Bounding and approximating Markov models

Simple expressions are developed for upper and lower bounds on the Markov state probabilities obtained from inspection of the terms in the Markov probability matrix. These bounds can be used for quick paper-and-pencil and calculator estimates. The bounds are also combined with the merging and decomposition methods in several examples of reliability and maintainability assessment. Use of these bounds can aid the well-known simplification technique of truncation (deleting the low probability states) by quickly obtaining upper bounds on the state probabilities, which ensures that only low-probability states are truncated.<>