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•A two-stage competing-risk system with hidden failures is considered.•A maintenance model of the ECR is developed.•The problem of optimal inspection policy is formulated.•The optimal periodic inspection interval is obtained by minimizing the ECR.•The rationality of the proposed model is validated through a numerical example.
In many complex industrial systems, failures are not always evident to the operating crew, thus inspections are used to identify such hidden failures and then make necessary maintenance actions. In this paper, we study a two-stage system that is subject to two competing risks of degradation and random shocks. Failures of this two-stage competing-risk system are hidden and could only be detected by periodic inspections. For such a system, a delay-time model is introduced to describe the evolution of the system behavior. Random shocks are assumed to follow a homogeneous Poisson process. A preventive maintenance policy is presented in response to the observed system state, based on which the expected cost rate of the system is derived. This paper aims to find the minimal expected cost rate by determining the optimal inspection interval. A numerical example is presented to demonstrate the applicability of the proposed method and results.