As the production orders are becoming multi-category and small-batch in the era of product personalization, these require frequent reconfiguration of reconfigurable flexible assembly system for cross-category products (RFAS-CCP). However, there is no suitable theoretical assembly model and systematic implementation framework. We first propose a five-element assembly model (FAM) for RFAS-CCP, i.e. product, process, resource, knowledge, and decision. The product, process, and resource element describe the objects, steps to be assembled, and the tools, fixtures, and other equipment used for assembly, respectively. The knowledge element is a form representation of various heterogeneous data, such as a knowledge graph. The decision element includes various assembly methods to achieve assembly automation, flexibility, and intelligence. Then, in order to standardize and easy the frequent reconfiguration process, we reorganize various decision methods into a three-phase systematic implementation framework according to which stage they are used: design, configuration, and operation phases. The design phase methods primarily design various assembly modules for a product family, forming an assembly resource library. The configuration phase methods primarily configure suitable assembly lines for a specific product in the product family. The operation phase methods monitor the status of the assembly line and ensures its stable operation through health management. Finally, the effectiveness and practicality of the proposed five-element assembly model and three-phase systematic implementation framework are experimented with a pressure reducing valve product.