A brief survey of different statistics for detecting multiplicative faults in multivariate statistical process monitoring

The recent explosion in different statistics for fault detection has meant that the practitioner is faced with the unenviable job of determining which to use in a given situation. Thus, this paper seeks to investigate the different test statistics that can be applied to detect multiplicative faults for multivariate Gaussian-distributed processes in order to provide the practitioner with some guidance. Three groups of methods are: traditional methods (e.g., T2 and Q statistics) and their extensions; the Wishart distribution-based methods; and those methods that are created in information and communication fields to describe the characteristics of measurement variance and covariance (e.g., mutual information and Kullback-Leibler divergence). Then, greater details on their interconnections and comparisons are presented and their performance for detecting multiplicative faults is evaluated and demonstrated using numerical simulations.

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