Evaluation of some methods for statistical surveillance of an autoregressive process

Abstract

Statistical surveillance is used for fast and secure detection of a critical event in a monitored process. This paper studies the performance for AR(l) processes. Two often suggested methods for detection of a shift in the mean, the modified Shewhart and the residual method, are compared and evaluated. Further, comparisons are made with direct Shewhart and a likelihood ratio method. New evaluation measures, the probability for successful detection and the predictive value, are also applied together with the average run length and run length distributions. We conclude that neither the modified nor the residual methods is uniformly optimal. The residual method is, however, optimal for immediate detection, but has inferior properties otherwise. For many parameter setups, the modified method will give the better performance.