Testing for Markov Properties

Most of the reliability models discussed in this book assume that the systems under consideration exhibit stationary Markov properties. To test whether this assumption is valid or not requires the use of various Chi Square and maximum likelihood statistical techniques. In this section much of the theory for testing Markov properties will be developed for Markov chains. Methods for extending the theory for continuous time parameter Markov processes will be mentioned. In particular, methods will be provided to estimate the transition probabilities from data, to test whether the transition probabilities indicate that the system is stationary, Markovian, or statistically independent, to test whether two processes are identical and to test whether the data is from a system with specific transition probabilities.