Grey-data envelopment analysis approach for solving the multi-response problem in the Taguchi method

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Abstract
In practice, a product or process possesses multiple quality responses of main interest. The Taguchi method has been found only efficient for optimizing a single quality response. This research, therefore, proposes an approach for solving the multi-response problem in the Taguchi method by integrating the grey relational analysis and super efficiency technique in data envelopment analysis (DEA). The quadratic loss is calculated for each response. The grey relational analysis is used to normalize the quality losses and to obtain grey relational coefficients. Each experiment in the Taguchi's orthogonal array (OA) is then treated as a decision-making unit (DMU) with grey relational coefficients set as the inputs for all DMUs. The super efficiency model is then adopted to estimate the efficiency of each DMU. Finally, the level efficiency, i.e. the average of efficiencies for DMUs at each factor level, is calculated and used to determine the optimal factor levels for the multi-response problem. Four real case studies, which were investigated previously in literature, are provided for illustration; in all of which the proposed approach provides lowest total quality loss. In conclusion, the grey-DEA approach proposed in this research shall provide great assistance to practitioners in solving the multi-response problem in a wide range of manufacturing applications on the Taguchi method.

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