Selecting the best system using transient means with sequential sampling constraints

The objective of this research to develop an efficient ranking and selection (R&S) procedure for selecting the best system when its transient mean value is used as the performance measure. In this research, the true underlying mean of each system is not constant but is a function of a discrete index such as observation number or discretely sampled time. This problem is motivated by using simulation to compare the multiple configurations in order to select the configuration with best performance after certain amount of time. For example, selecting the best prototype whose performance is measured by its reliability after a certain amount of time in new product development. Another motivating example can be found in a queuing system that is initially empty and idle. Suppose that we are interested in finding the best configuration of this queuing system such that the waiting time of the 20th customer can be minimized, before the steady state of the system is reached. In this example, the underlying mean of the system is a function of observation number while the discrete index is time in the new product development example.