Bayes inference for a bounded failure intensity process

The failure pattern of repairable mechanical equipment subject to deterioration phenomena sometimes shows a finite bound for the increasing failure intensity A non-homogeneous Poisson process with bounded increasing failure intensity is then illustrated and its characteristics are discussed. A Bayes procedure, based on prior information on model-free quantities, is developed in order to allow technical information on the failure process to be incorporated into the inferential procedure. Posterior inference on the model-free quantities, on the model parameters and on the expected number of failures is provided, as well as prediction on the future failure times and on the number of failures in a future time interval. Finally, a numerical example is given to illustrate the proposed inferential procedure.