A proportional intensity segmented model for maintained systems

The failure times of a maintained system are generally modelled using point processes, the most common being the homogeneous and the non-homogeneous point processes representing maximal and minimal repairs. Additional information obtained with regard to the maintained system which may have influenced the failure characteristics of the maintained system can be used in the form of covariates to ascertain their effect on the system's failure intensity. These covariates are deemed to act multiplicatively on the system's failure intensity using a suitable link function; the usual link function being the exponential. These processes are generally able to model maintained systems with a fair degree of accuracy. However, whenever there is a change in the environment of the maintained system these models are not able to exactly identify and take into account the corresponding change in the intensity unless the covariates chosen are able to totally account for the changes. Also, the covariates themselves may be subject to change, and then such systems need to be modelled by segmented models with the system domain divided into segments at the points of changes in the environment. The individual segments can then be modelled by a point process and/or proportional intensity model, and these can be combined to form a composite model. This paper develops a statistical model of the failure process of a maintained system in such an environment and applies it to the field data from an industrial setting to demonstrate that appropriate parameter estimates for such phenomena can be obtained, and such models are shown to more accurately describe the maintained system in a changing environment than the single point process/proportional intensity models usually used.