Comparison of Cuscore and GLR in Detecting Mean Shifts of Lévy Stable Processes

There is a class of problems in stochastic systems that have many important applications, namely how to quickly monitor change points. It can be applied in industrial quality control, and can also be applied in automatic fault monitoring of automatic systems, etc. In order to solve such problems quickly and effectively, different forms of control charts have been proposed. In the previous studies of various control charts, it is often assumed that the variance of the process is limited or that the random variables are normally distributed. However, in practical problems, many variables are stable and have infinite variance. Therefore, it is a practical problem to monitor the mean change point of Lévy stable process. In statistical process control, the average running length is widely used to evaluate and compare the monitoring effect of various control charts. In this paper, when monitoring the mean change point of Lévy stable process, the interval estimation of the average running length (ARL) of Cuscore and GLR control charts is given first, and then the monitoring effect is compared by using the method of digital simulation.