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系統識別號 U0026-2312200921540900
論文名稱(中文) 多變量損失函數與製程能力指標關係之探討與研究
論文名稱(英文) The Relationship between Multivariate Loss Functions and Process Capability Indices
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 98
學期 1
出版年 98
研究生(中文) 李晉誠
研究生(英文) Jin-Cheng Lee
學號 r2696407
學位類別 碩士
語文別 中文
論文頁數 57頁
口試委員 指導教授-潘浙楠
口試委員-鄭春生
口試委員-呂金河
中文關鍵字 多變量田口二次損失函數  多變量製程能力指標  關鍵品質特性 
英文關鍵字 multivariate Taguchi loss functions  multivariate process capability indices  key characteristics 
學科別分類
中文摘要 傳統上工業界係透過管制圖與直方圖對製程進行長期與短期製程能力分析,藉以了解關鍵品質特性的表現。當發現製程表現不佳時,便著手進行品質改善。而改善的成效除了藉由製程能力指標反映改善前後的結果外,工程師們亦應透過成本/損失的估算以凸顯品質問題的嚴重性,使高階主管能重視品質改善的迫切性而予以全力支持。因此透過損失成本的概念來探討多變量製程能力指標及其所對應之期望損失再進行製程改善,將更能反映製程改善的成效。
本研究係探討並建立產品品質特性呈望目及望小特性情形下,Taam et al. (1993)之多變量製程能力指標MCp和MCpm及Pan and Lee (2009) 所提出之新多變量製程能力指標NMCp和NMCpm,與多變量田口二次之期望損失間的關係式,以方便從事品管人員在進行對多變量製程期望損失估算時的參考。此外,我們將二變量常態分配下多變量製程能力指標MCp值及其所對應之不良率繪製成可供業界查詢之對照圖。最後,我們以兩個數值實例說明藉由多變量製程能力指標估算期望損失之流程與步驟。
英文摘要 Traditionally, engineers perform the long-term and short-term process capabilities to analyze the performance of key characteristics by using control charts and histograms. Quality improvement actions will be taken if the process is not capable of meeting specifications. In addition to use multivariate process capability indices to reflect the results of quality improvement, engineers should highlight the seriousness of the quality problem through cost /loss estimation, so the senior managers will pay more attention to the urgent need of quality improvement projects and render their support. In the research, we show that the expected quality losses can be estimated by the given multivariate process capability indices. The relationship between various formulae of multivariate process capability indices and Taguchi’s quadratic losses that been established for the nominal-the-better and the smaller-the- better case. Then, the correspondence figure between various MCp indices and then nonconforming rates are provided.
Finally, two numerical examples are given to demonstrate how the expected losses can be estimated by the given multivariate process capability indices. Hopefully, the research results are useful for quality practitioners in estimating the quality losses for multivariate manufacturing process.
論文目次 第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究架構 2
第二章 文獻回顧與探討 4
2.1 單變量製程能力指標 4
2.2 多變量製程能力指標 5
2.3 損失函數 9
2.3.1 傳統觀念的損失函數 9
2.3.2 田口二次損失函數 11
2.3.3 The Inverted Normal Loss Function (INLF) 13
2.3.4 The Revised Inverted Normal Loss Function (RINLF) 14
2.4 多變量田口二次損失函數 16
第三章 多變量製程能力指標與期望損失之關係 18
3.1 多變量製程能力指標與期望損失公式之整理 18
3.2 多變量製程能力指標MCp及MCpm與期望損失之關係 20
3.3 新多變量製程能力指標NMCp及NMCpm與期望損失之關係 25
3.4 多變量製程能力指標與不良率之對應關係 28
第四章 數值實例之探討 34
4.1 建立藉由多變量製程能力指標估算期望損失之方式 34
4.2 數值實例之探討 36
第五章 結論與未來研究方向 43
5.1 結論 43
5.2 未來研究方向 44
參考文獻 45
附錄A 48
附錄B 52
附錄C 56
參考文獻 1. Ayyub, B. M. (2003), Risk Analysis in Engineering and Economics, Boca Raton, FL: Chapman & Hall/CRC.
2. Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988), “A New Measure of Process Capability: Cpm,” Journal of Quality Technology, 20(3), pp.162-175.
3. Chan, L. K., Cheng, S. W. and Spiring, F. A. (1991), “A Multivariate Measure of Process Capability,” International Journal of Modeling and Simulation, 11(1), pp.1-6.
4. Johnson, R. A. and Wichern, D. W. (2007), Applied Multivariate Statistical Analysis, Pearson Prentice Hall, Upper Saddle River, New Jersey.
5. Juran, J. M. (1974), Quality Control Handbook, McGraw-Hill, New York.
6. Kane, V. E. (1986), “Process Capability Indices,” Journal of Quality Technology, 18(1), pp.41-52.
7. Mathai, A. M. and Provost, S. B. (1992), Quadratic Forms in Random Variables, Marcel Dekker, New York.
8. Pan, J. N. and Wang, J. H. (2000), “A Study of Loss Functions for Product Interference Analysis,” Industrial Engineering Research, 2(1), pp.80-100.
9. Pan, J. N. and Lee, C. Y. (2009), “New Capability Indices for Evaluating the Performance of Multivariate Manufacturing Processes,” Quality and Reliability engineering International.
10. Pan, J., Tonkay, G. L., Storer, R. H., Sallade, R. M. and Leandri, D. J. (2004), “Critical Variables of Solder Paste Stencil Printing for Micro-BGA and Fine-Pitch QFP,” IEEE Transactions on Electronics Packaging Manufacturing, 27(2), pp.125-132.
11. Pearn, W. L., Kotz, S. and Johnson, N. L. (1992), “Distributional and Inferential Properties of Process Capability Indices,” Journal of Quality Technology, 24(4), pp.216-231.
12. Pignatiello, J. J. (1993), “Strategies for Robust Multiresponse Quality Engineering,” IIE Transactions, 25(3), pp. 5-15.
13. Spiring, F. A. (1993), “The Reflected Normal Loss Function,” The Canadian Journal of Statistics, 21(3), pp.321-330.
14. Sultan, T.L. (1986), “An Acceptance Chart for Raw Materials of Two Correlated Properties,” Quality Assurance, 12(3), pp. 70-72.
15. Taam, W., Subbaiah, P. and Liddy, J. W. (1993), “A Note on Multivariate Capability Indices,” Journal of Applied Statistics, 20(3), pp. 339-351.
16. Taguchi, G. (1986), Introduction to Quality Engineering: Designing Quality Into Products and Process, Asian Productivity Organization, Tokyo.
17. 潘浙楠、李文瑞 (2003),品質管理,華泰書局。
18. 潘浙楠、李育宗 (2001),單邊規格下產品損失函數之研究,品質學報,第八卷,第一期,39- 66頁。
19. 潘浙楠、李婉瑜 (2006),修正型損失函數在制定經濟工程規格上之應用研究,品質學報,第十三卷,第三期,241-256頁。
20. 潘浙楠、林瑞益 (2003),製程能力指標與損失函數關係探討與研究,中國統計學報,第四十一卷,第二期,211- 248頁。
21. 潘浙楠、陳彥廷 (2007),主成份分析法在制定多變量製程能力指標上之應用研究,品質學報,第十四卷,第三期,317- 335頁。
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