Cumulative mean bounds for quality control analysis

We develop an alternative to confidence intervals, called cumulative mean bounds, for estimating the mean behavior of system performance. Cumulative mean bounds assess the probability that the cumulative sample mean stays within a given distance from the unknown true mean and rely on properties of standardized time series. We extend the properties of cumulative mean bounds to estimate the probability that the cumulative sample mean will reach a particular value. This idea can be used to analyze quality control methods for predicting mean simulation output behavior given an initial sample of output.