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研究生:黃信仁
論文名稱:綜合管制圖及其變動抽樣間隔計畫之建構
論文名稱(外文):Synthetic Control Charts with Variable Sampling Intervals
指導教授:陳飛龍陳飛龍引用關係
學位類別:博士
校院名稱:國立清華大學
系所名稱:工業工程與工程管理學系
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:2005
畢業學年度:93
語文別:中文
論文頁數:132
中文關鍵詞:管制圖合格連串長度變動抽樣間隔平均連串長度平均顯示訊號時間
外文關鍵詞:control chartconforming run lengthvariable sampling intervalsaverage run lengthaverage time to signal
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統計製程管制(statistical process control, SPC)技術因其能提升產品品質與節省生產成本,已大量在工業界實施,管制圖為其中主要的技術,其目的為監視可歸屬原因的發生。近年來被提出之綜合管制圖(synthetic control chart)在監視製程平均值、不合格數比率與平均到達間隔時間之變化均有良好之績效,為方便推廣於監視其他類型之製程參數,本研究建構無特定監視製程參數之綜合管制圖,其為Shewhart管制圖與合格連串長度(conforming run length, CRL)管制圖所組成,並提出變動抽樣間隔(variable sampling intervals, VSI)計畫以進一步提升績效。Shewhart管制圖、VSI Shewhart管制圖與綜合管制圖皆可視為VSI綜合管制圖之特例。
建構完成之無特定監視製程參數之綜合管制圖及其變動抽樣間隔計畫分別應用於監視品質特性服從常態分配之三類製程參數:製程變異性、製程平均值與變異性與製程平均值向量。上述綜合管制圖分別為Shewhart樣本全距(sample range, R)或樣本標準差(sample standard deviation, S)管制圖、Shewhart最大值(Max)管制圖、Shewhart卡方( )或T平方( )管制圖與CRL管制圖所組成。上述綜合管制圖之操作、設計、與其他監視同類製程參數管制圖之績效比較及數據例子均有探討。績效比較的管制圖包含具連串法則(runs rules)之Shewhart管制圖、警告界限之Shewhart管制圖、累和(cumulative sum, CUSUM)管制圖、指數加權移動平均(exponentially weighted moving average, EWMA)管制圖。綜合管制圖之最佳化設計表格可供實際應用,若目前管制圖之績效未達使用者要求時,可執行VSI計畫使績效進一步提升。
Statistical process control (SPC) techniques have been greatly implemented in industries for improving product quality and saving production costs. As a primary tool among these techniques, control charts are widely used to detect the occurrence of assignable causes. Recently proposed synthetic control charts perform well for monitoring process mean, fraction nonconforming and mean of interarrival times. For monitoring other types of process parameters conveniently, this study proposes a general model of synthetic control chart with regard to non-specified process parameter monitored. The chart is a combination of the Shewhart chart and conforming run length (CRL) chart. The variable sampling intervals (VSI) schemes of the synthetic chart are constructed for improving chart performance further. The Shewhart chart, VSI Shewhart chart, and synthetic chart can be regarded as special cases of the VSI synthetic chart.
The general model of synthetic control chart and its VSI schemes are then, respectively, applied to three kinds of parameters of a normally distributed process: process variability, process mean and variability, and process mean vector. These synthetic charts are composed of Shewhart sample range (R) chart or sample standard deviation (S) chart, Shewhart Max chart, and Shewhart chi-squared ( ) chart or T-squared ( ) chart, and CRL chart, respectively. The operation, design, performance comparisons with other types of control charts such as Shewhart chart with runs rules, Shewhart chart with warning line, cumulative sum (CUSUM) chart and exponentially weighted moving average (EWMA) chart, and numerical example are described. Tables of optimally designed synthetic charts can assist the users to design the chart, and the presented VSI schemes can be implemented to further improve the chart performance if the current one is unsatisfactory.
中文摘要 Ⅰ
英文摘要 Ⅱ
誌謝辭 Ⅲ
目錄 Ⅳ
表目錄 Ⅶ
圖目錄 Ⅸ
第一章 緒論
1.1 研究動機與目的 1
1.2 研究方法與架構 3
1.3 研究範圍與章節架構 6
第二章 文獻探討
2.1 合格連串長度管制圖 8
2.1.1 不合格數管制圖之缺點 8
2.1.2 合格連串長度管制圖 9
2.2 綜合管制圖 12
2.2.1 綜合平均值管制圖 12
2.2.2 綜合不合格數管制圖 13
2.2.3 綜合指數管制圖 14
2.3 變異性管制圖 15
2.3.1 全距與標準差管制圖 15
2.3.2 警告界限全距與標準差管制圖 17
2.3.3 修正標準差管制圖 18
2.3.4 累和管制圖 18
2.3.5 指數加權移動平均管制圖 20
2.4 平均值與變異性管制圖 22
2.4.1聯合平均值-全距管制圖與聯合平均值-標準差管制圖 22
2.4.2 單一管制圖 23
2.5 多變量管制圖 26
2.5.1 卡方與T平方管制圖 27
2.5.2 連串法則卡方管制圖 28
2.5.3 累和管制圖 30
2.5.4 指數加權移動平均管制圖 31
2.6 變動抽樣間隔管制圖 31
2.6.1 變動抽樣間隔平均值管制圖 32
2.6.2 變動抽樣間隔不合格點數管制圖 33
2.6.3 變動抽樣間隔卡方管制圖 33
第三章 綜合管制圖及其變動抽樣間隔計畫之建構
3.1 綜合管制圖 35
3.2 綜合管制圖之變動抽樣間隔計畫 37
3.2.1 變動抽樣間隔計畫之描述 37
3.2.2 平均顯示訊號時間 40
3.2.3 與固定抽樣間隔計畫之比較 41
第四章 綜合變異性管制圖
4.1 操作步驟 43
4.2 參數設計 46
4.3 績效比較 52
4.4 變動抽樣間隔計畫 58
4.4.1 變動抽樣間隔計畫之描述 58
4.4.2 平均顯示訊號時間 60
4.4.3 與固定抽樣間隔計畫之比較 61
4.5 數據例子 68
第五章 綜合平均值與變異性管制圖
5.1 操作步驟 72
5.2 參數設計 76
5.3 具連串法則最大值管制圖 81
5.4 績效比較 84
5.5 變動抽樣間隔計畫 89
5.5.1 變動抽樣間隔計畫之描述 89
5.5.2 平均顯示訊號時間 90
5.5.3 與固定抽樣間隔計畫之比較 91
5.6 數據例子 97
第六章 綜合多變量管制圖
6.1 操作步驟 101
6.2 參數設計 104
6.3 績效比較 111
6.4 變動抽樣間隔計畫 115
6.4.1 變動抽樣間隔計畫之描述 115
6.4.2 平均顯示訊號時間 116
6.4.3 與固定抽樣間隔計畫之比較 118
6.5 數據例子 122
第七章 結論與未來研究方向
7.1 結論 125
7.2 未來研究方向 127
參考文獻 129
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