Ying Liu - Reliability Theory Based on Uncertain Lifetimes

Jointly published with National Defense Industry Press

The print edition is not for sale in China Mainland. Customers from China Mainland please order the print book from: National Defense Industry Press.

ISBN of the Co-Publisher's edition: 978-7-118-11716-5

This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.

The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Reliability system engineering is an interdisciplinary subject whose main research object is the life characteristics of products. It involves many fields of basic mathematics, engineering technology and management science. In recent years, many related books have appeared in the field of reliability. However, there are relatively few books on reliability mathematical models, or reliability mathematical models established only on the basis of probability theory or fuzzy theory. According to the different life characteristics of systems, this book uses three different mathematical tools: probability theory, fuzzy theory and random fuzzy theory to model and analyze the reliability of systems, which is also the feature of this book. The contents of this book can not only enrich and improve the traditional reliability theory, but also promote the development of related disciplines, which has important theoretical significance.

The book is divided into six chapters, among which Chaps. extract some contents from the Introduction to Reliability Mathematics coauthored by Professor Jinhua Cao and Professor Kan Cheng, so as to facilitate readers to compare the reliability mathematical models established by the three mathematical tools.

Chapter , the reliability mathematical models of nonrepairable systems and repairable systems under random fuzzy environment are established, respectively.

This book can be used as a teaching material for senior undergraduates and postgraduates of science and engineering related majors, as well as a reference book for engineers and reliability practitioners to understand the basic theory of reliability. At the same time, readers are welcome to put forward valuable opinions and suggestions on this book.

As this book is to be published, I would like to express my heartfelt thanks to Prof. Wansheng Tang, Prof. Rui Kang, Prof. Xiaozhong Li, Prof. Ruiqing Zhao and Prof. Yanping Wang for their support and encouragement to publish this book. I would like to express my sincere thanks to my graduate students Yao Ma, Dongxue Liu, Liuying Ma, Lina Ha, Jinbang Shao, Zifeng Liu, Yunyun Yang and Shuqian Guan, who assisted the author to collate the literature! I would like to express my heartfelt thanks to editor Tianming Bai of National Defense Industry Press for editing and publishing the book!

Probability theory is a branch of mathematics that studies the behavior of random phenomena. It is generally believed that the study of probability theory was started by Pascal and Fermat in the seventeenth century when they succeeded in deriving the exact probabilities for certain gambling problems. After that, probability theory was subsequently studied by many researchers. A great progress was achieved when von Mises [1] initialized the concept of sample space in 1931. A complete axiomatic foundation of probability theory was given by Kolmogorov [2] in 1933. Since then, probability theory has been developed steadily and widely applied in science and engineering.

Let be a nonempty set, and let be a -algebra over . Each element in is called an event. In order to present an axiomatic definition of probability, the following three axioms are assumed: