针对两个正态随机变量比率(Ratio of Two Normal Random Variables,RZ)监控的研究是近年来统计过程控制的重要方向之一。为了进一步提高传统休哈特型RZ控制图对过程中较小或中等参数偏移的灵敏度,本文以指数加权移动平均(Exponentially ...针对两个正态随机变量比率(Ratio of Two Normal Random Variables,RZ)监控的研究是近年来统计过程控制的重要方向之一。为了进一步提高传统休哈特型RZ控制图对过程中较小或中等参数偏移的灵敏度,本文以指数加权移动平均(Exponentially Weighted Moving Average,EWMA) RZ控制图为基础,提出了一种新的RZ控制图。首先,对EWMA-RZ控制图的平滑系数进行两次加权,提出了二次指数加权移动平均(Double EWMA,DEWMA) RZ控制图,并进一步引入了变采样间隔(Variable Sampling Interval,VSI)特性,提出了VSI-DEWMA-RZ控制图;其次,采用蒙特卡罗(Monte-Carlo,MC)仿真模拟所提出控制图的运行链长分布特征,并详细分析了控制图的性能;再次,针对不同的控制图参数,比较了VSI-DEWMA-RZ控制图与DEWMA-RZ和VSI-EWMA-RZ控制图的性能。仿真结果表明,本文提出的VSI-DEWMA-RZ控制图优于DEWMA-RZ控制图,且其对过程中较小和中等偏移的监控效果优于现有的VSI-EWMA-RZ控制图。最后,通过监控食品加工过程中“南瓜籽”和“亚麻籽”的重量,进一步说明了所提出控制图的优越性。展开更多
This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is ...This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.展开更多
利用Burr分布来近似各种非正态分布对非正态情形下的EWM A均值控制图进行可变抽样区间设计,采用M arkov cha in方法计算过程的平均报警时间,数据结果显示,所设计的控制图较常规的固定抽样区间控制图可能够缩短过程失控时间从而提高控制...利用Burr分布来近似各种非正态分布对非正态情形下的EWM A均值控制图进行可变抽样区间设计,采用M arkov cha in方法计算过程的平均报警时间,数据结果显示,所设计的控制图较常规的固定抽样区间控制图可能够缩短过程失控时间从而提高控制图的效率。展开更多
文摘针对两个正态随机变量比率(Ratio of Two Normal Random Variables,RZ)监控的研究是近年来统计过程控制的重要方向之一。为了进一步提高传统休哈特型RZ控制图对过程中较小或中等参数偏移的灵敏度,本文以指数加权移动平均(Exponentially Weighted Moving Average,EWMA) RZ控制图为基础,提出了一种新的RZ控制图。首先,对EWMA-RZ控制图的平滑系数进行两次加权,提出了二次指数加权移动平均(Double EWMA,DEWMA) RZ控制图,并进一步引入了变采样间隔(Variable Sampling Interval,VSI)特性,提出了VSI-DEWMA-RZ控制图;其次,采用蒙特卡罗(Monte-Carlo,MC)仿真模拟所提出控制图的运行链长分布特征,并详细分析了控制图的性能;再次,针对不同的控制图参数,比较了VSI-DEWMA-RZ控制图与DEWMA-RZ和VSI-EWMA-RZ控制图的性能。仿真结果表明,本文提出的VSI-DEWMA-RZ控制图优于DEWMA-RZ控制图,且其对过程中较小和中等偏移的监控效果优于现有的VSI-EWMA-RZ控制图。最后,通过监控食品加工过程中“南瓜籽”和“亚麻籽”的重量,进一步说明了所提出控制图的优越性。
基金the National Science,Research and Innovation Fund(NSRF)King Mongkuts University of Technology North Bangkok under contract no.KMUTNB-FF-68-B-08.
文摘This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.
