Wiener and Gamma Processes Overview for Degradation Modelling and Prognostic

High reliability is an indispensable requirement for the operation of technical systems and infrastructure (like roads, railways, buildings, bridges and industrial plants). Failures in these areas can result in high costs and great hazards to humans and the environment. Many failure mechanisms can be traced to an underlying degradation process. Therefore, inspections and condition-based maintenance (CBM) are undertaken to monitor deterioration and to prevent damage and future failures. Prognostic of component lifetime is important for CBM in many application domains where safety, reliability and availability are considered of first importance. However, one of the condition indexes - the remaining useful lifetime (RUL) prediction is seldom taken into account in the decision making and maintenance planning in practice. To make up for it, the thesis focuses on a stochastic degradation process for RUL estimation and prognostic use. The thesis starts with reviewing some of the degradation models. The merits, limitations of each model are presented. By aggregating the information of each model, this paper provides the key information about circumstances for choosing suitable deterioration models in the context of maintenance optimization. Two stochastic process - Brownian motion and Gamma process are discussed in detail. Their statistical properties, methods for estimation, and simulation of are systematically reviewed with numerical examples. Also, each of the model is associated with the component's uncertainties in the observations while estimating its RUL. Since Gamma process has proven to be very useful in modeling degradation paths, determining optimal inspection and maintenance decisions, the paper then investigates the application of Gamma degradation process in maintenance policies. Two RUL related maintenance policies are proposed and compared with a traditional degradation level-based policy. The performances of the proposed policies are evaluated through numerical examples in previous papers and their advantages are stated in the end