Reputation systems have been extensively explored in various disciplines and application areas. A problem in this context is that the computation engines applied by most reputation systems available are designed from scratch and rarely consider well established concepts and achievements made by others. Thus, approved models and promising approaches may get lost in the shuffle. In this work, we aim to foster reuse in respect of trust and reputation systems by providing a hierarchical component taxonomy of computation engines which serves as a natural framework for the design of new reputation systems. In order to assist the design process we, furthermore, provide a component repository that contains design knowledge on both a conceptual and an implementation level. To evaluate our approach we conduct a descriptive scenario-based analysis which shows that it has an obvious utility from a practical point of view. Matching the identified components and the properties of trust introduced in literature, we finally show which properties of trust are widely covered by common models and which aspects have only rarely been considered so far.