The failure intensity process and the formulation of reliability and maintenance models

A unified approach to the formulation of failure event models is presented. This provides a common framework for the analysis of both repairable and nonrepairable items, preventive as well as corrective maintenance, and it also applies for items with dormant failures. The suggested procedure is supported by a set of graphs, thereby identifying the significance both of the inherent reliability (i.e., hazard rate) and of the maintenance/repair policy. The definition/interpretation of various failure intensity concepts is fundamental for this approach. Thus, interrelations between these intensities are reviewed, thereby also contributing to a clarification of these concepts. The most basic of these; concepts, the failure intensity process, is used in counting processes (Martingales), and is the rate of failures at time t, given the history of the item up to that time. The suggested approach is illustrated by considering some standard reliability and maintenance models.