Modeling repair events under intermittent failures and failures subject to unsuccessful repair

Intermittent failures are sometimes observed for a repairable system, such as an automobile. Such failures often lead to a series of unsuccessful repair attempts before the source of the failure has been identified and removed. Unsuccessful repair is also observed in cases where the failures are not intermittent. In order to model data involving repeated repair attempts related to the same failure, repair times cannot usually be assumed negligible and the model must be designed or modified to account for these. In this paper, we propose a modified version of the branching Poisson process model introduced by Lewis. We discuss statistical inference procedures for this model and demonstrate these procedures using the service history of a new automobile.