Probabilistic Reliability Models

Practical Approaches to Reliability Theory in Cutting-Edge Applications

Probabilistic Reliability Models helps readers understand and properly use statistical methods and optimal resource allocation to solve engineering problems. The author supplies engineers with a deeper understanding of mathematical models while also equipping mathematically oriented readers with a fundamental knowledge of the engineering related applications at the center of model building. The book showcases the use of probability theory and mathematical statistics to solve common, real-world reliability problems. Following an introduction to the topic, subsequent chapters explore key systems and models including:

• Unrecoverable objects and recoverable systems
• Methods of direct enumeration
• Markov models and heuristic models
• Performance effectiveness
• Time redundancy
• System survivability
• Aging units and their related systems
• Multistate systems

Detailed case studies illustrate the relevance of the discussed methods to real-world technical projects including software failure avalanches, gas pipelines with underground storage, and intercontinental ballistic missile (ICBM) control systems. Numerical examples and detailed explanations accompany each topic, and exercises throughout allow readers to test their comprehension of the presented material.

Probabilistic Reliability Models is an excellent book for statistics, engineering, and operations research courses on applied probability at the upper-undergraduate and graduate levels. The book is also a valuable reference for professionals and researchers working in industry who would like a mathematical review of reliability models and the relevant applications.

Table of Contents

1 What Is Reliability? 1
2 Unrecoverable Objects 9
3 Recoverable Systems: Markov Models 40
4 Recoverable Systems: Heuristic Models 72
5 Time Redundancy 95
6 “Aging” Units and Systems of “Aging” Units 103
7 Two-Pole Networks 123
8 Performance Effectiveness 143
9 System Survivability 162
10 Multistate Systems 169
Appendix A Main Distributions Related to Reliability Theory 195
Appendix B Laplace Transformation 209
Appendix C Markov Processes 214
Appendix D General Bibliography 227