Stochastic Processes

Reliability theory is of fundamental importance for engineers and managers involved in the manufacture of high-quality products and the design of reliable systems. In order to make sense of the theory, however, and to apply it to real systems, an understanding of the basic stochastic processes is indispensable.

As well as providing readers with useful reliability studies and applications, Stochastic Processes also gives a basic treatment of such stochastic processes as:

• the Poisson process,
• the renewal process,
• the Markov chain,
• the Markov process, and
• the Markov renewal process.

Many examples are cited from reliability models to show the reader how to apply stochastic processes. Furthermore, Stochastic Processes gives a simple introduction to other stochastic processes such as the cumulative process, the Wiener process, the Brownian motion and reliability applications.

Stochastic Processes is suitable for use as a reliability textbook by advanced undergraduate and graduate students. It is also of interest to researchers, engineers and managers who study or practise reliability and maintenance. 

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)

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.