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Prognostics for Deteriorating Systems Under Indirect Discrete Monitoring and Random Failure

Generally, the internal states of most engineering systems are inaccessible to sensors under operational conditions, permitting indirect measurements and failures to be observed discretely. For this type of system, a class of proportional hazard (PH) models with multistate process have been proposed for performing prognostics. However, existing studies use a constant degradation mechanism with a very limited number of states, which may fail to model the actual deterioration of the system. Therefore, this article presents a novel PH model that utilizes a nonconstant degradation mechanism with a large number of states to perform health prognostics. A matrix partition-based approximation method is developed to include all the possible state transitions and to estimate important health quantities of the system, such as conditional reliability (CR), mean remaining useful life (MRUL), and remaining useful life distribution (RULD). An online prognostic scheme based on this matrix approach is presented to provide an update with the latest health quantities of the system. The proposed approach provides appealing computational features and avoids difficulties in calculating uncountable transitions for PH model-based prognostics. The effectiveness of the proposed method is demonstrated via a case of helical gearboxes under indirect monitoring and random failure conditions.