An assurance case contains a structured argument supported by evidence, demonstrating that a system fulfils a certain quality attribute such as safety, cybersecurity or reliability. The traditional way of building assurance cases is, however, not well suited to continuous deployment, and difficult to maintain with a product structure where many variants and frequent new versions must be managed. By integrating the assurance work with product development in continuous assurance cases, which are updated and assessed iteratively, we claim continuous deployment of dependability-critical products is possible to achieve. In this paper we propose a work process combining the use of component-based design, contracts, modular assurance cases, and continuous assessment to enable continuous deployment in the context of product lines.