ENBIS edition:14 location:Linz, Austria date:21-25 September 2014
Control charts are tools developed in statistical process monitoring (SPM) to identify when a process is out-of-control. When constructing control charts, one or more tuning parameters should be chosen to obtain the desired properties. For classical control charts, approaches for this are well documented, but for multivariate control charts this still remains an open field of research. Control charts for high-dimensional data, including those based on principal component analysis (PCA) are no exception, with more complex methods designed for time-dependent data being in particular need of further elaboration. We first provide an example based overview of classical PCA-based control charts and identify the current approaches to choose their tuning parameters. Based on that discussion, we will then show how violation of the basic assumptions w.r.t. the data (e.g. with respect to autocorrelation and/or stationarity) also violates the underlying assumptions of commonly used parameter selection approaches, resulting in poor monitoring performance. An example of this is the problem of specifying the control limits based on analytic expressions that can even fail in stationary scenarios. In the case of time-dependent data, those issues are even more accentuated, and identifying a model, even for data exhibiting normal operating conditions, can be a challenge. As a result, the user is often compelled to select the tuning parameters based on inefficient trial and error approaches. In our previous research into extensions of classical PCA, which was presented to ENBIS in 2013, we compared the performance of those methods while using manually selected parameters. In this follow-up we will highlight existing, but less well-known solutions to some of these parameter selection challenges when setting up the control charts, and propose solutions for others. By addressing such issues we intend to provide a more straightforward application of PCA-based control charts in research and in practice so that these methods may be more accessible to users.