检测对数正态分布位置参数和尺度参数的控制图
|
摘要
多数传统的控制图都假定过程数据服从正态分布,然而在许多实际情况中,数据可能服从偏态分布,比如对数正态分布。因此,检测对数正态分布的参数漂移也变得尤为重要。本文基于似然比检验并结合指数加权移动平均方法,提出一种可用来同时检测对数正态分布的位置参数和尺度参数漂移的综合控制图,并通过平均运行长度、运行长度标准差两个指标来衡量控制图的性能表现,并和已有的几个控制图进行比较。结果显示,本文提出的控制图具有更高的检测效率。最后用一个实例来说明本文提出的控制图的实际应用。
The conventional control charts are based on the assumption that the distribution of the quality characteristic to be monitored follows the normal distribution. However, in real applications, many process distributions may follow a positively skewed distribution such as the lognormal distribution. In this paper, we propose a chart which integrates the exponentially weighted moving average(EWMA)procedure with the generalized likelihood ratio test statistics for jointly monitoring both the location and scale parameter under the assumption of lognormal. From the comparison with other charts based on average run length(ARL) and standard deviation of run length(SDRL), we can see that the proposed chart is more efficient than the other existing charts. The application of our proposed chart is illustrated by a real data example.
The conventional control charts are based on the assumption that the distribution of the quality characteristic to be monitored follows the normal distribution. However, in real applications, many process distributions may follow a positively skewed distribution such as the lognormal distribution. In this paper, we propose a chart which integrates the exponentially weighted moving average(EWMA)procedure with the generalized likelihood ratio test statistics for jointly monitoring both the location and scale parameter under the assumption of lognormal. From the comparison with other charts based on average run length(ARL) and standard deviation of run length(SDRL), we can see that the proposed chart is more efficient than the other existing charts. The application of our proposed chart is illustrated by a real data example.
引文
[1]Morrison J.The lognormal distribution in quality control[J].Applied Statistics,1958,7(3):160-172.
[2]Ferrel E D.Control charts for lognormal universe[J].Industrial Quality Control,1958,15(2):4-6.
[3]Joffe A D,Sichel H S.A chart for sequentially testing observed arithmetic means for lognormal populations against a given standard[J].Technometrics,1986,10:605-612.
[4]Choobineh F,Ballard J L.Control-limits of QC charts for skewed distributions using weightedvariance[J].IEEE Transactions on Reliability,1987,37(4):473-477.
[5]Bai D S,Choi I S.X and R control charts for skewed populations[J].Journal of Quality Technology,1995,27(2):120-131.
[6]Huang W H,Wang H,Yeh A B.Control chart for the lognormal mean[J].Quality and Reliability Engineering International,2016,32:1407-1416.
[7]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.
[8]Patterson R L.Difficulties involved in the estimation of a population mean using transformed sample data[J].Technometrics,1966,8(3):535-537.
[9]Land C E.An evaluation of approximate confidence interval estimation methods for lognormal means[J].Technometrics,1972,14(1):145-158.
[10]Montgomery D C.Statistical Quality Control,7th Ed[M].Hoboken,NJ:John Wiley&Sons,2013.
[11]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.
[2]Ferrel E D.Control charts for lognormal universe[J].Industrial Quality Control,1958,15(2):4-6.
[3]Joffe A D,Sichel H S.A chart for sequentially testing observed arithmetic means for lognormal populations against a given standard[J].Technometrics,1986,10:605-612.
[4]Choobineh F,Ballard J L.Control-limits of QC charts for skewed distributions using weightedvariance[J].IEEE Transactions on Reliability,1987,37(4):473-477.
[5]Bai D S,Choi I S.X and R control charts for skewed populations[J].Journal of Quality Technology,1995,27(2):120-131.
[6]Huang W H,Wang H,Yeh A B.Control chart for the lognormal mean[J].Quality and Reliability Engineering International,2016,32:1407-1416.
[7]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.
[8]Patterson R L.Difficulties involved in the estimation of a population mean using transformed sample data[J].Technometrics,1966,8(3):535-537.
[9]Land C E.An evaluation of approximate confidence interval estimation methods for lognormal means[J].Technometrics,1972,14(1):145-158.
[10]Montgomery D C.Statistical Quality Control,7th Ed[M].Hoboken,NJ:John Wiley&Sons,2013.
[11]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.