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Batch means are sample means of subsets of consecutive subsamples from a simulation output sequence. Independent and normally distributed batch means are not only the requirement for constructing a confidence interval for the mean of the steady-state distribution of a stochastic process, but are also the prerequisite for other simulation procedures such as ranking and selection (R&S). We propose a procedure to generate approXimately independent and normally distributed batch means, as determined by the von Neumman test of independence and the chi-square test of normality, and then to construct a confidence interval for the mean of a steady-state eXpected simulation response. It is our intention for the batch means to play the role of the independent and identically normally distributed observations that confidence intervals and the original versions of R&S procedures require. We perform an empirical study for several stochastic processes to evaluate the performance of the procedure and to investigate the problem of determining valid batch sizes.

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Indifference-zone selection procedures have been used to select a design with the minimum or maximum expected performance measure among a finite number of simulated designs. While there have been significant advancements in selection methodologies, the majority of the selection procedures are developed to process the selection when the performance measures are the mean of some output. In some situations, quantiles provide more suitable information. Quantiles are also more robust to outliers than the mean and standard deviation. Moreover, selection procedures are often derived based on the assumption that the input data are independent and identically distributed (i.i.d.) normal. In this paper we state and justify selection procedures when the ranking parameter is quantile. It is our intention for the quantile estimates to play the role of the i.i.d. normal observations that the original versions of selection procedures process. That is, we assume that our quantile estimates are approximately i.i.d. normal. We perform an empirical study of several stochastic processes to evaluate the performance of the procedure.

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