Competing Risks: Theory and Applications to Reliability

Abstract

Although the topic of competing risks has a long history, the methodology has apparently not been used to the extent that its applicability might suggest.? Nevertheless, it seems that this is about to change. In the recent statistics literature, particularly in biostatistics, competing risks is a hot topic. The competing risks framework is also very relevant for reliability analysis. It is clear that, if something can fail, there are usually many ways that this might happen. In particular, there are typically several failure modes of a component, and there may be several external factors that potentially lead to failures. The increased interest in competing risks has most probably to do with the availability of powerful computers, and the existence of huge data registers.? Furthermore, it turns out that the competing risks theory itself includes many fascinating aspects, the most prominent one being the identification problem. This occurs when competing risks are described in terms of latent failure times for each risk, a representation which is common in reliability, but rather controversial in medical statistics. The latent failure time approach is, however, useful in many applications where one tries to model physically what is going on in the phenomenon under study. The lecture provides an overview of the basic theory, and typical applications of competing risks, including aspects of statistical inference. We consider in particular the competing risks approach for a component or system which may be subject to either a failure or a preventive maintenance action. Here, the latter event will prevent the failure, and is therefore the preferred outcome.? It is reasonable to expect a dependency between the time to failure and the time to preventive maintenance, and we shall consider several modeling approaches for this case. References: Lawless JF. Statistical models and methods for lifetime data, 2nd ed. Wiley-Interscience: Hoboken NJ, 2003. Lindqvist BH, St?ve B, Langseth H. Modelling of dependence between critical failure and preventive maintenance: The repair alert model. Journal of Statistical Planning and Inference 2006 136: 1701-1717.