Presents foundational literature review appealing to mathematicians as well as practical fools for studying real systems The Handbook of Reliability, Maintenance, and System Safety through Mathematical Modeling makes an important contribution to applied mathematics because the world of the 21st century is a highly complex place in many respects. Many factors affect reliability and performance, and they must be taken into consideration. These factors include engineering design, materials, manufacturing, operations, maintenance, and many more. Reliability is one of the fundamental criteria in engineering systems design, and maintenance serves to support reliability throughout a system's life. Addressing the issues requires information, modeling, analysis, and testing. Different techniques are proposed and implemented to analyze various behavior measures (in terms of the functioning and performance) of systems. This handbook is a valuable resource for undergraduates and graduate students in mathematics working worldwide on applications of mathematics to engineering problems; researchers, professionals, and scientists applying mathematics to engineering problems. The book 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. Table of contents moves from simple to complex examples, starting with basic models and then refining modeling approaches step by step by including growth limitations, stochastic effects, time lags, and other structures such as temporal and spatial variability. Book jacket.