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研究生:蔡佩真
研究生(外文):Pei-Chen Tsai
論文名稱:探討允收管制界限對於製程管制的效益
論文名稱(外文):Investigation on the Efficiency of Acceptance Control Limits in Process Control
指導教授:童超塵童超塵引用關係
指導教授(外文):Dr.Chau-Chen Torng
學位類別:碩士
校院名稱:國立雲林科技大學
系所名稱:工業工程與管理研究所碩士班
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:48
中文關鍵詞:管制界限允收管制圖修華特管制圖
外文關鍵詞:Control LimitsAcceptance Control ChartShewhart control chart
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現在的製程已漸趨於零缺點,但當製程抽樣是零缺點時,我們仍執意使用Shewhart管制圖來管制製程,我們並無法計算出其管制界限,此時該如何管制?
管制圖使用初期尚未計算出管制界限時,該如何管制?
製程只需監測其是否合格而不需監測製程狀態時,該如何管制?
或許我們選擇換個方式,單單只用規格來管制,但又深怕製程一旦出現問題將面臨的是已有部分產品超出規格成為不良品,得重工甚至是報廢來處置,尤其生產快速的製程上這樣的錯誤影響更大。
所以,如何運用規格界限而兼顧生產者冒險率、消費者冒險率的要求,又能預先監控製程即是個重要課題了。
其中1957福祿得博士發展出的允收管制圖原理,相當符合上述的問題要求。其結合了規格界限、生產者冒險率(型一誤差)及消費者冒險率(型二誤差)兩種風險來求出管制界限,是一種結合了允收抽樣和管制圖的工具。
本研究研討運用允收管制界限到傳統的管制圖中,評估其對製程管制的效益,得到下列的結論:
1. 當製程在沒有偏移的狀態下,即製程良好時,無論其樣本大小,除非允收管制圖α訂的比0.0027小,否則皆是Shewhart管制圖較允收管制圖不容易出現假警報。
2. 當製程有偏移的情況下,即製程能力不見得都相當良好時,過程品質變動小(δ小)時,Shewhart管制圖的偵測能力較差,此時建議選擇允收管制圖較佳,當過程品質變動較大(δ大)時Shewhart管制圖的偵測能力較佳,此時建議選擇Shewhart管制圖較佳。
3. 訂定允收管制圖的β不一定得皆小於 Shewhart管制圖的β才會得到比Shewhart管制圖較少的損失成本。
As the process becomes zero-defection, especially when the process sampling is none defection and the Shewhart control chart is still the one used to control the none-defection process, we are not able to calculate the process control limit for it in this situation. How to control for none-defection process?
How to control when the process is under the initial application of control chart?
How to control when the production is requested to pass the standard only and the actual status of process is not concerned?
We may just change the way by using the specification to be the control limit, but we are also afraid of the re-work and scraps which is due to part of the products are out of specification when the process is out of control. The effect is even more serious when the mistake is found at a process with high through put rate.
Therefore, how to monitor the process in advance in according to the specification value and considering both the producer’s risk and customer’s risk in the same time would be an important subject.
The “Acceptance Control Chart” theory conducted by Dr. Freund on 1957 may fit with the requirement of above questions well. This theory combined the specification limit with both the Producer’s Risk (Type I Error) and the Customer’s Risk (Type II Error) to find the control limit for process. It’s a tooling put the Acceptance Sampling together with the Control Chart.
The investigation discuss the application of acceptance control limit to be used on the traditional control chart and estimate its efficiency on process control. This study found that:
1. When the process is at the status of no deviation, i.e. the process is under good condition , no matter how the size of the sample , unless the value of α is smaller than 0.0027 on the acceptance control chart , the Shewhart control chart is better than acceptance control chart.
2. When the process is deviated, i.e. the capability of the process is no longer under good condition, the detecting capability of Shewjart control chart is getting worse. The acceptance control chart is recommended for such case. When the variation of the process quality is getting higher, the setecting capability of the Shwhart control chart is better. The Shewhart control chart is recommended for such case.
1. The value of β on the acceptance control chart is not necessarily less than the one on the Shewhart control chart to get the better control on cost loss. The Shewhart control chart is recommended.
中文摘要i
英文摘要ii
誌 謝iv
目 錄v
表 目 錄vi
圖 目 錄vi
一、緒論1
1.1 研究背景1
1.2 研究目的2
1.3 論文架構4
二、文獻探討5
2.1 SHEWHART管制圖5
2.1.1 計量值管制圖7
2.1.2 計數值管制圖9
2.2 以規格為基準發展出的管制圖11
2.2.1 拒收管制界限(修正管制界限)11
2.2.2 預先管制界限13
2.2.3 允收管制圖17
2.2.4 拒收管制圖、預先管制圖、允收管制圖之比較22
2.3平均連串長度(ARL)23
2.4經濟性設計24
2.4.1符號說明….24
2.4.2成本模式….25
三、研究方法26
3.1 傳統管制圖之允收管制界限推導26
3.1.1 符號說明26
3.1.2 計量值管制圖之允收管制界限27
3.1.3 計數值管制圖之允收管制界限29
3.1.4 管制界限算式彙總32
3.2 衡量允收管制界限和傳統管制界限33
3.2.1 衡量尺度一-----ARL33
3.2.2 衡量尺度二-----經濟性設計33
四、允收管制界限對製程管制的效益評估35
4.1以平均連串長度(ARL)為衡量基準35
4.2以管制圖經濟性設計為衡量基準39
4.2.1做法說明39
4.2.2結果說明41
4.3驗證結果彙總43
五、結論45
參考文獻47
表 目 錄
表2.1 -R、 -S管制圖公式彙總表8
表2.2 預先管制界限判斷準則表15
表2.3 拒收管制圖、預先管制圖、允收管制圖比較表22
表4.1 不同樣本下,以ARL為衡量基準詳細結果列表36
表4.2 不同樣本下,以ARL為衡量基準,建議適用管制圖38
表4.3 不同成本結構下,以損失成本為衡量基準詳細結果列表41
圖 目 錄
圖1.1 研究架構4
圖2.1 管制圖形成原理5
圖2.2 計量值管制圖與計數值管制圖的運用時機7
圖2.3 拒收管制界限原理12
圖2.4 預先管制圖原理14
圖2.5 預先管制界限抽檢流程16
圖2.6 當指定n,P0 , 時計算允收管制界限19
圖2.7 當指定n,P1 , 時計算允收管制界限20
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[11] Logothetis, N. ,1990,"The Theory of Pre-Control: A Serious Method or a Colourful Naivity?",International Journal of Total Quality Management 1, pp. 207-220.
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[15] Moroney, M. J.,1953,Facts from Figures,2d ed,P.165-171,Penguin books,ltd.,Harmondworth
[16] Schilling, E. G.,1982,Acceptance Sampling in Quality control,Marcel Dekker,New York and Basel
[17] Shainin, D.,1984,“Better Than Good Old and R Charts Asked by Vendors.”,ASQC Quality Congress Transactions,pp.302-307
[18] Shewhart, W. A.,1931,Economic Control of Quality Manufactured Product,Van Nostrand,New York
[19] Sinibaldi, F. J.,1985,“Pre-Control Chart,Does It Really Work With N0n-Normality.”, ASQC Quality Congress Transactions,pp.428-433
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[21] Traver, R. W.,1985,"Pre-Control: A Good Alternative to and R Charts". Quality Progress 17, pp. 11-14.
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