On reliability improvement for coherent systems with a relevation

Taking repair action has proven to be an effective and flexible way to maintain the proper functioning of reliability systems. As a generalization of the minimal repair policy, the relevation is one of models for describing the repair effect. However, there are few studies in the literature dealing with the optimal allocation problem of repair resources to coherent systems because of their complex distribution theory. In this study, we tackle the allocation problem of a single relevation resource for coherent systems. Sufficient conditions based on the orderings among components lifetimes and repair effects are established for improving the system reliability by distinguishing the structural relationships of the minimal path/cut sets, which answer the problems proposed by Belzunce et al. Several numerical examples are also presented to illustrate the main results.