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Alumina composites reinforced with multiwalled carbon nanotubes (MWCNTs) at up to 3.7 vol% are prepared by a precursor method followed by a spark plasma sintering. We systematically and quantitatively investigate the effects of acid-treatment time of the MWCNTs on not only bending strength and fracture toughness of the composites but also on the mechanical strength and dispersibility of the MWCNTs, the grain size of the alumina matrix, and the interfacial strength between MWCNT and alumina. The main objective of this study is to evaluate how these parameters influence the mechanical properties with the aid of multiple regression analysis. We demonstrate that the matrix grain size, the mechanical strength of the MWCNTs, and the interfacial strength have little impact on the mechanical properties for the composites prepared in this study. On the other hand, the dispersibility of MWCNTs has the significant influence on the mechanical properties. Both the dispersibility of the MWCNTs and the mechanical properties of the composites increase as the acid-treatment time increases up to 2 h at low MWCNT content (0.9 vol%). Conversely, at a higher amount of MWCNTs, the degradation in the mechanical properties is shown to be associated with the deterioration of MWCNTs' dispersibility. As MWCNT agglomerates are anticipated to act as imperfections, they may override the effects of the strength of MWCNTs, matrix grain size, and interfacial strength. By means of the multiple regression analysis, we quantitatively show that improving MWCNTs' dispersibility is one of the most important factors in enhancing the mechanical properties of MWCNT/alumina composites. [ABSTRACT FROM AUTHOR]