In this paper we propose a framework based on Formal Concept Analysis (FCA) that can be applied systematically to (1) visualize a product family (PF) and (2) improve commonality in the product family. Within this framework, the components of a PF are represented as a complete lattice structure using FCA. A Hasse diagram composed of the lattice structure graphically represents all the products, components, and the relationships between products and components in the PF. The lattice structure is then analyzed to identify prospective components to redesign to improve commonality. We propose two approaches as part of this PF redesign methodology: (1) Component-Based approach, and (2) Product-Based approach. In the Component-Based approach, emphasis is given to a single component that could be shared among the products in a PF to increase commonality. In the Product-Based approach, multiple products from a PF are selected, and commonality is improved among the selected products. Various commonality indices are used to assess the degree of commonality within a PF during its redesign. In this paper, we apply the framework to represent and redesign a family of one-time-use cameras. Besides increasing the understanding of the interaction between components in a PF, the framework explicitly captures the redesign process for improving commonality using FCA.