Construction of cumulative mean bounds for simulation output

Abstract

We develop a new measure of reliability, called cumulative mean bounds, that assesses the mean behavior of a process by calculating the probability that the cumulative sample mean will stay below its long-term sample mean, with a given tolerance, over a period of time. In this report, we provide a derivation of a lower bound for the measure when the underlying data are independent and identically distributed with a normal distribution.This derivation provides a preliminary basis for parallel extensions to the two-sided limiting case when we calculate the probability that the sample mean stays within a given distance from the true mean when the assumptions of independence and normality are removed.