Mathematical Models for the Study of the Reliability of Systems

Evolved from the lectures of a recognized pioneer in developing the theory of reliability, Mathematical Models for Systems Reliability provides a rigorous treatment of the required probability background for understanding reliability theory. This classroom-tested text begins by discussing the Poisson process and its associated probability

In this study some mathematical models in reliability systems were investigated, such as series, parallel, series - parallel, parallel - series and complex systems by using some methods such as; path tracing method, reduction to series element method, minimal cut method, event space method, composite method and decomposition method . A comparison was done between those methods to get the best reliability. Reliability allocation had been studied .The aim of it is to establish a goal or objective for the reliability of each component. Two methods had been used to find the reliability allocation for series and complex systems. This study also discuss the reliability for non - maintenance depending on the application of Markov and non - Markov models.

Mathematical models for the study of the reliability of systems.

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 engineeringrelated 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.

The Handbook of Reliability, Maintenance, and System Safety through Mathematical Modeling discusses the many factors affect reliability and performance, including engineering design, materials, manufacturing, operations, maintenance, and many more. Reliability is one of the fundamental criteria in engineering systems design, with maintenance serving as a way to support reliability throughout a system's life. Addressing these issues requires information, modeling, analysis and testing. Different techniques are proposed and implemented to help readers analyze various behavior measures (in terms of the functioning and performance) of systems. Enables mathematicians to convert any process or system into a model that can be analyzed through a specific technique Examines reliability and mathematical modeling in a variety of disciplines, unlike competitors which typically examine only one Includes a table of contents with simple to complex examples, starting with basic models and then refining modeling approaches step-by-step