Theoretical and numerical investigations into the SPRT method for anomaly detection

The sequential probability ratio test developed by Wald is a powerful method of testing an alternative hypothesis against a null hypothesis. This makes the method applicable for anomaly detection, In this paper the method is used to detect a change of the standard deviation of a Gaussian distributed white noise signal. The false alarm probability, the alarm failure probability and the average time to alarm of the method, which are important parameters for anomaly detection, are determined by simulation and compared with theoretical results, Each of the three parameters is presented in dependence of the other two and the ratio of the standard deviation of the anomalous signal and that of the normal signal. Results show that the method is very well suited for anomaly detection, It can detect for example a 50 % change in standard deviation within I second with a false alarm and alarm failure rate of less than once per month.