進階搜尋


 
系統識別號 U0026-0812200911523834
論文名稱(中文) 主成份分析法在制定多變量製程能力指標上之應用研究
論文名稱(英文) Development of A New Multivariate Process Capability Index using Principal Component Analysis
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 94
學期 2
出版年 95
研究生(中文) 陳彥廷
研究生(英文) Yen-Ting Chen
電子信箱 ytchen@stat.ncku.edu.tw
學號 R2693114
學位類別 碩士
語文別 中文
論文頁數 121頁
口試委員 口試委員-鄭春生
口試委員-呂金河
指導教授-潘浙楠
中文關鍵字 主成份分析法  塑料方形扁平式封裝(QFP)製程  多變量製程能力指標 
英文關鍵字 quad flat package(QFP)  multivariate process capability index  principal component analysis 
學科別分類
中文摘要 產品之良窳是企業永續經營的關鍵,就目前科技產業而言,產品的功能越來越多,製程亦日趨複雜,僅憑單一品質特性並不足以反映產品品質,一般而言,工業製程中常有多個彼此相關的品質特性皆可能造成製程異常。為了建立多重品質特性下之製程能力指標,Chan (1991) 利用馬氏距離估算多變量製程能力指標。Taam et al. (1993) 提出以修正的規格區域估算多變量製程能力指標,Hubele et al. (1991)則以修正的製程區域估算多變量製程能力指標。潘與李(2003)則考慮產品品質特性間的相關程度並對Taam et al. (1993)所提之指標做進一步修正,提出一組估算多變量製程之NMCp及NMCpm指標。NMCp及NMCpm指標雖可如實反應多變量製程之表現,但其修正規格區域會有高估的情形。本研究主要是利用主成份分析法中主成份軸正交的幾何概念,提出以另一種制定多變量製程能力指標的方式並對上述修正規格區域再進行轉軸與調整。吾人所提出之新多變量製程能力指標PMCp及PMCpm與上述各種多變量製程能力指標相較,更能準確反映製程實際的表現。
最後本研究藉由Sultan(1986)所提出產品硬度及拉抗強度之實例及Pan, J. B.(2004)文中塑料方形扁平式封裝(QFP)製程之資料為例說明PMCp及PMCpm多變量製程能力指標可正確評估多重品質特性製程在高相關下的表現。此外,以主成份分析法制定PMCp及PMCpm指標的方式更容易進行具三個以上產品品質特性之製程能力分析。

關鍵詞:多變量製程能力指標、主成份分析法、塑料方形
扁平式封裝(QFP)製程



英文摘要 Good quality of products is the key factor of business success. With the advent of modern technology, manufacturing processes become highly sophisticated and merely single quality characteristic can not reflect the product quality. Generally speaking, the abnormality of an industrial process is caused by the problems of several interrelated quality characteristics. In order to establish the multivariate process capability index, Chan(1991) use Mahalanobis distance to calculate multivariate process capability index. Taam et al.(1993) use a modified tolerance region to estimate multivariate process capability index and Hubele et al.(1991) use a modified process region to estimate multivariate process capability index. In this paper, the multivariate process capability index established by Taam et al. has been modified according to the correlation of quality characteristics. On new PMCp and PMCpm indices are developed using principal component analysis. The modified tolerance region is adjusted and rotated using the geometric concept of orthogonal principal axes. The results of a comparative study shows that new PMCp and PMCpm indices can correctly reflect the real process capability.
Finally, two realistic examples of a product’s hardness and tensile strength as well as the quad flat package(QFP) process data analysis further demonstrate that the new PMCp and PMCpm indices can correctly evaluate the multivariate process capability.

