Markov‐Driven Reliability Improvement in Duplex and Triplex Standby Architectures With Variable Failure and Repair Rates

To enhance the reliability of industrial wireless sensor networks (IWSNs), this study develops a state‐based continuous‐time Markov model for duplex and triplex architectures equipped with warm and cold standby backup sensors. The proposed model explicitly defines the state space, transition structure, and failure–repair dynamics for one, two, and three simultaneous sensor failures. Failure rates β are assumed identical across nodes, while repair and replacement rates r are modeled as state‐dependent, allowing the system to accelerate maintenance when multiple failures occur. Warm and cold standby units follow different failure intensities, and numerical stability conditions (e.g., β  r ) are ensured for steady‐state availability. In the triplex configuration, two sensors operate in parallel, while the third remains in cold standby. Upon failure of any active sensor, the standby node is activated, and the faulty unit transitions to the repair state. This reversible mechanism enables continuous operation without service interruption. The model incorporates sleep–wake scheduling, parallel activation, and priority‐based repair, which collectively improve the repair and replacement rates. Analytical results demonstrate enhanced reliability, reduced downtime, and improved fault tolerance compared with classical Markov redundancy models. Sensitivity analysis highlights the impact of repair acceleration and standby activation on system availability. The proposed framework provides a practical basis for maintenance planning and reliability optimization in duplex and triplex IWSN architectures.