A product family design has received much attention over the last several decades, since a product family-based development shortens lead-times and reduces cost, as well as increases efficiency and effectiveness of the product realization process. It is challenging work, however, to define the product family design in the heterogeneous product development environments, due to myriads of products related information described in different ways across products in any companies. In this paper, we provided a way of defining product family design framework using formal concept analysis and ontology language. Based on this, the specific product family can be derived by ontological reasoning, and the new product concept can be also expanded in the framework. The proposed framework is formalized using OWL (Web Ontology Language) and implemented in $Prot{acute{e}}g{acute{e}}$. Actual product family design algorithm is carried out using FaCT++ engine, a plug-in to $Prot{acute{e}}g{acute{e}}$, and the benefits of the proposed method are also demonstrated through a case study.