We revisit the work of Chandra and Toueg on achieving
unreliable failure detectors
in an asynchronous system with crash stop failures. Following a brief review of their approach, we provide a probabilistic analysis of their consensus algorithm, which shows that the number of messages is exponentially proportional to the number of participating processes
. Based on our analysis, we study how their solution may be improved when we have
knowledge of the maximum number of process failures that may occur. Accordingly, we propose
as a generalization of the Chandra-Toueg algorithm, and give a probabilistic analysis of our algorithm. For
large relative to the bound on the number of failures
, this approach yields an improvement (in the expected case) in the message complexity.