Process Monitoring ROC Curve for Evaluating Dynamic Screening Methods

In practice, we often need to sequentially monitor the performance of individual subjects or processes, so that interventions can be made in a timely manner to avoid unpleasant consequences (e.g., strokes or airplane crashes) once the longitudinal patterns of their performance variables deviate significantly from the regular patterns of well-functioning subjects or processes. Some statistical methods are available to handle this dynamic screening (DS) problem. Because the performance of the DS methods is related to their signal times, the conventional false positive rate (FPR) and false negative rate (FNR) cannot be effective in measuring their performance. So far, there is no existing metrics in the literature for properly measuring the performance of DS methods. In this article, we aim to fill this gap by proposing a new performance evaluation approach, called process monitoring receiver operating characteristic curve, which properly combines the signal times with (FPR,FNR). Numerical examples and theoretical justifications show that this approach provides an effective tool for measuring the performance of DS methods. Supplementary materials for this article are available online.