累积和控制图主要用于对正态分布过程中均值的中小漂移的检测, 但 是对厚尾分布过程监测并不稳定. MacEachern等(2007)提出了用于监测厚尾分布过程的稳健似然比累积和(RLCUSUM) 控制图. 文章主要研究RLCUSUM控制图的性质, 包括可控平均运行长度关于控制限的性质和过程失控时不同真实均值对平均运行长度的影响等, 并提出了对于对数似然比函数进行斜线截断的方式, 同时分析总结了不同污染程度的混合正态分布下各种截断方式得到的RLCUSUM控制图的适用情况.

The cumulative sum (CUSUM) chart is usually used for detecting small shifts in the mean of a normally distributed process, but it performs poorly for heavy-tailed distributed processes. MacEachern, et al.(2007) proposed the robust-likelihood cumulative sum (RLCUSUM) chart which can be used when observations follows heavy-tailed distributions. This paper discusses the characters of RLCUSUM, such as property of average run length in control in different control limits, the impact of different real mean on the average run length when the process is out of control and so on. And we propose a new method to cut off the log-likelihood function by diagonal and conclude the suitable cases in which the RLCUSUM control chart, cut off by varies means, is more sensitive and robust when observations are contaminated normal distributed under different pollution levels.