Structural Identifiability and Reliability Assessment of a Nonidentical Cold‐Standby System Subject to Progressive Degradation and Imperfect Switching

In safety‐critical systems, the assumption of identical components often leads to an overestimation of reliability. This study develops a detailed continuous‐time Markov chain (CTMC) model for a complex three‐unit, nonidentical cold‐standby system. The model is unique in that it includes switch priority, progressive degradation (normal ⟶ partial ⟶ total failure), and hierarchical repair, addressing a gap in modeling heterogeneous redundancy. A 33‐state CTMC is created and validated using discrete‐event simulation (10 6 trials). Unlike previous studies, we perform a structural identifiability analysis to ensure parameter uniqueness from failure data, along with a global sensitivity analysis using Sobol′ indices. The analysis confirms that the model′s structure is identifiable. Sensitivity analysis shows that switch reliability is the most important factor ( S q = 0.387), more so than unit redundancy. The analytical mean time to failure (MTTF) closely matches the simulation results, with a small error (∈<0.6 % ). Therefore, this study shows that the reliability of the switching mechanism is the main limiting factor in heterogeneous standby systems. The proposed model establishes a mathematical framework for predictive maintenance in systems needing high availability. It further enables engineers to optimize the design of systems where reliability is critical to safety. The results indicate that focusing on the safety as well as reliability of the switch is more cost effective than increasing system reliability solely through unit redundancy. Under stringent failure criteria, the reliability of the switching mechanism surpasses the advantages provided by unit redundancy. Notably, the system mean time between failures is highly sensitive to switch failure parameters ( q , p ), whereas the basic unit repair rate ( θ A ) exerts minimal influence.