The initiatives Organic Computing and Autonomic Computing introduced challenging visions for future computer systems. They address the growing complexity of these systems that demands for new ways to control them. Future systems should be able to adapt dynamically to the current conditions of their environment. They should be characterised by so-called self-x properties like self-configuring, self-healing, self-optimising, self-protecting, and context-aware. For the incorporation of self-healing capabilities into distributed systems the detection of failures is a crucial part. Recently we proposed a new failure detector that can be described as an adaptive accrual algorithm. It has been designed for flexible generic usability as a basis to realise self-healing of distributed systems. This paper introduces variations of the proposed basic algorithm to improve its performance and provides an evaluation of all algorithms using message delay and loss models of the internet.