A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for the...A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.展开更多
The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outsid...The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outside the control limit is calculated. The above-mentioned results are substituted into the infinite definition expression of the average run length （ARL）, and then the final finite ARL expression is obtained. An example is used to demonstrate the procedures of the proposed method. In the comparative study, eight autocorrelated processes and four different mean shifts are performed, and the ARL values of the proposed method are compared with those obtained by simulation method with 50 000 replications. The accuracy of the proposed method can be illustrated through the comparative results.展开更多
The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the a...The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the average run length(ARL).Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p)model has not been reported previously.The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA con-trol chart for the trend AR(p)model as well as the trend AR(1)and trend AR(2)models with exponential white noise.The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numer-ical integral equation(NIE)method.The results show that the ARL obtained by the explicit formula and the NIE method is hardly different,but the explicit for-mula can help decrease the computational(CPU)time.Furthermore,this is also expanded to comparative performance with the Exponentially Weighted Moving Average(EWMA)control chart.The performance of the extended EWMA control chart is better than the EWMA control chart for all situations,both the trend AR(1)and trend AR(2)models.Finally,the analytical solution of ARL is applied to real-world data in the healthfield,such as COVID-19 data in the United Kingdom and Sweden,to demonstrate the efficacy of the proposed method.展开更多
This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of t...This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.展开更多
基金The research was supported by King Mongkut’s University of Technology North Bangkok Contract No.KMUTNB-62-KNOW-018.
文摘A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.
基金Supported by National Natural Science Foundation of China (No.70931004 and No. 70802043)
文摘The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outside the control limit is calculated. The above-mentioned results are substituted into the infinite definition expression of the average run length （ARL）, and then the final finite ARL expression is obtained. An example is used to demonstrate the procedures of the proposed method. In the comparative study, eight autocorrelated processes and four different mean shifts are performed, and the ARL values of the proposed method are compared with those obtained by simulation method with 50 000 replications. The accuracy of the proposed method can be illustrated through the comparative results.
基金Thailand Science ResearchInnovation Fund,and King Mongkut's University of Technology North Bangkok Contract No.KMUTNB-FF-65-45.
文摘The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the average run length(ARL).Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p)model has not been reported previously.The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA con-trol chart for the trend AR(p)model as well as the trend AR(1)and trend AR(2)models with exponential white noise.The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numer-ical integral equation(NIE)method.The results show that the ARL obtained by the explicit formula and the NIE method is hardly different,but the explicit for-mula can help decrease the computational(CPU)time.Furthermore,this is also expanded to comparative performance with the Exponentially Weighted Moving Average(EWMA)control chart.The performance of the extended EWMA control chart is better than the EWMA control chart for all situations,both the trend AR(1)and trend AR(2)models.Finally,the analytical solution of ARL is applied to real-world data in the healthfield,such as COVID-19 data in the United Kingdom and Sweden,to demonstrate the efficacy of the proposed method.
基金the Science,Research and Innovation Promotion Funding(TSRI)(Grant No.FRB660012/0168)managed under Rajamangala University of Technology Thanyaburi(FRB66E0646O.4).
文摘This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.
