Parameter estimation for a repairable system with imperfect maintenance: inverse Gaussian-based degradation

We consider a system whose intrinsic deterioration is represented by an inverse Gaussian process and undergoes imperfect repair at each time period T. The repair effects are modeled by the arithmetic reduction of degradation of order one and infinity. Within the context of the proposed imperfect repair models, we develop maximum likelihood estimation and moment estimation methods to determine the parameters. Additionally, we present a modified version of the moment estimator that demonstrates acceptable performance compared to the other estimators and is more robust than the standard moment estimators. Finally, a simulation study is conducted to evaluate the effectiveness of the estimators.