System Reliability Models with Dependent Degradation Processes

Interest and associated research for reliability and health prediction and maintenance of infrastructure and industrial products have increased continuously. The study of reliability and health prognosis has become an indispensable field in the overall design and evaluation of systems, industrial products and engineering projects. Previously, the common approaches and mathematical models to describe the condition of products were usually based on the statistical lifetime distribution of the target production. The lifetime distribution is obtained based on the observation and analysis of large quantities of components. However, when it comes to a single component, it can only quantify whether the component is functioning or not, rather than the detailed working condition or deterioration behavior. Therefore, degradation models are introduced to quantify the health conditions of the component based on time dependent observations. Alternatively, on the basis of the degradation model, by introducing the degradation threshold of product failure, the reliability model and the remaining useful life of the product and the corresponding maintenance strategy can also be derived. In practice, the evaluation of the degradation behavior of the system often needs to introduce multiple degradation processes while modeling, and these degradation processes are not always independent of each other. Due to factors inherent in the system or from the external environment, these degradation processes often affect each other and show some commonalities. Examples of such degradation include LED lighting systems (Sari et al. in Qual Reliab Eng Int 25:1067–1084, 2009), operating data of heavy-duty machine tools (Mi et al. in Reliab Eng Syst Saf 174:71–81, 2018), fatigue cracks of two terminals of an electronic device (Rodríguez-Picón et al. in Appl Stoch Model Bus Ind 35:504–521, 2019), etc. In this chapter, we will introduce various degradation models, as well as modeling approaches and reliability analysis to study dependent processes, such as dependent Markov chains, shared shock exposure models, joint distribution functions of degradation paths, and dependent random effects stochastic processes.