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題名 X bar-S square區域管制圖的最適設計
The Optimal Design of X bar-S Square Zone Control Charts
作者 陳智鴻
Chen, Chih-Hon
貢獻者 楊素芬<br>鐘崑仁<br>葉小蓁
Yang, Su-Fen<br>Chung, Kun-Jen<br>Yeh, Hsiaw-Chan
陳智鴻
Chen, Chih-Hon
關鍵詞 管制圖
馬可夫鏈
經濟設計
經濟統計設計
Control chart
Markov chain
Economic design
Economic statistical design
日期 1996
上傳時間 28-Apr-2016 11:48:25 (UTC+8)
摘要 自Duncan在1956年提出管制圖的經濟設計以來,陸續有許多學者提出各種不同型態管制圖的經濟設計,但是在這些文章中,尚無將描點的連串檢定列入考慮者,然而在管制圖中加入描點的連串檢定實有其必要性,加入描點的連串檢定可增加管制圖的偵測能力,但是這種作法頗為麻煩,因此Jaehn(1987)提出了區域管制圖來取代傳統管制圖加上連串檢定的不便,本研究提出X Bar-S Square 區域管制圖的經濟設計以改善一般經濟管制圖未將描點的連串檢定列入考慮的缺點.我們以製程中各項製程和成本資料為因子,對經濟區域管制圖的最佳設計參數值做敏感度分析,以找出製程中的關鍵參數.另外我們應用Saniga(1989)經濟統計管制圖的觀念設計經濟統計區域管制圖.雖然經濟統計區域管制圖所計算出的成本會比經濟區域管制圖稍大,但是在統計表現上卻符合我們的要求.
參考文獻 [1] .賀全慶(1 993) ,"區域管制圖"品質管制月刊，第二十九卷第四期， pp35-42.
     [2]. Champ,C.W.(1986),"Exact Results for Shewhart Control Cahrts With Supplementary Run Rules",unpublished Ph.D. dissertation, University of Southwestern Louisiana,Dept. of Statistics.,pp59.
     [3]. Ho Chuanching and Case K. (1994),"An Economic Design of The Zone Control Chart for Jointly Monitoring Process Centering And Variation",Computers and industryal Engineering, Vol. 26,pp213-221.
     [4]. Chung,K.J. and Chen,S.L.(1992),"Joint Economically Optimal Design of X and S2 Control Charts" ,Engineering Optimization, Vol. 19 ,pp 101-113 .
     [5]. Davis,R.B., Homer` A. and Woodall,W.H.(1990)"Performance of the Zone Control Chart" ,C0l111llUnication in Statistics-Theroy and Methods,VoII9,NO.5,pp1581-1587.
     [6]. Duncan A.(1956),"The economic Design of X Charts Used to Maintain Current Control of a Process" ,Journal of the American Statistical Association, Vol SI,pp228-242.
     [7]. IMSL Libraty (1989),yser`s Manual MathiLibrary,Fortran Su broutines, IMSL,Inc.
     [8]. Jaehn ` A.H.(l987)"Zone Control Charts: a New Tool for Quality Control" ,Tappi jounal,February,pp 159-161.
     [9]. Jaehn,A.H.(1987)"Zone Control Charts- SPC Made Easy",Quality, October,pp51-53.
     [10]. Jaelm,A.H.(199I)"The Zone Control Charts",Quality Progress, July,pp65-68.
     [11]. Jachn,A.H.(1990) , "Zone Control Charts-A New Way To Examine Variation ", Tappi J ournal,August,pp227 -229.
     [12]. John,G.K. and J.Laurie,S.(1976), Finite Markov Chains, Springer-Verlag,New York Heidelberg Berlin.
     [13]. Juran,J.H. and F.M.Gryna,JR .(1982),Quality Planning and Analysis, TATA McGraw-Hill,Inc.,New York, pp339-341.
     [14]. Kuester,J.L. and Mize,J.H.(1973),Optimization Techniques with Fortran,McGraw-Hill,Inc.,New York,NY.,pp309-319.
     [15]. Lorenzen,T.J. and Vance,L.C.(1986) ,"The Economic Design of Control Charts: A Unified Approach", Technometrics ,Vol. 28 ` NO.l,pp3-10.
     [16]. Montgomery,D.C. , Margaret ,R.P . and Russell,G.H. (1985) "Economic Design of X Control Charts for Tow Manufacturing Process Models",Naval Research Logistics Quarterly, Vol. 32,pp631-646.
     [17]. Montgomery,D.C. , Torng,J.C.-C. ,Cochran,J.k. and Lawrence F.P. (1995) "Statistically Constrained Economic Design of the EWMA Control Chart",J ournal of Quality Technology, Vol. 27 ,No.3,pp250-256.
     [18]. Montgomery,D.C. , Torng,J.C.-C. , Cochran,J.k. and Lawrence F.P. (1995) "Implementing Statistically Constrained Economic EWMA Control Charts",Journal of
     Quality Technology, Vol. 27 ,No.3 ,pp257-264.
