Monotone Markov models

Markov models are frequently used in connection with system reliability evaluations. In this paper we study Markov models both for single components and for systems of possibly dependent, components. The purpose of the paper is to indicate how certain monotonicity properties of the model can be utilized in order to derive inequalities for interesting reliability parameters. As another application it will be indicated how monotonicity properties can be used to simplify problems concerning optimal replacement of components or systems. The paper is based on results published in probability and operations research journals during the past few years.