Parameterization of cumulative mean behavior of simulation output data

We develop a new measure of reliability for the mean behavior of a process by calculating the probability that the cumulative sample mean will ever deviate from its long-term mean, and its true mean, over a period of time. This measure can be used as an alternative to estimating system performance using confidence intervals. We derive the tradeoffs between four critical parameters for this measure: the underlying variance of the data, the starting sample size of a procedure, and the precision and confidence in the result