This book was written for an introductory one-semester or two-quarter course in stochastic processes and their applications. The reader is assumed to have a basic knowledge of analysis and linear algebra at an undergraduate level. Stochastic models are applied in many fields such as engineering systems, physics, biology, operations research, business, economics, psychology, and linguistics. Stochastic modeling is one of the promising kinds of modeling in applied probability theory. This book is intended to introduce basic stochastic processes: Poisson pro cesses, renewal processes, discrete-time Markov chains, continuous-time Markov chains, and Markov-renewal processes. These basic processes are introduced from the viewpoint of elementary mathematics without going into rigorous treatments. This book also introduces applied stochastic system modeling such as reliability and queueing modeling. Chapters 1 and 2 deal with probability theory, which is basic and prerequisite to the following chapters. Many important concepts of probabilities, random variables, and probability distributions are introduced. Chapter 3 develops the Poisson process, which is one of the basic and im portant stochastic processes. Chapter 4 presents the renewal process. Renewal theoretic arguments are then used to analyze applied stochastic models. Chapter 5 develops discrete-time Markov chains. Following Chapter 5, Chapter 6 deals with continuous-time Markov chains. Continuous-time Markov chains have im portant applications to queueing models as seen in Chapter 9. A one-semester course or two-quarter course consists of a brief review of Chapters 1 and 2, fol lowed in order by Chapters 3 through 6."

This book contains 12 contributions on stochastic models in reliability and maintenance. Written by the leading researchers on each topic, each contribution surveys the current status on stochastic models emphasizing mathematical formulation and optimization applications. Each contribution is self-contained and has a thorough bibliography. The topics include renewal processes, semi-Markov processes, Markovian deterioration models, maintenance and replacement models, software reliability models and Monte-Carlo simulation. This book provides researchers, reliability engineers and graduate students with the current status of the field and future developments of the subject.

This monograph contains some ofthe papers presented at a UK-Japanese Workshop on Stochastic Modelling in Innovative Manufacturing held at Churchill College, Cambridge on July 20 and 21st 1995, sponsored jointly by the UK Engineering and Physical Science Research Council and the British Council. Attending were 19 UK and 24 Japanese delegates representing 28 institutions. The aim of the workshop was to discuss the modelling work being done by researchers in both countries on the new activities and challenges occurring in manufacturing. These challenges have arisen because of the increasingly uncertain environment of modern manufacturing due to the commercial need to respond more quickly to customers demands, and the move to just-in-time manufacturing and flexible manufacturing systems and the increasing requirements for quality. As well as time pressure, the increasing importance of the quality of the products, the need to hold the minimum stock of components, and the importance of reliable production systems has meant that manufacturers need to design production systems that perform well in randomly varying conditions and that their operating procedures can respond to changes in conditions and requirements. This has increased the need to understand how manufacturing systems work in the random environments, and so emphasised the importance of stochastic models of such systems.

Our daily lives can be maintained by the high-technology systems. Computer systems are typical examples of such systems. We can enjoy our modern lives by using many computer systems. Much more importantly, we have to maintain such systems without failure, but cannot predict when such systems will fail and how to fix such systems without delay. A stochastic process is a set of outcomes of a random experiment indexed by time, and is one of the key tools needed to analyze the future behavior quantitatively. Reliability and maintainability technologies are of great interest and importance to the maintenance of such systems. Many mathematical models have been and will be proposed to describe reliability and maintainability systems by using the stochastic processes. The theme of this book is "Stochastic Models in Reliability and Main tainability. " This book consists of 12 chapters on the theme above from the different viewpoints of stochastic modeling. Chapter 1 is devoted to "Renewal Processes," under which classical renewal theory is surveyed and computa tional methods are described. Chapter 2 discusses "Stochastic Orders," and in it some definitions and concepts on stochastic orders are described and ag ing properties can be characterized by stochastic orders. Chapter 3 is devoted to "Classical Maintenance Models," under which the so-called age, block and other replacement models are surveyed. Chapter 4 discusses "Modeling Plant Maintenance," describing how maintenance practice can be carried out for plant maintenance."

Operations research uses quantitative models to analyze and predict the behavior of systems and to provide information for decision makers. Two key concepts in such research are optimization and uncertainty. Typical models in stochastic operations research include queueing models, inventory models, financial engineering models, reliability models, and simulation models. This book contains a collection of peer-reviewed papers from the International Workshop on Recent Advances in Stochastic Operations Research (2007 RASOR Nanzan) held on March 5-6, 2007, at Nanzan University, Nagoya, Japan. It enables advanced readers to understand the recent topics and results in stochastic operations research.