Adaptive nonparametric CUSUM scheme for detecting unknown shifts in location

Abstract

In this paper, we provide a sequential rank-based adaptive nonparametric cumulative sum control chart for detecting a range of shifts in the location parameter. This chart is a self-starting scheme, and thus can be used to monitor processes at the start-up stages rather than having to wait for the accumulation of sufficiently large calibration samples. It does not require any prior knowledge of the underlying distribution. The choice of the chart parameters is studied and a simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also efficiently detects various magnitudes of shifts. An illustrative example is also given to introduce the implementation of this proposed control chart.