A Repairable System Subjected to Hierarchical Competing Risks: Modeling and Applications

In this paper, we propose modeling for a single repairable system with a hierarchical structure under the assumption that the failures follow a nonhomogeneous Poisson process (which corresponds to minimal repair action) with a power-law intensity function. The properties of the new model are discussed in detail. The parameter estimators are obtained using the maximum likelihood method. A corrective approach is used to remove bias with order
$O(n^{-1})$
, and the respective exact confidence intervals are proposed. A simulation study is conducted to show that our estimators are bias-free. The proposed modeling is illustrated via a toy example on a butterfly valve system, an example of an early-stage real project related to the traction system of an in-pipe robot, and also a real example on a blowout preventer system.