Industrial Internet of Things (IIoT) applications generate data in varying amounts with diverse quality of service requirements. The adaptive network access approach and distributed resource management in IIoT networks can reduce the communication overheads caused by centralized resource management approaches. In this regard, statistical learning is a promising tool for addressing decision-making problems in a dynamic environment. This article considers uplink dominant IIoT networks in which massive devices generate delay-sensitive and delay-tolerant data and communicate over shared radio resources. We propose a novel grant-free access scheme using a statistical learning approach that enables IIoT entities to perform delay-sensitive and delay-tolerant transmissions over dynamically partitioned resources in a prioritized manner. In order to improve utilization of available radio resources, we design an adaptive network access mechanism operating in a semi-distributed manner. This mechanism enables end devices to use their transmission history to choose between static and dynamic resource allocation-based grant-free schemes in a dynamic environment. Simulation results show that average latency and resource utilization vary in grant-free access schemes employing static and dynamic resource allocations. Thus, compared to a single transmission scheme, the proposed adaptive network access offers better channel utilization while meeting the application-specific latency bound in IIoT networks.