In this paper we extend the function of group membership to cover whether a process is correct or not with respect to specification. We introduce the concept of (m, n) Reliable Membership Failure Detectors and formally define three failure detector classes PMD, PMD, and WMD in terms of their ability to implement reliable group membership services. We show that the Perfect Failure Detectors and Eventually Perfect Failure Detectors are sub classes of (0, 0) PMD and (0, 0) WMD respectively in systems subject to only crash failures. Combining muteness failure detectors with the modular approach introduced for Byzantine systems, we propose a failure detector called RMSFD. By studying its reliability property, we prove that RMSFD is a failure detector of (0, 0) WMD