An improved method, called Simulation of System Operation for Reliability Analysis, for utilizing Monte Carlo techniques in the computer analysis of the reliability of complex systems is presented. This method is particularly applicable to systems which employ highly reliable elements with extremely low failure rates. Earlier techniques of Brunot simulate operation of a system through a sequential series of time steps and test for system failure in each time step. After a sufficient number of time steps, a system failure probability can be determined. When such methods are applied to systems composed of highly reliable components, computer time requirements can become excessive. This is due to the great number of time steps which must be examined to obtain statistically significant numbers of system failures. The method to be described begins by randomly selecting a “critical’ ’ time step of failure for each component. Failures are then examined to determine if a system failure combination has occurred in any time step. To continue the simulation, a second critical time step is chosen for each component and added to the first. The program proceeds in this fashion, considering only time steps in which at least one failure has occurred. Thus computer time requirements become essentially independent of failure rates.