联合检测过程位置参数和尺度参数的非参数Cusum控制图
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摘要
用于检测生产过程的多数传统控制图都假定过程的受控分布是已知的,并假定数据服从正态分布。然而在很多情况下,由于没有足够的数据来估计过程的分布,这种假定就变得不现实,而非参数控制图却不需要任何关于分布的特殊形式的假定。另外,多数的已有控制图都是使用两个单独的均值与方差控制图来同时检测生产过程.本文中,我们提出一个新的基于Cramer-von-Mises(CvM)检验的非参数累积和控制图(称为CvM图)来同时检测过程位置参数和尺度参数。文中给出了基于不同受控平均运行长度(ARL)下的CvM图的控制限,通过步长的均值、方差及分位数来研究控制图的性能表现。最后用一个实例来说明CvM图的实际应用。
Most traditional control charts used for sequential monitoring assume that full knowledge is available regarding the prechange distribution of the process and the assumption of normality is required.This assumption is unrealistic in many situations where insufficient data are available to accurately estimate the distribution, while the nonparametric charts do not assume any specific form for the process distribution. On the other hand, a separate mean and a standard deviation chart. In this paper, we propose a new cumulative sum control charts based on the Cramer-von-Mises(named as CvM chart)test for joint monitoring of location and scale. Control limits are tabulated for some typical nominal incontrol(IC) average run length(ARL) values. The in-control and out-of-control performance properties of the chart are investigated in simulation studies in terms of the means, the standard deviation, and some percentiles of the length distribution. The application of our proposed chart is illustrated by a real example.
Most traditional control charts used for sequential monitoring assume that full knowledge is available regarding the prechange distribution of the process and the assumption of normality is required.This assumption is unrealistic in many situations where insufficient data are available to accurately estimate the distribution, while the nonparametric charts do not assume any specific form for the process distribution. On the other hand, a separate mean and a standard deviation chart. In this paper, we propose a new cumulative sum control charts based on the Cramer-von-Mises(named as CvM chart)test for joint monitoring of location and scale. Control limits are tabulated for some typical nominal incontrol(IC) average run length(ARL) values. The in-control and out-of-control performance properties of the chart are investigated in simulation studies in terms of the means, the standard deviation, and some percentiles of the length distribution. The application of our proposed chart is illustrated by a real example.
引文
[1]Jones L,Case K.Economic design of a joint X and R charts[J].Technometrics,1981,13:182-195.
[2]Reynolds M J,Stoumbos Z G.Individuals control schemes for monitoring the mean and variance of processes subject to drifts[J].Stochastic Analysis and Applications,2001,19:863-892.
[3]Reynolds M J,Stoumbos Z G.Comparisons of some exponentially weighted moving average control charts for monitoring the process mean and variance[J].Technometrics,2006,48:550-567.
[4]Chen G,Cheng S W.Max-chart:combining X-bar and S chart[J].Statistica Sinica,1998,8:263-271.
[5]Chen G,Cheng S,Xie H.Monitoring process mean and variability with one EWMA chart[J].Journal of Quality Technology,2001,33:223-233.
[6]Zhang J,Zou C,Wang Z.A control chart based on likelihood ratio test for monitoring process mean and variability[J].Quality and Reliability Engineering international,2010,26(1):63-73.
[7]Zhang X,Zhang J.CUSUM procedures for monitoring process mean and variability[J].Communications in Statistics-Simulation and Computation,2012,42:1455-1471.
[8]Cheng S W,Thaga K.Single variable control chart:an overview[J].Quality and Reliability Engineering international,2006,22:811-820.
[9]Chakraborti S,Graham M A.Nonparametric Control Charts:Encyclopedia of Statistics in Quality and Reliability[M].John Wiley,New York,2007,1:415-429.
[10]Mukherjee A,Chakraborti S.A distribution-free control chart for the joint monitoring of location and scale[J].Quality and Reliability Engineering international,2012,28(3):335-352.
[11]Chowdhury S,Mukherjee A,Chakraborti S.A new distribution-free control chart for joint monitoring of unknown location and scale parameters of continuous distributions[J].Quality and Reliability Engineering international,2014,30(2):191-204
[12]Anderson T W.On the distribution of the two sample Cramer-Von Mises criterion[J].Annals of Mathematical Statistics,1962,33(3):1148-1159.
[13]王兆军,巩震,邹长亮.ARL计算方法综述[J].数理统计与管理,2011,30(3):467-497.
[14]Montgomery D C.Introduction to Statistical Quality Control(6th edn)[M].New York:John Wiley,2007.
[2]Reynolds M J,Stoumbos Z G.Individuals control schemes for monitoring the mean and variance of processes subject to drifts[J].Stochastic Analysis and Applications,2001,19:863-892.
[3]Reynolds M J,Stoumbos Z G.Comparisons of some exponentially weighted moving average control charts for monitoring the process mean and variance[J].Technometrics,2006,48:550-567.
[4]Chen G,Cheng S W.Max-chart:combining X-bar and S chart[J].Statistica Sinica,1998,8:263-271.
[5]Chen G,Cheng S,Xie H.Monitoring process mean and variability with one EWMA chart[J].Journal of Quality Technology,2001,33:223-233.
[6]Zhang J,Zou C,Wang Z.A control chart based on likelihood ratio test for monitoring process mean and variability[J].Quality and Reliability Engineering international,2010,26(1):63-73.
[7]Zhang X,Zhang J.CUSUM procedures for monitoring process mean and variability[J].Communications in Statistics-Simulation and Computation,2012,42:1455-1471.
[8]Cheng S W,Thaga K.Single variable control chart:an overview[J].Quality and Reliability Engineering international,2006,22:811-820.
[9]Chakraborti S,Graham M A.Nonparametric Control Charts:Encyclopedia of Statistics in Quality and Reliability[M].John Wiley,New York,2007,1:415-429.
[10]Mukherjee A,Chakraborti S.A distribution-free control chart for the joint monitoring of location and scale[J].Quality and Reliability Engineering international,2012,28(3):335-352.
[11]Chowdhury S,Mukherjee A,Chakraborti S.A new distribution-free control chart for joint monitoring of unknown location and scale parameters of continuous distributions[J].Quality and Reliability Engineering international,2014,30(2):191-204
[12]Anderson T W.On the distribution of the two sample Cramer-Von Mises criterion[J].Annals of Mathematical Statistics,1962,33(3):1148-1159.
[13]王兆军,巩震,邹长亮.ARL计算方法综述[J].数理统计与管理,2011,30(3):467-497.
[14]Montgomery D C.Introduction to Statistical Quality Control(6th edn)[M].New York:John Wiley,2007.