A new engineering-driven factor analysis (EDFA) method has been developed to assist the variation source identification for multistage manufacturing processes (MMPs). The proposed method investigated how to fully utilize qualitative engineering knowledge of the spatial variation patterns to guide the factor rotation. It is shown that ideal identification can be achieved by matching the rotated factor loading vectors with the qualitative indicator vectors (IV) that are defined according to spatial variation patterns based on the design constraints. However, the random sampling variability may significantly affect the estimation of the rotated factor loading vectors, leading to the deviations from their true values. These deviations may change the matching results and cause misidentification of the actual variation sources. By using implicit differentiation approach, this paper derives the asymptotic distribution and the associated variance-covariance matrix of the rotated factor loading vectors. Therefore, by considering the effect of sample estimation variability, the variation sources identification problem is reformulated as an asymptotic statistical test of the hypothesized match between the rotated factor loading vectors and the indicator vectors. A real-world case study is provided to demonstrate the effectiveness of the proposed matching method and its robustness to the sample uncertainty.