     [19]. Panagos,M.R. ,Russell,G.H. and Montgomery,D.C.(1985) "Economic Design of X Control Chart for Two Manufacturing Process Models",Naval Research Logistics Quarterly,Vol. 32,pp631-646.
     [20]. Rahim,M.A. , Lashkari,R.S. and Banerjee,P.K.(1988),"Joint Economic Design of Mean and Variance Control Charts", Engineering Optimization, Vol. 14,pp65 -78.
     [21]. Ross,S.M.(1993),Introdllction to Probability Models, Academic Press.
     [22]. Saniga,E.M.(1989):`Economic Statistical Control-Chart Designs With an Application to X and R Chart" Technometrics , Vol. 31 ,NO.3, pp313-320.
     [23]. Shewhart, W.(1931), Economic Control of Quality of Manufactured Product,D.Van Nostrand Company,Inc.
描述 碩士
國立政治大學
統計學系
83354011
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002002786
資料類型 thesis
dc.contributor.advisor 楊素芬<br>鐘崑仁<br>葉小蓁zh_TW
dc.contributor.advisor Yang, Su-Fen<br>Chung, Kun-Jen<br>Yeh, Hsiaw-Chanen_US
dc.contributor.author (Authors) 陳智鴻zh_TW
dc.contributor.author (Authors) Chen, Chih-Honen_US
dc.creator (作者) 陳智鴻zh_TW
dc.creator (作者) Chen, Chih-Honen_US
dc.date (日期) 1996en_US
dc.date.accessioned 28-Apr-2016 11:48:25 (UTC+8)-
dc.date.available 28-Apr-2016 11:48:25 (UTC+8)-
dc.date.issued (上傳時間) 28-Apr-2016 11:48:25 (UTC+8)-
dc.identifier (Other Identifiers) B2002002786en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/87301-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 83354011zh_TW
dc.description.abstract (摘要) 自Duncan在1956年提出管制圖的經濟設計以來,陸續有許多學者提出各種不同型態管制圖的經濟設計,但是在這些文章中,尚無將描點的連串檢定列入考慮者,然而在管制圖中加入描點的連串檢定實有其必要性,加入描點的連串檢定可增加管制圖的偵測能力,但是這種作法頗為麻煩,因此Jaehn(1987)提出了區域管制圖來取代傳統管制圖加上連串檢定的不便,本研究提出X Bar-S Square 區域管制圖的經濟設計以改善一般經濟管制圖未將描點的連串檢定列入考慮的缺點.我們以製程中各項製程和成本資料為因子,對經濟區域管制圖的最佳設計參數值做敏感度分析,以找出製程中的關鍵參數.另外我們應用Saniga(1989)經濟統計管制圖的觀念設計經濟統計區域管制圖.雖然經濟統計區域管制圖所計算出的成本會比經濟區域管制圖稍大,但是在統計表現上卻符合我們的要求.zh_TW
dc.description.tableofcontents 壹．緒論.........1
     壹．緒論.........1
     一．前言.........1
     二．文獻回顧.........5
     三．研究動機與目的.........8
     （一）研究動機.........8
     （二）研究目的.........9
     四．研究方法.........9
     五．本文架構.........10
     貳．傳統區域管制圖之設計與優缺點.........12
     一．傳統區域管制圖之介紹.........12
     二．區域管制圖與Shewhart管制圖考慮連串法則時之異同.........15
     三．區域管制圖之優缺點.........16
     參．X-S2區域管制圖之經濟設計.........18
     一．Rahim et al.........的X-S2的經濟管制圖成本模型.........18
     （一）損失模式基本假設.........18
     （二）模式中符號的定義.........19
     （三）目標函數的推導.........20
     二．X-S2區域管制圖平均連串長度的計算.........23
     （一）平均連串長度、型Ⅰ誤差機率和檢定力之關係.........23
     （二）區域管制圖平均連串長度的計算.........24
     （三）X-S2區域管制圖之型Ⅰ誤差機率和檢定力.........40
     肆．資料分析.........42
     一．X-S2區域管制圖最佳設計參數值的決定.........43
     二．各種管制圖之最佳解和最佳值的比較.........45
     （一）不同連串法則對區域管制圖最佳設計參數值及最佳損失之影響.........45
     （二）經濟區域管制圖、經濟管制圖和Shewhart管制圖之最佳設計參數值及最佳損失之變化.........49
     （三）Shewhart管制圖加上連串法則與區域管制圖之最佳設計參數值及最佳值的比較.........50
     三．敏感度分析.........57
     （一）區域分數為（0,0,0,8）時最佳設計參數和最佳損失之敏感度分析.........62
     （二）區域分數為（1,2,4,8,）時最佳設計參數和最佳損失之敏感度分析.........66
     （三）區域分數為（0,0,0,8）和（1,2,4,8）時關鍵參數之比較.........70
     伍．區域管制圖之經濟統計設計.........71
     一．經濟統計設計的方法.........71
     （一）以平均連串長度作為限制式.........72
     （二）以直至警訊發生之平均時間作為限制式.........72
     二．最佳設計參數值的搜尋法.........73
     三．兩種搜尋法的比較.........76
     四．X-S2經濟區域管制圖和X-S2經濟統計區域管制圖最佳解之比較.........76
     陸．結論與建議.........81
     柒．參考文獻.........83
     捌．附錄一.........85
     附錄二.........98		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002002786en_US
dc.subject (關鍵詞) 管制圖zh_TW
dc.subject (關鍵詞) 馬可夫鏈zh_TW
dc.subject (關鍵詞) 經濟設計zh_TW
dc.subject (關鍵詞) 經濟統計設計zh_TW
dc.subject (關鍵詞) Control charten_US
dc.subject (關鍵詞) Markov chainen_US
dc.subject (關鍵詞) Economic designen_US
dc.subject (關鍵詞) Economic statistical designen_US
dc.title (題名) X bar-S square區域管制圖的最適設計zh_TW
dc.title (題名) The Optimal Design of X bar-S Square Zone Control Chartsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] .賀全慶(1 993) ,"區域管制圖"品質管制月刊，第二十九卷第四期， pp35-42.
