Stochastic Processes

Toshio Nakagawa has published more than 150 papers, mainly on the subject of reliability theory, in research journals. He has already published Maintenance Theory of Reliability (2005), Shock and Damage Models in Reliability (2007) and Advanced Reliability Models and Optimum Policies (2008) with Springer.His research group in Nagoya has studied reliability theory and its applications continuously since 1988, and has presented a large number of papers in reliability journals and at international conferences. Most papers have been written using some techniques and results of stochastic processes.

• 1. Introduction.- 2. Poisson Processes.- 3. Renewal Processes.- 4. Markov Chains.- 5. Semi-Markov and Markov Renewal Processes.- 6. Cumulative Processes.- 7. Brownian Motion and Lévy Processes.- 8. Redundant Systems.

From the book reviews: "This book provides a fundamental description of the main stochastic processes of interest in reliability theory. It also addresses and solves several problems related to maintenance and redundancy. Teachers and students at the undergraduate or the graduate level will find it useful." (Antonio Di Crescenzo, Mathematical Reviews, March, 2015) "This book by Prof. Nakagawa bridges the gap between theoretical achievements in the field of stochastic processes and the need of researchers and practical engineers to use the theory in reliability investigations. ... this book would be useful for researchers and teachers as well. ... this book by Prof. Nakagawa is exactly what the reliability community (researchers, engineers, and industrial managers) has long been waiting for. ... the book may also be used as a textbook for senior undergraduate or graduate courses ... ." (Anatoly Lisnianski, SIAM Review, Vol. 54 (4), 2012) "The addressed readership of this book is the reliability engineering community, especially engineers looking for a 'book written in an easy style on stochastic processes to be able to understand readily reliability theory'. ... book can serve as a first attempt to find needed facts in the area of stochastic processes ... . there is also another audience for this book: teachers of courses in stochastic processes on an undergraduate or graduate level who want to include examples of applications of stochastic processes in reliability." (Hans Daduna, Zentralblatt MATH, Vol. 1244, 2012)