Estimating parameters of a log-linear intensity for a repairable system

The log-linear intensity is often used in survival analysis of technical products with rapid deterioration. It is an extremely important intensity to characterize the probabilistic behavior of a large number of real phenomena. In this paper we develop statistical methods for an alternating repair model using a log-linear 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 parameters. The proposed model is demonstrated using the well known data on airplane air-conditioning failures from Plane 7.