On the modeling and analysis of repaired and maintained systems

We consider some aspects of the modeling and analysis of repaired and maintained systems. The purpose of the paper is to point out some topics that have to a certain degree been overlooked in much of reliability practice. The first point concerns the use of the NHPP as the "single" model for repairable systems with trend. Although this is appropriate in perhaps most cases, there are cases where renewal effects caused by repair or maintenance destroy the randomness associated with Poisson processes. One way of checking NHPP models is to embed them in larger models, for example the trend-renewal process. Secondly, we consider the handling of a possible heterogeneity between systems of the same kind. The heterogeneity of failure behavior of systems or components may have important implications for reliability analyses. If such heterogeneity is not identified and taken into account, the decisions made to maintain or to replace equipment can be non-optimal or even erroneous. The third point to be mentioned regards the use, or lack of use, of methods for competing risks in reliability applications. In such applications, the cause, mode, or type of failure are usually registered and may be just as important as the time to failure. Still, in most of the published work in reliability there is no mentioning of competing risks.