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In the design of robot skills, the focus generally lies on increasing the flexibility and reliability of the robot execution process; however, typical skill representations are not designed for analysing execution failures if they occur or for explicitly learning from failures. In this paper, we describe a learning-based hybrid representation for skill parameterisation called an execution model, which considers execution failures to be a natural part of the execution process. We then (i) demonstrate how execution contexts can be included in execution models, (ii) introduce a technique for generalising models between object categories by combining generalisation attempts performed by a robot with knowledge about object similarities represented in an ontology, and (iii) describe a procedure that uses an execution model for identifying a likely hypothesis of a parameterisation failure. The feasibility of the proposed methods is evaluated in multiple experiments performed with a physical robot in the context of handle grasping, object grasping, and object pulling. The experimental results suggest that execution models contribute towards avoiding execution failures, but also represent a first step towards more introspective robots that are able to analyse some of their execution failures in an explicit manner.