Key words:multivariate process capability index,
principal component analysis, quad
flat package (QFP)



論文目次 目錄.....................................................................I
表目錄..................................................................III
圖目錄................................................................... V
第一章 緒論.............................................................. 1
1.1 研究背景與動機........................................................1
1.2 研究目的..............................................................1
1.3 研究架構與流程........................................................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
2.2.1 多變量製程能力指標Cpm...............................................5
2.2.2 多變量製程能力指標[CpM,PV,LI].......................................6
2.2.3 多變量製程能力指標Cp與MCpm..........................................8
2.2.4 多變量製程能力指標C*pM.............................................10
2.2.5 多變量製程能力指標NMCp與NMCpm......................................10
2.2.6 主成份分析法(Principal Component Analysis:PCA)....................13
2.2.7 主成份分析法:多變量製程能力指標MCp與MCpk..........................15
2.2.8 主成份分析法:多變量製程能力指標MC*p與MC*pk........................17
第三章 新多變量製程能力指標之修正與推導..................................20
3.1 新多變量製程能力指標之修正...........................................20
3.2 主成份轉軸後製程區域橢圓與修正規格區域橢圓之長短軸長.................24
3.3 與其他多變量製程能力指標之比較.......................................25
第四章 各種多變量製程能力指標之電腦模擬與比較............................26
4.1 各種多變量製程能力指標之比較.........................................26
4.1.1 多變量標準常態資料之模擬...........................................26
4.2 電腦模擬結果比較之標準...............................................27
4.3 多變量常態分配下各種多變量製程能力指標之比較.........................28
4.3.1 各種多變量製程能力指標在多變量常態分配之下之表現(二變量)...........28
4.3.1.1 多變量(二變量)製程能力指標之估計標準差、偏差(Bias)與均方差(MSE)..44
4.3.2 各種多變量製程能力指標在多變量常態分配之下之表現(三變量)...........52
4.3.2.1 多變量(三變量)製程能力指標之估計標準差、偏差(Bias)與均方差(MSE)..61
4.4 各種多變量製程能力指標優缺點之比較與製程評估準則之建立...............69
4.5 多變量製程能力指標信賴區間的建立.....................................71
第五章 敏感度分析與數值實例之探討........................................80
5.1 敏感度分析...........................................................80
5.1.1 樣本大小參數(n)....................................................80
5.1.2 相關係數參數(ρ)....................................................81
5.2 建立計算多變量製程能力指標與製程評估之流程...........................82
5.3 數值實例之探討.......................................................84
5.3.1 以Sultan, T. L.之資料為例..........................................84
5.3.2 以QFP焊接製程之資料為例............................................93
第六章 結論與未來研究方向...............................................100
6.1 結論................................................................100
6.2 未來研究方向........................................................102
參考文獻................................................................103
附錄A...................................................................106
附錄B...................................................................108
附錄C...................................................................109

