(176b) Fault Detection Using Multiscale Shewhart Charts: Algorithm and Applications

Fault detection is an important requirement for the safe and reliable operation of various processes. Control charts (such as the Shewhart chart, exponentially weighted moving average (EWMA) chart, and others) are among the most commonly used univariate fault detection methods in practice due to their simplicity and computational efficiency [1]. Most of these control charts, however, rely on the assumptions that the evaluated residuals are Gaussian, independent, and contain a moderate level of noise [2]. Violating any of these three assumptions can greatly degrade the effectiveness of these methods. Wavelet-based multiscale representation of data is a powerful data analysis tool that can help deal with these violations, since it can effectively separate noise from important features in the data and because the wavelet coefficients are closer to being Gaussian and independent at multiple scales [3].  Therefore, in this work, multiscale representation is utilized to improve the fault detection performance of the Shewhart chart (which is used here as an example of a univariate fault detection technique) over the conventional Shewhart chart, especially under violations of its main assumptions [4]. The developed multiscale Shewhart chart relies on decomposing the data at multiple scales, applying the Shewhart chart using the detail signals and the last scaled signal, and then applying the Shewhart chart again using the reconstructed signal in the time domain. The performance of the developed multiscale Shewhart chart is illustrated and compared to that of the conventional Shewhart chart using simulated examples at different levels of deviations from the main assumptions. Three different evaluation metrics are used in this comparison, which include the missed detection rate, false alarm rate, and average run length (ARL).  The results of these examples show that the developed multiscale Shewhart chart provides a reduction in the missed detection rate for all violations of the fundamental assumptions, while maintaining comparable false alarm rates and ARL values to those obtained using the conventional method.  The developed multiscale Shewhart chart was also applied using simulated data from a distillation column and genomic copy number data in order to further assess its applicability. The results clearly show the advantages of the developed multiscale Shewhart chart in both applications, which motivates the extension of the developed algorithm to other univariate and multivariate methods.

References

[1]      D. C. Montgomery, Introduction to Statistical Quality Control, 7th ed. Hoboken, NJ: John Wiley & Sons, 2013.
[2]      A. Cinar, A. Palazoglu, and F. Kayihan, Chemical Process Performance Evaluation, 1st ed. Boca Raton, FL: CRC Press, 2007.
[3]      R. Ganesan, T. K. Das, and V. Venkataraman, “Wavelet-based multiscale statistical process monitoring: A literature review,” IIE Trans., vol. 36, no. 9, pp. 787–806, Sep. 2004.
[4]      M. Z. Sheriff, F. Harrou, and M. Nounou, “Univariate process monitoring using multiscale Shewhart charts,” in 2014 International Conference on Control, Decision and Information Technologies (CoDIT), 2014, pp. 435–440.