  Recent algorithms of time-series anomaly detection have been evaluated by
applying a Point Adjustment (PA) protocol. However, the PA protocol has a
problem of overestimating the performance of the detection algorithms because
it only depends on the number of detected abnormal segments and their size. We
propose a novel evaluation protocol called the Point-Adjusted protocol with
decay function (PAdf) to evaluate the time-series anomaly detection algorithm
by reflecting the following ideal requirements: detect anomalies quickly and
accurately without false alarms. This paper theoretically and experimentally
shows that the PAdf protocol solves the over- and under-estimation problems of
existing protocols such as PA and PA\%K. By conducting re-evaluations of SOTA
models in benchmark datasets, we show that the PA protocol only focuses on
finding many anomalous segments, whereas the score of the PAdf protocol
considers not only finding many segments but also detecting anomalies quickly
without delay.
