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An improved multivariate loss function approach to optimization

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Abstract

The basic purpose of a quality loss function is to evaluate a loss to customers in a quantitative manner. Although there are several multivariate loss functions that have been proposed and studied in the literature, it has room for improvement. A good multivariate loss function should represent an appropriate compromise in terms of both process economics and the correlation structure among various responses. More important, it should be easily understood and implemented in practice. According to this criterion, we first introduce a pragmatic dimensionless multivariate loss function proposed by Artiles-Leon, then we improve the multivariate loss function in two respects: one is making it suitable for all three types of quality characteristics; the other is considering correlation structure among the various responses, which makes the improved multivariate loss function more adequate in the real world. On the bases of these, an example from industrial practice is provided to compare our improved method with other methods, and last, some reviews are presented in conclusion.

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Authors and Affiliations

  1. Institute of Economic and Management, Nanjing University of Science and Technology, Nanjing, 210019, P.R. China

    Yizhong Ma

  2. College of Computer Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, P.R. China

    Fengyu Zhao

Authors
  1. Yizhong Ma
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  2. Fengyu Zhao
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Additional information

This work is supported by the National Natural Science Foundation of China under Grant 79900018 and the Aeronautical Science Foundation of China under Grant 02J55001

Yizhong Ma is now a post-doctor research at School of Business and Management, Beijing University of Aeronautics and Astronautics (BUAA). He is also a Professor in quality engineering at Nanjing University of Science and Technology. He holds a B.S. degree in mathematics from Central-China Normal University in 1985, and both a M.S. degree in applied statistics in 1990 and a Ph. D in engineering control theory in 2002 from Northwestern Polytechnical University. He is in charge of two items the National Natural Science Foundation of China. He has published over 50 papers on statistical process control, quality management, engineering process control and robust design. More than 10 papers are indexed by SCI, EI and ISTP.

Fengyu Zhao is now a professor in computer science and application at University of Shanghai for Science and Technology. He holds a B.S degree in 1984 and M.S. degree in 1989 in computer science and engineering from Nanjing University of Aeronautics and Astronautics. He is the author of 20 papers on software development, technology assessment and process improvement.

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Ma, Y., Zhao, F. An improved multivariate loss function approach to optimization. J. Syst. Sci. Syst. Eng. 13, 318–325 (2004). https://doi.org/10.1007/s11518-006-0167-x

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  • DOI: https://doi.org/10.1007/s11518-006-0167-x

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