A Comparison of Different Statistics for Detecting Multiplicative Faults in Multivariate Statistics-Based Fault Detection Approaches

The explosion of different fault detection (FD) statistics in multivariate statistics-based FD approaches has meant that the practitioner is faced with the unenviable job of determining which to use in a given circumstance. Moreover, compared to extensive investigations on additive faults, the performance of commonly used FD statistics for detecting multiplicative faults has not been holistically evaluated. Therefore, this paper seeks to investigate the different statistics that can be applied to detect multiplicative faults in order to provide users and practitioners in the FD field with guidance to select an appropriate method. The considered statistics are broadly classified into three groups: traditional methods (e.g. T
²
-statistic) and their extensions; the Wishart distribution-based methods; and those methods created in the information and communication fields to describe the measurement variance and covariance (e.g. Kullback-Leibler divergence). These three groups are compared by considering the required probability distributions, interconnections, and detection performance for multiplicative faults. Using simulated data from numerical examples and the Tennessee Eastman benchmark process, the theoretical results are validated, and the applicability of multivariate statistics-based FD methods incorporating all considered statistics for detecting multiplicative faults is examined at the end of this paper.