Parameter estimation in an alternating repair model

The Weibull intensity is often used in survival analysis of technical products, it is an extremely important intensity to characterize the probabilistic behavior of a large number of real phenomena. This intensity is especially useful as a failure model analyzing the reliability of different types of systems. In this paper we develop statistical methods for an alternating repair model using Weibull intensity. The maximum likelihood estimator is considered for determining the estimations of the model parameters. The distribution of the life times after perfect repairs and imperfect repairs are obtained. The estimation of the Fisher information matrix is given. Simultaneous confidence regions based on the likelihood ratio statistics are developed for the estimators of the shape and scale parameter of the Weibull intensity. Finally simulation study will be given.