臺灣博碩士論文加值系統

隨著工業製程複雜度增加，影響製程表現之品質特性不再只有一種，為同時考量多種品質特性，從而發展出多變量製程能力指標（Multivariate Process Capability Index，MPCI）。目前已有多位學者提出相關多變量製程能力指標，但多假設產品品質特性為常態，然而，許多工業製程之品質特性無法滿足此假設，因此，本研究藉由資料深度（Data Depth）概念說明如何定義製程資料規格區域，進而提出兩個無須分佈假設之多變量製程能力指標。本研究將分別藉由統計模擬及數值實例，評估提出方法的表現及說明如何運用本研究提出之指標來評估製程的表現。

Generally, an industrial product has more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several multivariate process capability indices have been developed in the past. Most of the proposed in the literature MPCIs are defined under an assumption, that process quality characteristics are normally distributed. However, this assumption may not hold in practice In this research, based on the data depth concept, we proposed two multivariate process capability indices, which could be used regardless on data distribution. Finally, simulation results show that our proposed indices outperform than existing model. A numerical example further demonstrate the usefulness of the proposed indices.

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 文獻探討 4
2.1 資料深度（Data Depth） 4
2.1.1半空間深度函數（Halfspace Depth） 5
2.1.2單純形深度函數（Simplicial Depth） 5
2.1.3馬氏深度函數（Mahalanobis Depth） 6
2.1.4投影深度函數（Projection depth） 6
2.1.5空間深度函數（Spatial depth） 6
2.1.6 Zonoid深度函數 7
2.1.7 歐式深度函數（Euclid Depth） 7
2.2 單變量製程能力指標 8
2.3 多變量製程能力指標 9
2.3.1 多變量製程能力指標 MCp 與 MCpm 9
2.3.2 多變量製程能力指標 MCp*、MCpk*、MCpm*與 MCpmk* 10
2.3.3 多變量製程能力指標 Cn 11
2.3.4多變量製程能力指標 NMCp 與 NMCpm 12
2.3.5 多變量製程能力指標 MPCDD 13
2.4複式信賴區間 14
第三章 研究方法與結果 15
3.1 多變量製程區域之制定 15
3.2 多變量製程能力指標之制定 17
第四章 模擬與實例分析 19
4.1 多變量製程能力指標之模擬 19
4.1.1模擬資料設定 19
4.1.2非常態分配之製程能力指標比較 20
4.1.3非常態分配製程偏移之製程能力指標 24
4.2 實例分析 28
第五章 結論與未來研究方向 31
5.1 結論 31
5.2 未來研究方向 32
參考文獻 33
附錄A 35

1.Chan, L. K., Cheng, S. W., ＆ Spiring, F. A. (1988). A new measure of process capability. Journal of Quality Technology, 20(3), 162-175.
2.Ciupke, K. (2016). Multivariate process capability index based on data depth concept. Quality and Reliability Engineering International, 32(7), 2443-2453.
3.Efron, B. (1987). Better bootstrap confidence intervals. Journal of the American statistical Association, 82(397), 171-185.
4.Einmahl, J. H., Li, J., ＆ Liu, R. Y. (2015). Bridging centrality and extremity: Refining empirical data depth using extreme value statistics. The Annals of Statistics, 43(6), 2738-2765.
5.González, I., ＆ Sánchez, I. (2009). Capability indices and nonconforming proportion in univariate and multivariate processes. The International Journal of Advanced Manufacturing Technology, 44(9-10), 1036-1050.
6.Grau, D. (2007). Multivariate capability indices for processes with asymmetric tolerances. Quality Technology ＆ Quantitative Management, 4(4), 471-488.
7.Joseph M. Juran, Frank M. Gryna, Richard S. Bingham (1974) Quality control handbook. McGraw-Hill, New York.
8.Kane, V. E. (1986). Process capability indices. Journal of quality technology, 18(1), 41-52.
9.Mosler, K.(2013). Depth statistics. In Robustness and complex data structures. Festschrift in Honour of Ursula Gather, Springer, Berlin, 17-34.
10.Li, J., ＆ Liu, R. Y. (2008). Multivariate spacings based on data depth: I. Construction of nonparametric multivariate tolerance regions. The Annals of Statistics, 36(3), 1299-1323.
11.Pan, J. N., ＆ Lee, C. Y. (2010). New capability indices for evaluating the performance of multivariate manufacturing processes. Quality and Reliability Engineering International, 26(1), 3-15.
12.Pearn, W. L., Kotz, S., ＆ Johnson, N. L. (1992). Distributional and inferential properties of process capability indexes. Journal of Quality Technology, 24(4), 216-231.
13.Taam, W., Subbaiah, P., ＆ Liddy, J. W. (1993). A note on multivariate capability indices. Journal of applied statistics, 20(3), 339-351.
14.Yeh, A. B., ＆ Chen, H. (2001). A nonparametric multivariate process capability index. International Journal of Modelling and Simulation, 21(3), 218-223.
15.Zuo, Y., ＆ Serfling, R. (2000). General notions of statistical depth function. Annals of statistics, 28(2), 461-482.
16.石維謙. (2012). 望目及望小特性下, 非常態多變量製程能力指標之制定與評估. 成功大學統計學系學位論文, 1-62.