Sequential Performance Analysis of Systems that Age and Rejuvenate

Sequential performance analysis aims at evaluating performance indicators in an online fashion. The process stops in accordance with a pre-defined stopping rule, as soon as an anomaly that should produce an alarm is observed. Traditional sequential performance analysis techniques include CUSUM and sequential probability ratio test (SPRT). More recent techniques include the bucket algorithm, wherein tokens are accumulated into buckets when the system degrades, and removed when the system naturally recovers. If the number of tokens in the system reaches a threshold, an alarm is triggered. In this paper, we analyze sequential performance analysis algorithms applied to a system that is subject to rejuvenation. Among our results, we indicate how rejuvenation impacts the time until false alarms, and how to set the optimal rejuvenation rate accounting for the fact that systems can recover from transient performance degradation either naturally, as in standard sequential performance analysis models, or due to rejuvenation.