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系統識別號 U0026-0812200911115553
論文名稱(中文) 用偏移量與可容散度之比修正的製程能力指標
論文名稱(英文) The modifications of capability indices based on the ratio of shift to allowable spread
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 92
學期 2
出版年 93
研究生(中文) 王牡丹
研究生(英文) Mu-dan Wang
電子信箱 wmd0608@yahoo.com.tw
學號 r2691110
學位類別 碩士
語文別 中文
論文頁數 109頁
口試委員 口試委員-陳坤盛
指導教授-呂金河
口試委員-潘浙楠
中文關鍵字 不良率  非對稱規格  製程能力指標  對稱規格 
英文關鍵字 asymmetric tolerances  process yield  symmetric tolerances  process capability indices 
學科別分類
中文摘要   由於製程能力指標提供了一簡單的數值方法就能決定製程是否有能力製造出符合顧客要求的產品,所以近年來在工業品管上廣泛的運用。常用的製程能力指標有Cp、Cpk、Cpm及Cpmk,指標Cpm及Cpmk為了對製程平均值偏移目標值做出懲罰,分別在Cp及Cpk定義式的分母部分加了(-T)2項,由於這部分並沒有考慮到當製程平均較靠近規格界限或是製程變異較大時其不良率會增加的問題,我們認為製程平均值偏移目標值的懲罰須與製程平均值離規格界限之遠近及製程變異數之大小有關,因此在本文中提出五個新定義的指標。
  本論文的第三章比較了近年來各學者提出的指標,並在常態假設下,推導出新指標估計式的機率密度函數,且針對規格不對稱及規格對稱下,分析指標估計式的統計性質,結果顯示本文提出的新指標的表現並不亞於其他指標。最後部份,我們提出二個實例來做新指標實際運用的說明,也討論了指標值與不良率的關係。
英文摘要   Since the PCI (process capability index) provides a simple numerical measure on whether the production process is capable of producing the qualified products that satisfied the customer’s demands, the PCI is applied extensively in the industry. The most used PCI’s are Cp, Cpk, Cpm, and Cpmk. Moreover, in order to add additional penalties for being off-target, Cpm and Cpmk add a term (-T)2 in the denominator of the definitions of the Cp and Cpk, respectively. However, when they use these penalties they don’t consider the problems that the non-conforming is increased when the process center is closer to the specification limits or the process variance is larger, we suggest that the penalty should be related to the distance between the process center and the specification limits and the magnitude of the process variance. Therefore, the new definitions of five PCI’s are considered in this thesis.
  In chapter three, we compare the performance of PCI’s which are put forward in recent years. Moreover, under the hypothesis of the normal distribution we also demonstrate the sampling distributions of the index estimators for our new PCI’s and discuss the corresponding statistical properties under the asymmetric and symmetric tolerances, which show that our new PCI’s are as good as the others. Two numerical examplea are provided in chapter four to illustrate the application of our new PCI’s, and we also discuss the correlation between the values of the PCI’s and the process yield.
論文目次 第一章 緒論 1
第二章 文獻探討 7
2.1 Cp(u,v) 7
2.2 Cpa(u,v) 8
2.3 Cpm” 9
2.4 Spk 9
2.5 Cpm”’(s,t)及Cpm(s,t) 11
第三章 新指標的定義及其性質 13
3.1 新指標的定義 14
3.2 新舊指標的比較 17
3.3 Cpr及Cpr*估計式的抽樣分配 21
3.4 Cpr及Cpr*估計式的修正及其統計性質 27
3.5 Cprk及Cprk*估計式的統計性質 30
3.6 指標Cpr的進一步修正 35
第四章 實例 41
第五章 結論與建議 52
參考文獻 54
附錄A 56
附錄B 61
附錄C 66
附錄D 67
附錄E 75
附錄F 82
附錄G 90
附錄H 97
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潘浙楠、李文瑞 (2002). 品質管理,俊傑書局,台北市。
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