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Distributed cloud computing environments suffer from frequent node failures, dynamic workload variations, and trust uncertainty, which collectively degrade system reliability and service availability. Existing studies largely treat reliability modelling (e.g., failure-rate-based approaches) and trust management (e.g., reputation systems) as independent mechanisms, leading to inefficient task allocation and delayed failure recovery in large-scale distributed systems. This paper proposes a unified failure-adaptive framework that integrates trust persistence with probabilistic reliability modelling to enable intelligent and resilient cloud operations. Unlike conventional approaches, the proposed model introduces two novel components:(i) a persistence- aware trust formulation incorporating Behavioral Consistency Coefficient (BCC) and Recovery Efficiency Score (RES), and (ii) a trust-augmented reliability function that dynamically adjusts node reliability based on long-term behavioral stability. The key contributions of this paper are as follows: 1. A multi-dimensional trust model incorporating both short-term performance and long- term behavioral stability. 2. A unified mathematical formulation integrating trust persistence with exponential reliability modelling. 3. A failure-adaptive task allocation mechanism that prioritizes nodes based on combined trust–reliability scores. 4. A conceptual self-healing architecture enabling real-time fault detection, isolation, and workload redistribution. By embedding trust persistence into reliability estimation, the proposed framework enables proactive failure handling, reduces trust oscillation, and improves system resilience. The model is particularly suitable for large-scale, heterogeneous cloud environments where node behavior is uncertain and dynamically evolving. The proposed model is analytically evaluated and validated using simulated reliability–trust scenarios.