Finding heterogeneity in a multivariate process

When a manufacturing process runs in normal conditions, its performance usually displays consistency that may be observed over time. This consistency in a process is called process homogeneity. Disruption of process homogeneity leads to process heterogeneity, which usually indicates abnormality. Detection of heterogeneity in a process enables one to isolate heterogeneous segments and investigate the assignable causes for the existing heterogeneity and obtain knowledge about the potential abnormality.; A plethora of classical statistical methods have been developed for homogeneity segmentation in a process with low volumes of observations and variables. However, for a process with a large numbers of variables and observations, these methods are limited. This research suggests that heterogeneity in a multivariate process may be found using data mining techniques, such as tree-based learners.; This work first studies the heterogeneity detection in a multivariate process with dozens of variables and hundreds of observations. Generally, only a small number of variables are responsible for the changes in a process. The proposed approach uses a supervised learner to identify these variables. The supervised learner is realized by predicting the time when a particular observation from the process variables is obtained. This approach is demonstrated by simulated examples and is shown to have better performance than the classical methods.; Supervised learners are also useful for applications characterized by batches, such as chemical processes. The heterogeneity of a batch process is concerned with the similarity of the batches. To address this problem, a particular supervised learner generates measures of similarity between pair-wise batches. An unsupervised learner explores homogeneity of the batches based on this similarity. In addition, the supervised learner identifies the subset of variables that contribute to the heterogeneity in the batches. This method is illustrated using a real world data set.; Finally, given a homogenous batch set, this research attempts to determine whether an unknown batch is consistent with the given set, which is usually obtained from normal operations. The proposed scheme combines discrete wavelet decomposition and principal component analysis to summarize batch characteristics. A real data set, along with simulated faults, is used to validate this work.