Statistical process monitoring is a key requirement for many industrial processes. Many of these processes utilize Principal Component Analysis (PCA) in order to carry out statistical process monitoring due to its computational simplicity. Two fault detection charts that are commonly used with the PCA method are the Hotelling T2and Q statistics. Although these charts are reasonably able to detect most shifts in the process mean, they may be unable to accurately detect other process faults, such as shifts in the process variance. Hypothesis testing methods such as the Generalized Likelihood Ratio (GLR) chart have been developed in order to detect different types of deviations from normal operating conditions, i.e., process faults. Although, GLR charts have shown superior performance in terms of fault detection compared to other existing techniques, literature has only examined the performance of a PCA-based GLR chart designed to detect shifts in the mean. Through a simulated synthetic example, this work evaluates the performance of PCA-based GLR charts designed to independently detect a shift in the mean, independently detect a shift in the variance, and simultaneously detect shifts in the mean and/or variance. The results show that in order to detect a shift in the mean or a shift in the variance, the GLR charts designed to independently detect either type of fault need to be implemented in parallel as they provide significantly lower missed detection rates, than a GLR chart designed to detect shifts in both the process mean and variance simultaneously. The GLR chart designed to simultaneously detect both a shift in the mean and variance does not perform as well as the other GLR charts, since two parameters (both the mean and variance) need to be estimated for this method while maximizing the GLR statistic, as opposed to just a single parameter for the other GLR charts. The practical applicability of the PCA-based GLR charts is demonstrated through the well-known benchmark Tennessee Eastman process, and through a case where autocorrelation is present in the data. Therefore, in order to detect shifts in the mean and/or variance, we recommend parallel implementation of the GLR charts designed to independently detect shifts in the mean, and independently detect shifts in the variance Parallel implementation of these two GLR charts aids with fault classification as well. This work also discusses the importance of selecting an appropriate window length of previous data to be used when computing the maximum likelihood estimates (MLEs) and maximizing the GLR statistic, keeping all fault detection criteria in mind in order to ensure that the desired fault detection results are obtained.
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