The large interest granted to this book made a 4th edition necessary. The structure of the book is unchanged, with its main part in Chapters 1 - 8 and self contained appendices Al - A5 on management aspects and A6 -A8 on basic probability theory, stochastic processes & statistics. Such a structure allows rapid access to practical results and a comprehensive introduction to the mathematical foundation of reliability theory. The content has been extended and reviewed. New models & considerations have been added to Appendix A 7 for stochastic processes (NHPP), Chapter 4 for spare parts provisioning, Chapter 6 for complex repairable systems (imperfect switching, incomplete coverage, items with more than two states, phased-mission systems, fault tolerant reconfigurable systems with reward and frequency / duration aspects, Monte Carlo simulation), and Chapters 7 & 8 for reliability data analysis. Some results come from a stay in 2001 as Visiting Fellow at the Institute of Advanced Study of the University of Bologna. Performance, dependability, cost, and time to market are key factors for todays products and services. However, failure of complex systems can have major safety consequences.