The main purpose of this book is to present an introduction to flowgraph models for time-to-event data. The focus is on stochastic models for censored time-to-event data with competing risks and recurrent events. The applications are geared to survivalanalysis and reliability. I view flowgraph models as providing a methodology for data analysis of semi-Markov processes that can be applied without becoming intimately familiar with the mathematical theory of stochastic processes. My early experience with stochastic processes left me with the impression that there were lots of nice models, but I could not think of how to analyze data with them except in the simplest cases. I found myself unhappy with the exponential assumption and limit theorems, which although they provided some approximation, did not reflect the real system. My early work in flowgraphs was on queues, but I soon found myself drawn to interesting applications in survival analysis. Consequently, I continued to work in both survival analysis and engineering systems. Flowgraphs bring together applied probability techniques such as transforms and saddlepoint methods and meld them with data analysis and statistical methods. Flowgraph models are analyzed using Bayesian methods, or if one prefers, maximum likelihood techniques.
This book is intended for students and practitioners of statistics who have some background at the level of a one-year graduate course in probability and statistics. Although background in survival analysis or systems reliability is not assumed, a one-semester course or some experience with standard methods in these areas would be helpful. The first seven chapters are structured for a one-semester topicscourse. The remaining two chapters are more advanced. A large number of worked examples are presented along with computer code as needed. For readers who are not as interested in computation, Section 3.5 and Chapter 6 can be skipped without loss of continuity.