linear discrimination between different faults and projects original data on to perpendicular scores, is used as a dimensionality reduction tool. Classification trees use the scores to separate observations into different fault classes. A procedure identifies the order of FDA scores that results in a minimum tree cost as the optimal order. Comparisons to other popular multivariate statistical analysis based methods indicate that the new scheme exhibits better performance on a benchmarking problem.