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.