监测L\'evy稳定过程均值变点的平均运行时间估计

监测L\'{e}vy稳定过程均值变点的平均运行时间估计

Department of Mathematics, Shanghai Jiao Tong University, Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology

摘要: 平均运行长度(时间) (ARL)是判断一控制图监测变点效果好坏的一个重要工具\bd 本文主要研究L\'{e}vy 稳定过程的均值变点监测问题\bd 我们给出了三个控制图, 即EWMA, GEWMA和GLR的ARL 估计, 并通过数值模拟比较了4个控制图监测均值变点的效果和差异.
- 变点监测 /
- 平均运行长度 /
- L\'{e}vy稳定过程 /
- EWMA /
- GLR /
- GEWMA /
- CUSUM
Abstract: As we know that the average run length (ARL) is an extensively used measure in statistical process control (SPC) for evaluating and comparing the detection performance of various control charts. In this paper we not only present the asymptotic estimation of the ARL for the exponentially weighted moving average (EWMA), generalized EWMA (GEWMA) and generalized likelihood ratio (GLR) control charts but also compare the detection performance by the numerical simulation among the four charts: EWMA, GEWMA, GLR and CUSUM in detecting the mean change of a stable L\'{e}vy process.
- Change point detection /
- average run length /
- stable L\'{e}vy process /
- EWMA /
- GEWMA /
- GLR /
- CUSUM