Software specialization exists in various forms in the literature ranging from product lines to adaptation of high-performance applications. In particular, specialization of component assemblies has been the focus of extensive research throughout the years and brings about specific challenges such as variant selection and hierarchy. We argue that many (possibly automatic) assembly specialization processes share a common structure. This paper presents a calculus which aims at providing a generic framework to ease reuse and composition of component assembly specialization processes. We show how this calculus can encode various features from the component model literature and discuss the existence of specialization processes in the literature and the usefulness of reusing and composing them.