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研究生:范振球
論文名稱:靴環法與參數式模擬在檢定製程能力上的應用
論文名稱(外文):Application of Bootstrap and Parametric Simulation in Examining the Process Capability Cpu
指導教授:馮文俊馮文俊引用關係
學位類別:碩士
校院名稱:明新科技大學
系所名稱:工業工程與管理研究所
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:2009
畢業學年度:97
語文別:中文
論文頁數:99
中文關鍵詞:製程能力指數蒙地卡羅模擬參數式模擬靴環法
外文關鍵詞:Process Capability IndicesMonte Carlo simulationParametric simulationBootstrap
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製程能力指數 (Process Capability Indices, PCIs) 是製造業衡量製程是否符合產品規格的重要工具,其主要功能在於有效控制製程以製造出高品質的產品。為檢定某公司產品品質製程是否達到既定標準,本研究使用SAS IML程式執行蒙地卡羅(Monte Carlo)、參數式模擬(Parametric simulation)與靴環法(bootstrap)等反覆抽樣方法以及檢定假說 對 ;主要目的在檢查以參數式模擬與靴環法模擬得出的 的抽樣分配檢定假說 對 時的實用性。考慮的非常態分配包含均勻與Gamma;常態分配亦屬研究範圍,做為推展應用蒙地卡羅、參數式模擬與靴環法到非常態特性分配的比較基礎。
主要研究結果包含:(一)參數式模擬的效果高於靴環法。(二)靴環法在檢定常態與均勻和Gamma分配資料時的正確檢定機率沒有差異。(三)參數式模擬在檢定Gamma分配資料時的效果較佳。(四)參數式模擬與靴環法在樣本大小 時的檢定效果較差。




Keyword:製程能力指數、蒙地卡羅模擬(Monte Carlo simulation)、參數式模擬(Parametric simulation)、靴環法(Bootstrap)。

Abstract
Process Capability Indices (PCIs) are important tools for the manufacturing industry to examine whether the manufacturing process meets the product specifications. The main function of PCIs is to effectively control the manufacturing process to produce high-quality products. To check whether the manufacturing process of a certain company meets the intended standards, this research used SAS IML program to implement Monte Carlo, Parameter Simulation, and Bootstrap re-sampling methods, and to test the hypotheses versus . The main purpose was to examine the practicality of using sampling distributions of obtained by parameter simulation and bootstrap methods to test the above hypotheses.
The distributions considered were Normal, Uniform, and Gamma. The results showed that:(1)parameter simulation performed better than bootstrap did, (2)the correct test proportions of bootstrap on normal, uniform, or Gamma had no significant differences, (3)the correct test proportions of parameter simulation on Gamma were higher than those on normal and Uniform, and (4) parameter simulation and bootstrap performed worse with small samples.


Keywords:Process Capability Indices, Parametric Simulation, Bootstrap.

目 錄
中文摘要 .…………………………………..……………………………… ii
英文摘要 .…………………………………..……………………………… iii
致謝……………………………………………………..……………………… iv
目錄.…………………………………………………...……………………. v
表目錄…………………………………………………………………………vi
圖目錄………………………………………………………………………vii
第一章 緒論…. .……………………………………………………….…… 1
1.1 研究背景與動機…..………………………………...…………… 1
1.2 研究目的……...………………………………………...………… 3
1.3 研究範圍與限制…………………..…………………...………… 4
1.4 研究流程……...………………………………………...………… 4
第二章 文獻與理論………………………………..…….……….……. …5
2.1 Monte Carlo模擬……………………………………..………5
2.2參數式模擬…………………………………………….………8
2.3 Bootstrap方法…..…………………………………………….9
第三章 研究方法………………….…….…….……………………….11
第四章 模擬結果…….…………………………………………….……. …17
第五章 結論…….……………………………………………..….……. …26
參考文獻 …………………………………………………………………….30
附錄 …………………………………………………………………………..32
附錄一 常態資料分配表…………………………………………………………….33

附錄二 均勻資料分配表…………………………………………………………….41

附錄三 Gamma資料分配表…………………………………………………………49

參考文獻
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3. Christopher Z. Mooney, Robert D. Duval. Bootstrapping : a nonparametric approach to statistical inference, Sage University papers series. no.1993,pp 07-095.
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5. Cheng,S.W.Is the process capable? Tables and graphs in assessing , Quality Engineering,Vo1.4No.4,1992,pp.563-76.
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7. Chen, K. S.. “Estimation of the process incapability index”. Communications in Statistics-Theory and Methods, 27(4),1998, 1263-1274.
8. Chen, K. S., “Estimatiom of the Process Incapability Index”, Communications in Statistics-Theory and methods, 27(5),1998, pp. 1263-1274 .
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10. Efron, B. Bootstrap methods: another look at the Jackknife. The Annals of Statistics, 7, 1979,1-26.
11. Franklin, L. A. and Wasserman, G. S. “Bootstrap lower confidence limits for capability indices. ”Journal of Quality Technology, 24(4), 1992,pp158-172.
12. Harry,M.J.The nature of six sigma quality,Motorola,Schaumburg,IL1988,
13. Kane, V.E. Process capability indices, Journal of Quality Technology, Vol. 18 No.1, 1986,pp.41-52.
14. Pearn, W. L. and Chen, K. S.A practical implementation of the process capability index .1996a,
15. Pearn, W. L. and Chen, K. S.Marking decisions in assessing process capability index .1996b,
16. Pearn, W. L. and Chen, K. S. One-sided capability indices CPU and CPL: decision making with sample information, International Journal of Quality & Reliability Management, 19, 2002,pp221-245.
17. Pearn, W. L. and Shu, M. H. An algorithm for calculating the lower confidence bounds of CPU and CPL with application to low-drop-out regulators, Microelectronics Reliability, 43(3), 2003,pp495-502.
18. Pearn, W.L., Kotz, S., Johnson, N.L. Distributional and inferential properties of process capability indices, Journal of Quality Technology, Vol. 24 No.4, 1992,pp.216-33.
19. Tong, L. I., and Chen, J. P.,“Lower confidence limits of process capability indices for non-normal process distributions,”International Journal of Quality &Reliability Management, 15(8)*(9),1998, pp.907-919.

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