This paper presents an integrated approach combining principal component analysis (PCA) and Taguchi methods to develop a ball grid array (BGA), gold (Au) wire bonding process with multiple quality characteristics optimization. Eight main process factors of BGA wire bonding technology are selected as the control factors for parameter design. They are the factor A (seating ultrasonic generator (USG)), factor B (TIP height), factor C (C/V), factor D (USG current), factor E (USG bond time), factor F (bond force), factor G (FS threshold), and factor H (FAB size). The quality characteristics of the process in the study, including the wire pull strength, the ball shear strength, the ball thickness difference, the ball size difference, and the percentage of the Au–Al intermetallic compound (IMC) are measured. The optimal process parameters that meet the requirements for multiple quality characteristics are A1B3C1D3E3F1G1H2. They are then used to be tested for verification. Experimental results confirm that the optimal process design indeed enhances the quality characteristics investigated. The analysis of variance (ANOVA) results also show that the most important control factors affecting the quality characteristics are factor B (TIP height), factor C (C/V), and factor G (FS threshold), which accounts for 72.34% of total process variance. Thus, they must be strictly monitored during processing.