Martingale and reliability Theory

The existing literature on reliability covers "inter alia" lifetime analysis, complex systems, redundancy operations and the book from Barlow and Proschan, 1981, can be view as a first milestone in this area. However the approach is under stochastic independence. Any engineer working under independence conditions hypothesis is leads to underestimating critical events with negative consequences. The reliability of a complex system has to be analysed taking into account the statistical dependence and time dynamics. These can be done considering a point process martingale approach to reliability theory.In this monograph we study component reiability importance for system reliability, redundancy operations and a generalizatio of system signature.