This paper discusses implementation of two sequential procedures to construct confidence intervals for a simulation estimator of the steady-state mean of a stochastic process. Our quasi-independent-mean (QIM) methods attempt to obtain i.i.d. samples. We show that our sequential procedures give valid confidence intervals. The two assumptions required are that the stochastic-process output sequence is continuous and satisfies the phi-mixing conditions. The algorithm dynamically increases the simulation run length so that the mean estimate satisfies a pre-specified precision requirement.