System States, Reliability and Availability

This chapter deals with techniques to determine the availability of systems that can come back into service after at least one down‐state. Markov chains offer an elegant method to determine availability, reliability and average down‐time. As an introduction to Markov chains, the most simple system consisting of one component is studied. The chapter discusses concepts such as states, state value, transition rates, availability, and steady state. It introduces the general approach with Markov chains and Laplace transform. States that do not allow repair cause permanent system failure. Such states are called 'absorbing states'. The chapter shows how the expected lifetime of a system with one or more absorbing states can be calculated. It introduces the concepts of the mean lifetime until first failure (MTTFF) and the mean lifetime between failures (MTBF) with an adapted Markov‐Laplace method.