Semi Markov Processes and Reliability

Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility. This work provides an overview of semi-Markov processes and their applications in reliability. It contains examples which aid in the understanding of the theoretical notions and shows how to apply them to concrete physical situations including algorithmic simulations. Many examples of the concrete applications in reliability are given. The topics covered in the book include: processes associated to semi-Markov kernel for general and discrete state spaces; asymptotic theory of processes and of additive functionals; statistical estimation of semi-Markov kernel and of reliability function; and Monte Carlo simulation.