Statistical Inference on δ Shock Model with Censored Data

In this paper we study some statistical problems of the parameter δ of the δ-shock model associated with a Poisson process with intensity λ under censoring data. Where the system fails when the length of an interval of two successive shocks falls below δ, and the failure time is denoted by T. Firstly we analyze the shape of the density function of T on condition that S is less than the mean time 1/λ of the Poisson shock. Next open window method is used to compensate some of the information which is lost due to type I censoring. Then we take advantage of Class-K method so as to obtain an unbiased and consistent estimator of E(T), simultaneously to get both a point estimator and an approximate confidence interval of δ. In the end a more accurate confidence interval of δ is given by means of Edgeworth expansion and Boostrap.