Point Processes for Reliability Analysis: Shocks and Repairable Systems

Introduction -- Preliminaries: Reliability and Point Processes -- Renewal Processes and Applications -- Poisson Process -- Advanced Poisson Shock Models -- Advanced Poisson Shock Models -- Generalizations of Renewal Process -- Generalized Polya Process -- Applications of the Generalized Polya Process -- Multivariate Generalized Polya Process -- Applications of the Mixed Poisson Process -- Shocks as the Discrete Scale.;Focusing on the theory and applications of point processes, Point Processes for Reliability Analysis naturally combines classical results on the basic and advanced properties of point processes with recent theoretical findings of the authors. It also presents numerous examples that illustrate how general results and approaches are applied to stochastic description of repairable systems and systems operating in a random environment modelled by shock processes. The real life objects are operating in a changing, random environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some stochastic point processes. The Poisson (homogeneous and nonhomogeneous) process, the renewal process and their generalizations are considered as models for external shocks affecting an operating system. At the same time these processes model the consecutive failure/repair times of repairable engineering systems. Perfect, minimal and intermediate (imperfect) repairs are discussed in this respect. Covering material previously available only in the journal literature, Point Processes for Reliability Analysis provides a survey of recent developments in this area which will be invaluable to researchers and advanced students in reliability engineering and applied mathematics.