Condition-based maintenance considering imperfect inspection for a multi-state system subject to competing and hidden failures

Unexpected failures may cause huge economic losses and bring about uncontrolled risks and damage to humans and the environment. Condition-based maintenance is considered one of the most effective maintenance methods, which can reduce and eliminate possible failures and consequently ensure the safety and operating process effectiveness of systems. Inspection quality is an important factor affecting the effect of condition-based maintenance since imperfect inspection may result in inappropriate maintenance decisions. However, the factor of imperfect inspection is rarely considered when maintaining multi-state systems subjected to competing and hidden failures. In this paper, a periodical inspection policy is utilized to identify all states of a system subject to a three-state degradation process and random shocks. Inspections for all system states are considered imperfect. Upon the inspection outcome, the system may be replaced by a failure-based corrective replacement once it is detected as failed, or is renewed by a defect-based preventive replacement if a defect is identified. Moreover, an age-based preventive replacement is also required if the system is still normal up to the preset number of inspections. Subsequently, a condition-based maintenance model is constructed based on the probabilities of different renewal scenarios. Eventually, the applicability and effectiveness of the proposed model are verified by a numerical example. The results indicate that minimizing the constructed maintenance model can achieve the optimal inspection interval, which is greatly influenced by the factor of imperfect inspection. This research can provide references for decision-makers to optimize inspection and maintenance strategies.