參考文獻 1. Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988), “A New Measure of
Process Capability: ,” Journal of Quality Technology, Vol. 20, No. 3, pp.
162-173.
2. Chan, L. K., Cheng, S. W. and Spiring, F. A. (1991), “A Multivariate
Measure of Process Capability,” International Journal of Modeling and
Simulation, Vol. 11, No. 1, pp. 1-6.
3. Chen, S., M., Hsu, Y., S. and Pearn, W. L. (2003), “Capability Measures for
M-dependent Stationary Processes,” Statistics, Vol. 37, No. 2, pp. 145-168.
4. Choi, B. C. and Owen, D. B. (1990), “A Study of A New Process Capability
Index,” Commun. Statist. − Theory Method, Vol. 19, No. 4, pp. 1231-1245.
5. Croux, C. and Haesbroeck, G. (2000), “Principal Component Analysis Based on
Robust Estimators of the Covariance or Correlation Matrix:Influence
Function and Efficiencies,” Biometrika, Vol. 87, No. 3, pp.603-618.
6. Hubele, N. F., Shahriari, H. and Cheng, C-S. (1991), A Bivariate Process of
Capability Vector in Statistics and Design in Process Control, Statistical
Process Control in Manufacturing edited by J. B. Keats, and D. C.
Montgomery. Marcel Dekker, New York, NY. pp. 299-310.
7. Jackson, J. E. (1980), “Principal Component and Factor Analysis:Part I –
Principal Components,” Journal of Quality Technology, Vol. 12, No. 4, pp.
201-213.
8. Johnson, N. L., Kotz, Samuel and Pearn, W. L. (1994), “Flexible Process
Capability Indices,” Pakistan Journal of Statistics, Vol. 10, No. 1, pp. 23-
21.
9. Johnson, R. A. and Wichern, D. N. (1998), Applied Multivariate Statistical
Analysis, Prentice Hall International, Upper Saddle River, N.J..
10.Kane, V., E. (1986), “Process Capability Indices,” Journal of Quality
Technology, Vol. 18, No. 1, pp. 41-52.
11.Kocherlakota, S. and Kocherlakota, K. (1991), “Process Capability Index:
Bivariate normal distribution,” Commun. Statist. − Theory Method, Vol. 20,
No. 8, pp. 2529-2547.
12.Kotz, S. and Lovelace, C. R. (1998), Process capability indices in theory
and practice, Arnold, New York, London.
13.Kotz, S. and Johnson, N. L. (1993), Process Capability Indices, Chapman &
Hall, London.
14.Kotz, S. and Johnson, N. L. (2002), “Process Capability Indices – A
Review, 1992 – 2000,” Journal of Quality Technology, Vol. 34, No.1, pp. 2-
19.
15.Lin, H. C. (2004), “The Measurement of A process Capability for Folder
Normal Process Data,” International Journal of Advanced Manufacturing
Technology, Vol. 24, pp. 223-228.
16.Lin, Y. C. and Chou, C. Y. (2005), “On the Design of Variable Sample Size
and Sampling Intervals Charts Under Non-normality,” International Journal
of Production Economics, Vol. 96, pp. 249-261.
17.Pan, Jianbiao (2004), “Critical Variables of Solder Paste Stencil Printing
for Micro-BGA and Fine-Pitch QFP,” IEEE Transactions, Vol. 27, pp. 125-132.
18.Pearn, W. L. and Chen, K. S. (1997-98), “Multivariate Performance Analysis:
A Case Study,” Quality Engineering, Vol. 10, No. 1, pp. 1-8.
19.Pearn, W. L., Kotz, S. and Johnson, N. L. (1992), “Distributional and
Inferential Properties of Process Capability Indices,” Journal of Quality
Technology, Vol. 24, No. 8, pp. 216-231.
20.Spiring, F., Leung, B., Chen, S. and Yeung, A. (2003), “A Bibliography of
Process Capability Papers,” Quality Reliability Engineering International,
Vol. 19, pp. 445-460.
21.Sultan, T. L. (1986), “An Acceptance Chart for Raw Materials of Two
Correlated Properties,” Quality Assurance, Vol. 12, pp. 70-72.
22.Taam, W., Subbaiah, P. and Liddy, J. W. (1993), “A Note on Multivariate
Capability Indices,” Journal of Applied Statistics, Vol. 20, No. 3, pp. 339-
351.
23.Wang, C. H. (2005), “Constructing Multivariate Process Capability Indices
for Short-Run Production,” International Journal of Advanced Manufacturing
Technology, Vol. 26, pp. 1306-1311.
24.Wang, F. K. and Chen, J. C. (1998-99), “Cpability Index Using Principal
Component Analysis,” Quality Engineering, Vol. 11, No. 1, pp. 21-27.
25.Wang, F. K. and Du, T. C. T. (2000), “Using Principal Component Analysis in
Process Performance for Multivariate Data,” The International Journal of
Management Science, Vol. 28, pp. 185-194.
26.Wang, F. K., Hubele, N. F., Lawrence, F. P., Miskulin, J. D. and Shahriari,
H. (2000), “Comparison of Three Multivariate Process Capability Indices,”
Journal of Quality Technology, Vol. 32, No. 3, pp. 263-275.
27.潘浙楠、李文瑞(2003),品質管理,華泰書局。
28.潘浙楠、李仁凱(2003),多重品質特性下製程能力指標之比較研究,品質學報,第十
期,第一卷,149-176頁。
29.潘浙楠、李婉瑜(2005),修正型損失函數在制定經濟工程規格上之比較研究,accepted
by品質學報。
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2009-06-23起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2009-06-23起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw