Stochastic Processes for Dependability Assessment

The view taken in this monograph is that Reliability Theory is essentially an application of the theory of stochastic processes. However, the real life context in which Reliability Theory exists must also be given due consideration for three reasons. First, the theory serves a well-defined purpose: to assist in the modelling of technical systems as far as their dependability aspects are concerned. Second, there is ample scope for fertilization with ideas in the other direction. This latter point is relevant in particular for our subject since new technical systems in need of assessment from a reliability point of view are emerging with predictable regularity. Finally, the evolution of the reliability field is considerably influenced by the rapid development of the computational tools it uses (both software and hardware). Thus even though the present work is essentially a mathematical treatise, the intention was to make it of some benefit also to the reliability engineer who is perhaps more interested in how new theory might assist him in the analysis of actual systems rather than in the theory itself. In this first chapter, in addition to an informal summary of the results, the notation is established and the prerequisites from the (elementary) theory of stochastic processes are reviewed. The presentation is deliberately restricted to those aspects of the theory which will be used subsequently. The application examples are mainly power transmission reliability models.