Semiparametric Estimation For Recurrent Failure Data Subject To Time Censoring

Recurrent failure data often appears in engineering supervision,to be more specific,in repair actions on machines.Building applicable models on the repairable system is a common method to estimate the properties of survival function of the machine after several repairs.Many people have studied the analysis of this topic.In this thesis,we consider a geometric failure rate reduction model,that is,the hazard function of the machine is change with a geometric scale when the maintenance times increasing.Besides,we consider the time censored condition rather than failure censored condition to obtain the semiparametric estimator of the model by partial likelihood.Then we prove the consistency of our estimator and get the interval estimation with respect with the method.In simulation an application part,we simulate the statistics to study the asymptotic properties of our estimator.In addition,we compare the result with the classic failure censoring method with respect to the same model.As a result,we find that the estimator with the time censored have a more approximate fitting to the true value,both the bias and the variate.Then we apply the method to the data of the taxi replacement.Compared with the classic method,the time censored estimator have a better fitting to the first-failure curve.The result shows that the time censored semiparametric estimator has excellent usage on repairable system.