The Method of Stages for Non-Markov Models

Several techniques are available for solving reliability models containing non-exponential state residence times. All of these techniques, other than the method of stages, involve derivation of closed-fonn expressions in time domain or Laplace form. Though the closed-form solutions are useful, they are often impossible to derive due to complexity of the interstate transition rates. Stage combinations can be used either to fit the available data or approximate a known probability distribution. The main advantage with this method is that though an explicit mathematical expression does not emerge, the numerical solution can be generally obtained. This paper briefly describes some fundamental stage combinations that can be used to simulate a wide range of distributions, and refers to more-extensive explanations.