Markov chain approximation methods in a class of level-crossing problems

Level-crossing problems are encountered in a number of stochastic processes such as queueing, dams, inventory and in the cumulative sum (CUSUM) charts of statistical quality control. Approximate computational methods, using Markov chains to determine expected first-crossing times in CUSUM charts, are reviewed and extended to more general stochastic processes and examples are given. Formulas are presented when the underlying processes can be represented or approximated by either normal distributions or generalized hyperexponential distributions.