Criticality-based allocation of active redundancies for asymmetric components in coherent systems

The active redundancy technique is widely used in reliability engineering to enhance the performance of reliability systems. In this paper, we utilize the criticality ordering to study optimal allocations of active redundancies in coherent systems comprising independent components. Firstly, we establish optimal allocation strategies for two heterogeneous active redundancies for components ranked by the criticality ordering, which is characterized by the structure relationships induced from the associated minimal cut sets. Our findings demonstrate that, under certain conditions where the criticality ordering (and reliability performances) between any two original components is required, the stronger redundancy should be allocated to the more critical component. Secondly, we investigate the best allocation policies for a batch of homogeneous active spares for different components while preserving the criticality ordering. It is shown that allocating more active redundancies to the more critical component results in a more reliable coherent system. Additionally, we prove that under certain conditions, an imbalance in the numbers of allocated spares leads to even greater reliability in the system. Thirdly, we study optimal allocations for any two components in coherent systems when their locations are quantified by minimal path sets. The optimal allocation policies are further derived, most of which are similar to those obtained by applying minimal cut sets. Numerical examples are provided to illustrate the main findings, and we apply our findings to a real-world scenario in an airplane cockpit system to enhance its reliability.