控制圖中的平均運(yùn)行長(zhǎng)度在l233;vy穩(wěn)定過程中的應(yīng)用

1、上海交通大學(xué)碩士學(xué)位論文控制圖中的平均運(yùn)行長(zhǎng)度在Lévy穩(wěn)定過程中的應(yīng)用姓名：張晨申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：韓東20060101The Average Run Lengths of Control Chartsfor Stable L´ evy ProcessesABSTRACTThe problem of quick detection of change point in a stochastic

2、 system has manyimportant applications, including industrial quality control, automated fault detection incontrolled dynamical systems, segmentation of signals, and so on. To deal with the problem,various control charts,

3、 such as Shewhart chart, the CUSUM, EWMA , GEWMA and GLRcontrol charts, etc., were proposed.As can be seen that all research work in the above literature is based on an assumptionthat the observation stochastic system (o

4、r process) is subject to the normal distribution orthe variance of the process is fi nite. In fact, there are many stochastic systems such as thebankroll trading volume in the fi nance network, the return rate of stock m

5、arket, temperaturedistributions in unclear reactors and the volume of annual rainfall, which are neither normalor have fi nite variance. These stochastic systems are usually subject to a stable distributionwith infi nite

6、 variance, which is called a stable L´ evy process. Thus, there are two interestingproblems in the following which have received minimal attention. How the popular controlcharts such as the EWMA, CUSUM and GLR can b

7、e effectively used in the stable L´ evyprocess? What is the performance of the control charts for monitoring the change point inthe process? One way to deal with the second problem is to estimate the ARL of the cont

8、rolchart, since the estimation of the ARL can establish the clear asymptotic relations betweenthe ARL, control limit and statistical properties of the observation processes.As we know that the average run length (ARL) is

9、 an extensively used measure in statisti-cal process control (SPC) for evaluating and comparing the detection performance of variouscontrol charts. In this paper we not only present the asymptotic estimation of the ARL f

10、or theexponentially weighted moving average (EWMA), generalized EWMA (GEWMA) and gen-eralized likelihood ratio (GLR) control charts but also compare the detection performanceby the numerical simulation among the four cha