We pose the maintenance planning for systems using probabilistic Remaining Useful Life (RUL) prognostics as a renewal reward process. Data-driven probabilistic RUL prognostics are obtained using a Convolutional Neural Network with Monte Carlo dropout. The maintenance planning model is illustrated for aircraft turbofan engines. The results show that in the initial monitoring phase, the accuracy and sharpness of the RUL prognostics is relatively small. The maintenance of the engines is therefore scheduled far in the future. As the usage of the engine increases, the accuracy of the prognostics improves, while the sharpness remains relatively small. As soon as the estimated probability of the RUL is skewed towards 0, the maintenance planning model consistently indicates it is optimal to replace the engines immediately, i.e., "now". This shows that probabilistic RUL prognostics support an effective maintenance planning of the engines, despite being imperfect with respect to accuracy and sharpness. @en

Health indicators are crucial to assess the health of complex systems. In recent years, several studies have developed data-driven health indicators using supervised learning methods. However, due to preventive maintenance, there are often not enough failure instances to train a supervised learning model, i.e., the data is unlabelled with an unknown actual Remaining Useful Life (RUL). In this paper, we therefore propose an unsupervised learning model to construct a health indicator for an aircraft system. The considered system is operated under highly-varying operating conditions. We train a Convolutional Neural Network (CNN) to predict the sensor measurements from the operating conditions. We train this neural network solely with the sensor measurements of just-installed, non-degraded systems. The CNN therefore learns the normal range of the sensor measurements, given the operating conditions, for non-degraded systems only. For a degraded system, the predicted sensor measurements deviate from the actual sensor measurements. Based on the prediction errors, we construct a health indicator for the aircraft system. We apply this approach to develop a health indicator for the aircraft turbofan engines of dataset DS02 and DS06 of N-CMAPSS. The resulting health indicators have a high prognosability of 0.91 for DS02 and of 0.83 for DS06, a mean trendability of 0.86 for DS02 and of 0.87 for DS06, and a mean monotonicity of 0.31 for DS02 and of 0.33 for DS06, and can thus be used to make a reliable assessment of the system's health. @en