Fault diagnosis in multivariate statistical process monitoring - Mostert, Andre George (Department of Statistical Sciences, 2022)
The application of multivariate statistical process monitoring (MSPM) methods has gained considerable momentum over the last couple of decades, especially in the processing industry for achieving higher throughput at sustainable rates, reducing safety related events and minimizing potential environmental impacts. Multivariate process deviations occur when the relationships amongst many process characteristics are different from the expected. The fault detection ability of methods such as principal component analysis (PCA) and process monitoring has been reported in literature and demonstrated in selective practical applications. However, the methodologies employed to diagnose the reason for the identified multivariate process faults have not gained the anticipated traction in practice. One explanation for this might be that the current diagnostic approaches attempt to rank process variables according to their individual contribution to process faults. However, the lack of these approaches to correctly identify the variables responsible for the process deviation is well researched and communicated in literature. Specifically, these approaches suffer from a phenomenon known as fault smearing. In this research it is argued, using several illustrations, that the objective of assigning individual importance rankings to process variables is not appropriate in a multivariate setting. A new methodology is introduced for performing fault diagnosis in multivariate process monitoring. More specifically, a multivariate diagnostic method is proposed that ranks variable pairs as opposed to individual variables. For PCA based MSPM, a novel fault diagnosis method is developed that decomposes the fault identification statistics into a sum of parts, with each part representing the contribution of a specific variable pair. An approach is also developed to quantify the statistical significance of each pairwise contribution. In addition, it is illustrated how the pairwise contributions can be analysed further to obtain an individual importance ranking of the process variables. Two methodologies are developed that can be applied to calculate the individual ranking following the pairwise contributions analysis. However, it is advised that the individual rankings should be interpreted together with the pairwise contributions. The application of this new approach to PCA based MSPM and fault diagnosis is illustrated using a simulated data set.