Process monitoring and control with high-dimensional data
Creators: name: Kim, Sangahn
Publisher: name: No Publisher Supplied
Year: 2018

description: The increased accessibility of a large number of data streams makes it possible to use multivariate statistical process control (SPC) in various modern industries. However, as the number of quality characteristics and process parameters to be monitored increases such simultaneous monitoring becomes less sensitive to the out-of-control signals especially when only a few variables are responsible for abnormal situations or changes in the processes output. This dissertation proposes several efficient statistical process control methodologies for monitoring high-dimensional processes such as chemical production processes, semiconductor manufacturing processes and liquefied natural gas (LNG) processes. More specifically, we investigate and develop methodologies for monitoring the shifts in the means of the quality characteristics under sparsity. It is intended to detect these shifts as soon as they occur regardless of their magnitudes.  We first investigate approaches for monitoring high-dimensional processes with an application of the multistage process. Due to the properties of multistage processes such as variance propagation and the specific structure of correlation, monitoring such multistage processes becomes much more challenging. We introduce a fault diagnosis procedure-integrated SPC chart for monitoring a multistage process, especially with beta-distributed output variables by adopting a model-based approach. For fault diagnosis, we propose a partial regression-based variable selection (VS) approach to choose several “suspicious” variables that might be regarded as the ones causing out-of-control signals. This approach is effective and its performance is compared with other VS-based charts such as forward variable selection approach.   Second, we consider that some high-dimensional processes have grouped patterns of the data structure. In other words, the quality characteristics’ pattern can be grouped by the relevance or the correlation structure of these characteristics. Moreover, these processes would possibly shift by changes only in a few relevant quality characteristics. The multistage process is another example where the stages can be considered as groups and a few variables in a group may shift together. In this case, exploiting the grouped patterns would provide more advantages in the VS than choosing the variables individually. Therefore, we develop a sparse group variable selection approach to reflect the grouped behavior of the process shift. We modify the selection procedure appropriately to implement sparsity within a group and between groups. Extensive simulation studies are conducted to demonstrate the numerical performance of the proposed method.   Third, we consider the cases where quality characteristics (or process parameters) are strongly correlated and introduce small size of shifts. In complex modern industries, the highly correlated data structure is present in numerous applications such as monitoring spatially correlated data streams, surveillance of wafer surface and monitoring connected job-shop manufacturing processes in chemical plants. In such processes, the existing VS-based charts including the proposed partial regression based chart suffer from the detection of small process changes since the strong correlation often confuses the correct selection of the faulty variables. Therefore, we introduce a ridge penalized likelihood in order to improve the efficiency in monitoring processes when small process shifts occur in highly correlated data structures. Accurate probability distributions of the monitoring statistics under null and alternative hypotheses corresponding to in-control and out-of-control situations, respectively, are obtained. In addition, we investigate several theoretical properties of the proposed scheme and present further extensions of the proposed methods to other existing methods. We demonstrate the performance of the proposed chart theoretically and empirically.   Fourth, we investigate a new approach for change detection by utilizing the correlation information among variables. While a traditional multivariate exponentially weighted moving average (MEWMA) chart is an extension of univariate EWMA, we develop a generalized model for the MEWMA that uses appropriate non-diagonal elements in the smoothing matrix based on the correlation among variables. We offer the interpretation of the relationship between the correlation and the non-diagonal elements of the smoothing matrix. We also suggest an optimal design for a proposed method and compare the proposed chart fairly with existing EWMA-based charts.   Finally, we develop a new method for monitoring high-dimensional processes based on the Bayesian approach. The approach sequentially updates a posterior distribution of the process parameter of interest through the Bayesian rule. In particular, a sparsity promoting prior distribution of the parameter is applied properly under sparsity and is sequentially updated in online processing. A data-driven Bayesian hierarchical model enables the monitoring scheme to be effective to the detection of process shifts and improves the efficiency of the computational complexity in the high-dimensional processes. Comparisons with recently proposed methods for monitoring high-dimensional processes demonstrate the superiority of the proposed method in detecting small shifts. In addition, graphical presentations in tracking the process parameter provide information about decisions regarding whether a process needs to be adjusted before it triggers the alarm.