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An Integrative Loss Function Approach to Multi‐Response Optimization
Author(s) -
Ouyang Linhan,
Ma Yizhong,
Byun JaiHyun
Publication year - 2015
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1571
Subject(s) - function (biology) , constraint (computer aided design) , mean squared error , computer science , mathematical optimization , dispersion (optics) , interval (graph theory) , mathematics , statistics , physics , geometry , combinatorics , evolutionary biology , optics , biology
Loss function approach is effective for multi‐response optimization. However, previous loss function approaches ignore the dispersion performance of squared error loss and model uncertainty. In this paper, a weighted loss function is proposed to simultaneously consider the location and dispersion performances of squared error loss to optimize correlated multiple responses with model uncertainty. We propose an approach to minimize the weighted loss function under the constraint that the confidence intervals of future predictions for the multiple responses should be contained in specification limits of the responses. An example is illustrated to verify the effectiveness of the proposed method. The results show that the proposed method can achieve reliable optimal operating condition under model uncertainty. Copyright © 2013 John Wiley & Sons, Ltd.