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低缺點率製程管制圖其最佳管制界限之研究 = The Optimal Co...

國立高雄大學亞太工商管理學系碩士班

低缺點率製程管制圖其最佳管制界限之研究 = The Optimal Control Limits of Control Charts for Monitoring Low-Defect Processes

Record Type:	Language materials, printed : monographic
Paralel Title:	The Optimal Control Limits of Control Charts for Monitoring Low-Defect Processes
Author:	莊宜璋,
Secondary Intellectual Responsibility:	國立高雄大學
Place of Publication:	[高雄市]
Published:	撰者;
Year of Publication:	2009[民98]
Description:	54面圖、表 : 30公分;
Subject:	CQC-r
Subject:	CQC-r
Online resource:	http://handle.ncl.edu.tw/11296/ndltd/16767941528787144345
Notes:	指導教授：陳榮泰
Notes:	參考書目：面
Summary:	由於c管制圖是假設卜瓦松分配滿足逼近常態分配之前提下所建立，當製程缺點率λ0極低時，會因為卜瓦松分配無法滿足常態性假設之條件，而造成c管制圖錯誤警訊增加。並因為缺點率極小，管制圖上易有許多為零的點，且管制下限容易設為零之情形，導致無法作為判斷製程是否有顯著改善。因此，c管制圖並不適合用來監控低缺點率製程，而後續才發展出CQC-r及數據轉換法用來取代c管制圖。　　CQC-r及數據轉換法管制圖通常應用於監控高產出率製程，但目前所提出的方法在設定管制界限時，可能導致管制內的ARL無法達到最大或有偏誤。當ARL在管制內為非最大或有偏誤時，可能無法快速偵測製程缺點率已逐漸偏離目標值。也就是說，當製程缺點率偏離目標值時，管制內及管制外的ARL值會高於正常值。而此篇論文最大貢獻就是提出新方法來改善及建立管制界限，使得第一次發生事件間隔時間(time-between-events)管制圖在管制內的ARL近似最大及不偏，並且針對常見的第一次發生事件間隔時間(time-between-events)伽瑪管制圖及韋伯管制圖進行實驗分析，其實驗結果證明新方法可以有效使管制內的ARL為最大及不偏。　　The c chart approximated by normal distribution is widely used to monitor the low-defect. However, the low-defect processes due to process improvement and small sample size usually make the assumptions invalid and generate too many false alarms. Since the defect is low, the lower control limit of a c chart is usually negative and no process improvement can be detected. For above mentioned reasons, the c chart is inadequate for monitoring and control of product attributes in the processes of very high yields.　　Cumulative quantity of conforming (CQC-r) charts or transformed data are usually used to monitor defect fraction λ in high-yield processes. Existing approaches to setting the control limits may cause non-maximal or biased in-control average run length (ARL). Non-maximal in control ARL implies that the chart might not quickly detect the upward shift of λ from its nominal value λ0. On the hand, biased in-control ARL means that both the in-control and out-of-control ARLs are inflated. This paper develops a new approach to setting control limits for time-between-events charts with near-maximal and near-unbiased in-control ARL. Experiments for common time-between-events such as gamma and weibull control chart analysis. Experimental results show that the new approach is effective in terms of the maximization and unbiasedness of in-control ARL.

低缺點率製程管制圖其最佳管制界限之研究 = The Optimal Control Limits of Control Charts for Monitoring Low-Defect Processes
莊, 宜璋

低缺點率製程管制圖其最佳管制界限之研究 = The Optimal Control Limits of Control Charts for Monitoring Low-Defect Processes / 莊宜璋撰 - [高雄市] : 撰者, 2009[民98]. - 54面 ; 圖、表 ; 30公分.
指導教授：陳榮泰參考書目：面.
CQC-rCQC-r

低缺點率製程管制圖其最佳管制界限之研究 = The Optimal Control Limits of Control Charts for Monitoring Low-Defect Processes
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330 $a 　　由於c管制圖是假設卜瓦松分配滿足逼近常態分配之前提下所建立，當製程缺點率λ0極低時，會因為卜瓦松分配無法滿足常態性假設之條件，而造成c管制圖錯誤警訊增加。並因為缺點率極小，管制圖上易有許多為零的點，且管制下限容易設為零之情形，導致無法作為判斷製程是否有顯著改善。因此，c管制圖並不適合用來監控低缺點率製程，而後續才發展出CQC-r及數據轉換法用來取代c管制圖。　　CQC-r及數據轉換法管制圖通常應用於監控高產出率製程，但目前所提出的方法在設定管制界限時，可能導致管制內的ARL無法達到最大或有偏誤。當ARL在管制內為非最大或有偏誤時，可能無法快速偵測製程缺點率已逐漸偏離目標值。也就是說，當製程缺點率偏離目標值時，管制內及管制外的ARL值會高於正常值。而此篇論文最大貢獻就是提出新方法來改善及建立管制界限，使得第一次發生事件間隔時間(time-between-events)管制圖在管制內的ARL近似最大及不偏，並且針對常見的第一次發生事件間隔時間(time-between-events)伽瑪管制圖及韋伯管制圖進行實驗分析，其實驗結果證明新方法可以有效使管制內的ARL為最大及不偏。　　The c chart approximated by normal distribution is widely used to monitor the low-defect. However, the low-defect processes due to process improvement and small sample size usually make the assumptions invalid and generate too many false alarms. Since the defect is low, the lower control limit of a c chart is usually negative and no process improvement can be detected. For above mentioned reasons, the c chart is inadequate for monitoring and control of product attributes in the processes of very high yields.　　Cumulative quantity of conforming (CQC-r) charts or transformed data are usually used to monitor defect fraction λ in high-yield processes. Existing approaches to setting the control limits may cause non-maximal or biased in-control average run length (ARL). Non-maximal in control ARL implies that the chart might not quickly detect the upward shift of λ from its nominal value λ0. On the hand, biased in-control ARL means that both the in-control and out-of-control ARLs are inflated. This paper develops a new approach to setting control limits for time-between-events charts with near-maximal and near-unbiased in-control ARL. Experiments for common time-between-events such as gamma and weibull control chart analysis. Experimental results show that the new approach is effective in terms of the maximization and unbiasedness of in-control ARL.
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