Coherent Systems: Structural and Statistical Reliability Analysis under load-sharing models

• Applicant: Professorin Dr. Maria Kateri
• Subject Area: Mathematics ; Statistics and Econometrics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 556726536

Coherent systems (CS), i.e., systems consistent of connected components whose overall performance is determined by the functionality of the individual components, play a vital role and find applications in various fields like, e.g., machine engineering and telecommunications. The study of coherent systems with several possibly dependent components is of central interest in reliability theory and its applications. The two most common types of depending failures in system reliability are the cascading failures and the common cause failures, corresponding to failure processes in which the failure of a component causes the failure of other items as well (in case of a long sequence of failures, it shows a domino effect) and to processes in which several components may fail simultaneously or in a short time interval due to a common shock or stress, respectively. We focus on cascading failures, which are relevant in reliability analysis and design of technical systems with interacting components, not affected by external factors. These typically arise when two or more components are sharing a load and are usually described by load sharing (LS) models. The interest on LS models for CS has a long history and the associated literature is rich. However, the various types of LS models considered were tailored for a specific type of CS (e.g., k-out-of-n or parallel systems) and focused mainly on the stochastic modelling of the system as a whole and the estimation or prediction of the system’s reliability. However, they neither considered the prediction of the components’ lifetimes nor the investigation of the effects of targeted modifications on system reliability. These aspects are important for stochastically controlling a system, designing systems with desired reliability properties and for identifying areas that need to be improved. They will be problems of interest in this project, to be tackled under the framework of general CS that are flexible and adaptable to every structure function of systems and with every number of components. In particular, we shall develop the associated methodology, study reliability properties of such systems and provide results with regard to maintenance policy targeting at lengthening the expected lifetime of the system by operating on the components with higher hazard. We shall start studying CS with components having a joint distribution following a time-homogeneous load sharing (THLS) model and then continue with order-dependent THLS (ODTHLS) models, i.e., models under which the order of components’ failures affects the redistribution of load and thus the failure rates of the remaining components. CS and THLS models will be studied also under censoring and interval monitoring, which are realistic considerations for real-world applications of CS.

• DFG Programme: Research Grants
• International Connection: Italy, Spain
• Cooperation Partners: Professor Dr. Francesco Buono; Professor Dr. Jorge Navarro