(122c) A Review of Generalized Likelihood Ratio Based Monitoring Techniques

Fault detection is an integral part of process monitoring, which is essential for the safe and economical operation of many processes. Statistical hypothesis testing methods, such as the Generalized Likelihood Ratio chart have been utilized in order to provide improved detection results, by using the concepts of likelihood ratio and maximum estimation of their hyper-parameters in order to accurately distinguish between normal and faulty operating conditions [1,2].

Unfortunately, most of the currently available fault detection methods in literature utilize a GLR chart designed specifically to detect only shifts in the mean. However, in practice an industrial process can experience a wide variety of fault types, i.e., shifts in the variance, and drifts. The GLR charts designed specifically for different scenarios, i.e., to detect shifts in the mean, and to detect shifts in the variance, have shown that they are capable of efficiently detecting the different classes of faults, and that they provide extremely low missed detection rates, and out-of-control average run length (ARL₁) values even for small fault magnitudes [3,4].

Exponential Likelihood Ratio (ELR) charts were developed in order to enhance the performance of the GLR chart by incorporating exponential weights in order to obtain a more accurate estimate of the current state of the process [5]. Like the GLR charts, the ELR charts can also be designed to detect different classes of faults. However, the performance of the ELR charts are tied to the choice of its smoothing parameter, and therefore one objective of this work is to provide an algorithm to select the appropriate value of the smoothing parameter for monitoring purposes.

Other exponentially weighted GLR techniques exist [6]. Unfortunately a comparison and review of the performance of all likelihood-based monitoring techniques is unavailable in literature. Therefore, another objective of this work is to compare the performance of all likelihood-based monitoring techniques, in order to conclude which chart provides the best monitoring performance. Illustrative examples, such as the Tennessee Eastman Process will be utilized in order to evaluate the performances of the different techniques.

References

[1] M.R. Reynolds, J.Y. Lou, An Evaluation of a GLR Control Chart for Monitoring the Process Mean, J. Qual. Technol. 42 (2010) 287–310.

[2] D.C. Montgomery, G.C. Runger, Applied Statistics and Probability for Engineers, 5th ed., John Wiley & Sons, Inc., Hoboken, NJ, 2011.

[3] M.R. Reynolds Jr., J. Lou, A GLR control chart for monitoring the process variance, in: W.P. Lenz HJ., Schmid W. (Ed.), Front. Stat. Qual. Control 10, 2012: pp. 3–17. doi:https://doi.org/10.1007/978-3-7908-2846-7.

[4] M.R. Reynolds, J. Lou, J. Lee, S.A.I. Wang, The Design of GLR Control Charts for Monitoring the Process Mean and Variance, 45 (2013) 34–60.

[5] J. Zhang, C. Zou, Z. Wang, A control chart based on likelihood ratio test for monitoring process mean and variability, Qual. Reliab. Eng. Int. 26 (2010) 63–73. doi:10.1002/qre.1036.

[6] M.-F. Harkat, M. Mansouri, M. Nounou, H. Nounou, Enhanced data validation strategy of air quality monitoring network, Environ. Res. 160 (2018). doi:https://doi.org/10.1016/j.envres.2017.09.023.