带马尔可夫均值估计量的非参数自适应CUSUM控制图

Nonparametric Adaptive CUSUM Procedures with Markovian Mean Estimation

本文提供了一个带马尔可夫均值估计量的非参数自适应CUSUM控制图用于监测位置参数的持续性漂移。它可以通过马尔可夫均值估计量预测未知的漂移大小,自适应的调整控制图参数,来对不同大小的未知漂移进行一个很好的监控。这是一个自启动非参数控制图,可以用于监控开始阶段,并且不需要依赖于任何样本的分布.通过数据模拟研究显示出这个控制图不仅在各种不同分布下具有很好的稳健性,并且对各种大小的漂移都很有效。

In this paper,we provide a nonparametric adaptive CUSUM(NACU) procedure with Markovian mean estimation for detecting persistent shifts in the location parameter.It can forecast the magnitude of unknown shift by the Markovian estimation to update its reference value in an adaptive way.So it can achieve the aim of providing an overall good performance over a range of unknown mean shifts.Moreover,this NACU chart is a self-starting nonparametric scheme and thus can be used to monitor processes at the start-up stages and we needn't require any prior knowledge of the underlying distribution.A simulation study demonstrates that the proposed control chart not only performs robustly for different distributions,but also is efficient in detecting various magnitude of shifts.