Parameter estimation for load-sharing systems with degrading components

This paper aims to develop a parameter estimation approach for load-sharing systems subject to continuous degradation. The system consists of multiple components in parallel structure. The components of the system suffer a degradation process, characterized respectively by Wiener process and Inverse Gaussian process. When components fail one by one, the total workload is redistributed among the remaining components, which accelerates the degradation process of the surviving components, which is referred to as a load-sharing system. Maximum likelihood estimation (MLE) is used to estimate the parameters for a load-sharing system. The available data are the failure times of the components and the degradation level of the remaining components at failure time. For Wiener process, a close-form MLE is derived and an analytical solution is achieved. For inverse Gaussian process, however, it is difficult to obtain a close-form MLE and numerical method is adopted instead. Finally, numerical studies are conducted to illustrate the estimation procedure.