Variation source identification is an important task of quality assurance in multistage manufacturing processes (MMPs). However, existing approaches, including the quantitative engineering-model-based methods and the data-driven methods, provide limited capabilities in variation source identification. This paper proposes a new methodology that does not depend on accurate quantitative engineering models. Instead, engineering domain knowledge about the interactions between potential variation sources and product quality variables is represented as qualitative indicator vectors. These indicator vectors guide the rotation of the factor loading vectors that are derived from factor analysis of the multivariate measurement data. Based on this engineering-driven factor analysis, a procedure is presented to identify multiple variation sources that are present in a MMP. The effectiveness of the proposed methodology is demonstrated in a case study of a three-stage assembly process.