Focusing on foundational concepts in stochastic processes, this book serves as a comprehensive guide for students with a basic understanding of analysis and linear algebra. It covers essential topics such as Poisson processes, renewal processes, and both discrete and continuous-time Markov chains, emphasizing practical applications in various fields like engineering and economics. The initial chapters establish probability theory, laying the groundwork for advanced stochastic modeling techniques, including reliability and queueing models, suitable for a one-semester course.
Our daily lives rely heavily on high-technology systems, particularly computer systems, which enhance our modern experiences. However, maintaining these systems without failures is crucial, and predicting their failures and resolving issues promptly remains a challenge. A stochastic process, which involves outcomes of random experiments indexed by time, is essential for quantitatively analyzing future behaviors. Reliability and maintainability technologies are vital for the upkeep of these systems, leading to the development of various mathematical models that utilize stochastic processes to describe reliability and maintainability.
The book explores the theme of stochastic models in reliability and maintainability across 12 chapters, each offering unique perspectives on stochastic modeling. Chapter 1 focuses on renewal processes, surveying classical renewal theory and computational methods. Chapter 2 delves into stochastic orders, defining concepts and characterizing aging properties. Chapter 3 presents classical maintenance models, including age, block, and other replacement models. Chapter 4 discusses the modeling of plant maintenance, outlining effective maintenance practices for plant operations. This comprehensive exploration emphasizes the significance of stochastic modeling in enhancing system reliability and maintainability.
