Fault isolation

When multivariate observations are monitored, detection of a fault is merely the first step of the process. Knowledge of the existence of the fault is not particularly informative in high-dimensional settings. Thus, the field of fault isolation has developed to identify those variables that have been affected by the fault. Variables affected by a fault are termed shifted variables, regardless of the nature of the fault. In this chapter, we will first present some pitfalls to be avoided when performing fault isolation and also illustrate the importance of isolating important variables associated with the fault, which can also improve the speed of fault detection. Traditional approaches to removing variables and recalculating monitoring statistics, such as and Q, to isolate the variables will be presented. Next, more modern approaches using variable selection techniques, which typically involve penalized regression, will be described. Both prior approaches work in unsupervised settings where the types of faults that will be observed cannot be anticipated in advance. In settings where a process is very well-studied, a catalogue of data associated with multiple types of faults may exist, so supervised classification methods may be used. We close with some metrics that may be used to assess the performance of fault isolation methods along with two detailed case studies for illustration.