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The Taguchi method (TM) and TM-combined methods [e.g., TM fuzzy method (TM-Fuzzy), TM data envelopment analysis (TM-DEA), TM coupled with grey relational analysis (TM-GRA), etc.] have been proven to be effective to achieve robust design performance. However, the efficient strategy to identify the significant design parameters, and the link between different quality characteristics and design parameters have not been fully studied. To fill the gaps, a combined method, i.e., TM–response surface methodology (RSM)–desirability function (DF), (TM–RSM–DF), was proposed. The significance of the TM–RSM–DF method is able to address the relationship between design parameters and quality characteristics, which facilitated to sort out the most significant design parameters precisely; besides, it also provided a robust strategy to optimize the multiple quality characteristics of the precision product. A design process of a precision amplification (PA) was taken as an example to prove the effectiveness of the TM–RSM–DF. The results showed that the TM–RSM–DF method improved the estimation performance of displacement amplification ratio (DAR) and natural frequency (NF) by 6.148% and 0.537% compared with the initial desired design. Besides, compared with others, the TM–RSM–DF method reduced the stress amount about 16% and had the lowest DAR and NF errors of 2.882% and 1.305%, respectively. Overall, the proposed TM–RSM–DF method outperformed the TM-DEA, TM-GRA, and TM-Fuzzy in the robustness of the PA design. [ABSTRACT FROM AUTHOR]