In many real-world simulation studies the several measures of performance are of interest simultaneously. There exist very limited number of studies that explain and suggest the methods or procedures of inferencing the system performances at the same time. This study presents a procedure for determining the number of simulation observations required to achieve the prespecified confidence level for several measures of system performance. Mean values are selected as the measures, for instance, expected ordering cost, expected holding cost, and expected shortage cost for a given period of time in the study of inventory problems. Basically, the batch means approach is applied and extended to develop an algorithm to carry out the procedure handling more than single parameter. The efficacy of the presented method is assessed through the experiments. The empirical results based on some stochastic systems such as queues and inventory problems show that the suggested method produces as excellent result in terms of the precision of estimated means and the number of observations required.