多维系统优化中马氏田口强相关问题研究

工业工程 ›› 2012, Vol. 15 ›› Issue (2): 71-77.

多维系统优化中马氏田口强相关问题研究

1.上海大学管理学院，上海 200444； 2.天津大学管理与经济学部，天津 300072

出版日期:2012-04-30 发布日期:2012-05-17
作者简介: 韩亚娟(1979-),女, 陕西省人, 讲师, 博士, 主要研究方向为质量管理、工业工程.
基金资助:
高等学校博士学科点专项科研基金(新教师类)资助项目(20093108120023); 国家自然科学基金重点资助项目(70931004); 国家自然科学基金(青年基金)资助项目(71101086)

Multicollinearity Analysis of MahalanobisTaguchi System Method in Multidimensional System Optimization

1.School of Management, Shanghai University, Shanghai 200444, China;
2. Faculty of Management and Economics, Tianjin University, Tianjin 300072, China

Online:2012-04-30 Published:2012-05-17

摘要/Abstract

摘要： 对传统马氏田口方法进行了介绍，分析了多维系统马氏田口优化中强相关问题的影响，提出了解决强相关问题的新方法——马氏田口MP广义逆矩阵法。相对于传统的马氏田口逆矩阵法，马氏田口MP广义逆矩阵法具有存在性、唯一性和通用性的优点，能更有效地应用于多维系统的优化实践。通过对某医院血粘度诊断系统的优化与分析，进一步证实了马氏田口MP广义逆矩阵法的有效性。

关键词: 多维系统优化, 马氏田口, 强相关问题, MP广义逆矩阵

Abstract: After the effect of multicollinearity on the existing MahalanobisTaguchi system (MTS) methods in multidimensional system optimization is analyzed, a new method called MoorePenrose (MP) generalized inverse matrix method of MTS is put forward. Then, comparison is made between the new method and the existing ones. It shows that the new method outperforms the existing ones in three ways: 1) it guarantees the existence of a solution; 2) the solution obtained is unique; and 3) the solution is a generic one. Thus, it is more effective than the existing ones in multidimensional system optimization. As a case study, the new method is used for the optimization of a bloodviscositydiagnose system and the results obtained in this paper are verified.

Key words: multidimensional system optimization, Mahalanobis Taguchi system, multicollinearity, Moore Penrose (M P)generalized inverse matrix

韩亚娟1，何桢2，宋国防1. 多维系统优化中马氏田口强相关问题研究[J]. 工业工程, 2012, 15(2): 71-77.

Han Yajuan1, He Zhen2, Song Guofang1. Multicollinearity Analysis of MahalanobisTaguchi System Method in Multidimensional System Optimization[J]. Industrial Engineering Journal , 2012, 15(2): 71-77.

参考文献

［1］Taguchi G, Jugulum R. New trends in multivariate diagnosis［J］. The Indian Journal of Statistics, 2000, 62B (2): 233-248. ［2］Taguchi G, Chowdhury S, Wu Y. The Mahalanobis Taguchi system［M］. New York: McGraw Hill, 2001. ［3］Nagao M, Yamamoto M, Suzuki K, et al. A face identification system based on the Mahalanobis Taguchi system［J］. International Transactions in Operational Research,2001,8(1):31-45. ［4］薛跃, 韩之俊, 盛党红. MTS法用于上市公司财务质量评估初探［J］. 数理统计与管理, 2005,24(1):81-85. Xue Y, Han Z J, Sheng D H. Evaluation of company financial quality by using MTS［J］. Application of Statistics and Management,2005,24(1):81-85. ［5］Cudney E A, Paryani K, Ragsdell K M. Applying the MahalanobisTaguchi system to vehicle handling［J］. Concurrent Engineering, 2006, 14(4): 343-354. ［6］Itagaki M, Takamiya E, Watanabe K. Diagnosis of quality of fresh water for carbon steel corrosion by Mahalanobis distance［J］.Corrosion Science,2007,49(8):3408-3420. ［7］Khanzode V V, Maiti J. Implementing MahalanobisTaguchi system to improve casting quality in grey iron foundry［J］.International Journal of Productivity and Quality Management,2008,3(4):444-456. ［8］Lee Y C, Teng H L. Predicting the financial crisis by MahalanobisTaguchi system–examples of Taiwan’s electronic sector［J］. Expert Systems with Applications, 2009,36(4):7469-7478. ［9］Saygin C, Mohan D,Sarangapani J. Real time detection of grip length during fastening of bolted joints: a Mahalanobis Taguchi system (MTS) based approach［J］. Journal of Intelligent Manufacturing,2010,21(4):377-392. ［10］Yang T H, Cheng Y T. The use of MahalanobisTaguchi system to improve flip chip bumping height inspection efficiency［J］. Microelectronics Reliability,2010,50(3):407-414. ［11］赵松山.对多重共线性的深入思考［J］. 当代财经, 2003(6): 125-128. Zhao S S. A deep thinking in multicollinearity［J］. Contemporary Finance & Economics, 2003(6):125-128. ［12］鲁茂, 贺昌政. 对多重共线性问题的探讨［J］. 统计与决策, 2007(8): 6-9.Lu M, He C Z. A study on multicollinearity［J］. Statistics and Decision,2007(8):6-9. ［13］ztürk F, Akdeniz F. Ill conditioning and multicollinearity［J］. Linear Algebra and Its Applications, 2000,321(13):295-305. ［14］aguchi G, Jugulum R. The Mahalanobis Taguchi strategy:a pattern technology system ［M］. New York:John Wiley & Sons, 2002. ［15］Hawkins D M. Discussion a review and analysis of the Mahalanobis Taguchi system ［J］.Technometrics,2003, 45(1): 25-29. ［16］何桢, 韩亚娟, 李菊栋. 马氏田口两种不同方法的比较研究［J］. 中国卫生统计,2007,24(5):531-535. He Z, Han Y J, Li J D. A comparative study on two different methods of Mahalanobis Taguchi system［J］. Chinese Journal of Health Statistics, 2007, 24(5): 531-535. ［17］Masami M, Yasushi N. On countermeasures against multicollinearity in Mahalanobis Taguchi system［J］.Quality,2003,33(4):467-475. ［18］Chen Y, Phillips J. ECU software abnormal behavior detection base on Mahalanobis Taguchi technique［C］.Proceeding of the Society of Automotive Engineers World Congress, USA:Detroit, Michigan,2008. ［19］黄廷祝, 钟守铭. 矩阵理论［M］. 北京: 高等教育出版社, 2003.

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