Theoretical Analysis and Case Application of Intelligent Joint Predictive Ordering-Replacement Policy Driven by Real-Time Prognostics for IMU

More and more sensor data reflecting the health condition of a practical system can be real time collected in current big data era, owing to the rapid development of the advanced sensing technology. These sensor data can be used to facilitate the decision-making of spare ordering and system replacement, which can decrease the operation risk of practical systems. However, few studies can be found in literature to jointly determine the spare ordering time and system replacement time for a partially degraded system (referring to a system whose health condition is between blankly new and completely failed) based on the real-time updated lifetime distributions, which are obtained from the real-time observed condition monitoring (or health condition) data of the interested system. Lack of coordination between spare ordering and system replacement (also shortened as order-replacement in this paper) for non-repairable systems may lead to unexpected failures as well as the increasing of life-cycle costs. Aiming at this problem, this paper focuses on the theoretical analysis of the intelligent joint order-replacement policy for a partially degraded system with real-time predicted lifetime distributions from an adaptive Wiener degradation process. The theoretical results obtained in this paper primarily respond to the following two practical issues: how to find the optimal decision variables (i.e., spare ordering time and system replacement time), and how to ensure the existence and uniqueness of the optimal decision variables. The obtained results provide some important points with respect to optimality and convexity properties of the dynamic joint predictive ordering-replacement policy and can facilitate the decision-making process in engineering from the theoretical angle. To demonstrate the feasibility and applicability, we then apply the derived theoretical results to a practical case of an inertial measurement unit (IMU), which is widely used in consumer electronics products.