In this paper, we investigate the reliable decentralized supervisory control of discrete event systems (DESs) under the general architecture, where the decision for controllable events is a combination of the conjunctive and disjunctive fusion rules. By reliable control, we mean that the performance of closed-loop systems will not be degraded even in the face of possible failures of some local supervisors. The main contributions are twofold. First, a necessary and sufficient condition for the existence of a k-reliable decentralized supervisor under the general architecture is presented after introducing notions of (Sigma) over tilde (uc)-controllability and k-reliable (Sigma) over tilde (c)-coobservability. Second, a polynomial-time algorithm to verify the reliable (Sigma) over tilde (c)-coobservability of a specification is proposed. (c) 2010 Elsevier Ltd. All rights reserved.