Improved Fault Detection Using a Moving Window Generalized Likelihood Ratio Test

Process monitoring is essential for proper, productive, and safe operation of various chemical processes. Univariate process monitoring techniques are frequently used in process industries due to their simplicity and computational efficiency [1]. The Generalized Likelihood Ratio Test (GLRT) chart is a powerful fault detection technique that seeks to maximize the detection probability for a given false alarm rate [2].  For detecting shifts in the mean, where the residuals are assumed to follow a normal distribution, the GLRT statistic reduces to computing the norm of the residuals at every time instant [3]. In this work, we show that the performance of the GLRT chart can be further improved through its implementation in a moving window of lagged residuals.  In the moving window GLRT method, the detection statistic equals the norm of the residuals in that window, which is equivalent to applying a mean filter on the squares of the residuals. This means that a proper moving window length needs to be selected, which is similar to estimating the mean filter length in data filtering. Various fault detection evaluation metrics can be used to estimate the moving window length, which include the missed detection rate, false alarm rate, and average run length (ARL). An assessment of the moving window length on the performance of the moving window GLRT method showed that at larger window lengths, the missed detection rate and ARL decrease (which means more effective and faster detection, respectively), but the false alarm rate increases. This means that there is a trade-off between more effective detection and false alarms. Thus, a compromise needs to be made to achieve an acceptable performance with respect to the rate and speed of detection and false alarms when using the moving window GLRT method. The performance of the moving window GLRT method is also illustrated and compared to that of the conventional GLRT method using a simulated continuously stirred tank reactor (CSTR) example.

References

[1]      D. C. Montgomery, Introduction to Statistical Quality Control, 7th ed. Hoboken, NJ: John Wiley & Sons, 2013.
[2]      F. Harrou, M. N. Nounou, H. N. Nounou, and M. Madakyaru, “Statistical fault detection using PCA-based GLR hypothesis testing,” J. Loss Prev. Process Ind., vol. 26, no. 1, pp. 129–139, 2013.
[3]      M. R. Reynolds and J. Y. Lou, “An Evaluation of a GLR Control Chart for Monitoring the Process Mean,” J. Qual. Technol., vol. 42, no. 3, pp. 287–310, 2010.