A nonparametric cumulative sum scheme based on sequential ranks and adaptive control limits

摘要

We consider the problem of quickest detection, i.e. we sequentially monitor a data sequence to detect a shift in the sampling distribution which may occur at an unknown time instance. Conventional quickest detection procedures typically require a-priori knowledge of the underlying pre- and post-change distributions of the process. Such knowledge may not be available in practice or be flawed, e.g. because the distributional assumptions itself or the respective parameter estimates are inadequate. In this paper we propose a distribution-free cumulative sum (CUSUM) procedure based on sequential ranks and adaptive control limits. The presented procedure does not require a historical set of training data and is therefore especially suited for initial monitoring phases.