     [2]. Champ,C.W.(1986),"Exact Results for Shewhart Control Cahrts With Supplementary Run Rules",unpublished Ph.D. dissertation, University of Southwestern Louisiana,Dept. of Statistics.,pp59.
     [3]. Ho Chuanching and Case K. (1994),"An Economic Design of The Zone Control Chart for Jointly Monitoring Process Centering And Variation",Computers and industryal Engineering, Vol. 26,pp213-221.
     [4]. Chung,K.J. and Chen,S.L.(1992),"Joint Economically Optimal Design of X and S2 Control Charts" ,Engineering Optimization, Vol. 19 ,pp 101-113 .
     [5]. Davis,R.B., Homer` A. and Woodall,W.H.(1990)"Performance of the Zone Control Chart" ,C0l111llUnication in Statistics-Theroy and Methods,VoII9,NO.5,pp1581-1587.
     [6]. Duncan A.(1956),"The economic Design of X Charts Used to Maintain Current Control of a Process" ,Journal of the American Statistical Association, Vol SI,pp228-242.
     [7]. IMSL Libraty (1989),yser`s Manual MathiLibrary,Fortran Su broutines, IMSL,Inc.
     [8]. Jaehn ` A.H.(l987)"Zone Control Charts: a New Tool for Quality Control" ,Tappi jounal,February,pp 159-161.
     [9]. Jaehn,A.H.(1987)"Zone Control Charts- SPC Made Easy",Quality, October,pp51-53.
     [10]. Jaelm,A.H.(199I)"The Zone Control Charts",Quality Progress, July,pp65-68.
     [11]. Jachn,A.H.(1990) , "Zone Control Charts-A New Way To Examine Variation ", Tappi J ournal,August,pp227 -229.
     [12]. John,G.K. and J.Laurie,S.(1976), Finite Markov Chains, Springer-Verlag,New York Heidelberg Berlin.
     [13]. Juran,J.H. and F.M.Gryna,JR .(1982),Quality Planning and Analysis, TATA McGraw-Hill,Inc.,New York, pp339-341.
     [14]. Kuester,J.L. and Mize,J.H.(1973),Optimization Techniques with Fortran,McGraw-Hill,Inc.,New York,NY.,pp309-319.
     [15]. Lorenzen,T.J. and Vance,L.C.(1986) ,"The Economic Design of Control Charts: A Unified Approach", Technometrics ,Vol. 28 ` NO.l,pp3-10.
     [16]. Montgomery,D.C. , Margaret ,R.P . and Russell,G.H. (1985) "Economic Design of X Control Charts for Tow Manufacturing Process Models",Naval Research Logistics Quarterly, Vol. 32,pp631-646.
     [17]. Montgomery,D.C. , Torng,J.C.-C. ,Cochran,J.k. and Lawrence F.P. (1995) "Statistically Constrained Economic Design of the EWMA Control Chart",J ournal of Quality Technology, Vol. 27 ,No.3,pp250-256.
     [18]. Montgomery,D.C. , Torng,J.C.-C. , Cochran,J.k. and Lawrence F.P. (1995) "Implementing Statistically Constrained Economic EWMA Control Charts",Journal of
     Quality Technology, Vol. 27 ,No.3 ,pp257-264.
     [19]. Panagos,M.R. ,Russell,G.H. and Montgomery,D.C.(1985) "Economic Design of X Control Chart for Two Manufacturing Process Models",Naval Research Logistics Quarterly,Vol. 32,pp631-646.
     [20]. Rahim,M.A. , Lashkari,R.S. and Banerjee,P.K.(1988),"Joint Economic Design of Mean and Variance Control Charts", Engineering Optimization, Vol. 14,pp65 -78.
     [21]. Ross,S.M.(1993),Introdllction to Probability Models, Academic Press.
     [22]. Saniga,E.M.(1989):`Economic Statistical Control-Chart Designs With an Application to X and R Chart" Technometrics , Vol. 31 ,NO.3, pp313-320.
     [23]. Shewhart, W.(1931), Economic Control of Quality of Manufactured Product,D.Van Nostrand Company,Inc.		zh_TW