Estimating the Probability of Being the Best System: A Generalized Method and Nonparametric Hypothesis Test

This thesis provides two new approaches for comparing competing systems. Instead of making comparisons based on long run averages or mean performance, the first paper presents a generalized method for calculating the probability that a single system is the best among all systems in a single trial. Unlike current empirical methods, the generalized method calculates the exact multinomial probability that a single system is best among competing systems. The ability to avoid time consuming empirical estimate techniques could potentially result in significant savings in both time and money when comparing alternate systems. A Monte Carlo simulation is conducted comparing the empirical probability estimates of the generalized integral method, calculated using a bootstrapping procedure and density estimation technique, with those of two related estimation techniques, Procedure BEM (Bechhofer, Elmaghraby, and Morse) and Procedure AVC (All Vector Comparisons). All test cases show comparable performance in empirical estimation accuracy of the generalized integral method with that of the current methods analyzed. The second paper proposes the use of a distribution-free ordered comparisons procedure to test whether one population is stochastically larger (or smaller) than the other. This procedure is suggested as a useful alternative to the well-known Wilcoxon rank sum and Mann-Whitney tests. A Monte Carlo study is conducted, comparing the methods based on simulated power and type I error. All test cases show a marked improvement in performance of the ordered comparisons test versus the Wilcoxon rank sum test, when testing for stochastic dominance. A table of critical values is presented and a large sample approximation is given

The multinomial selection problem

In this thesis, we study indifference-zone multinomial selection procedures, that is, procedures for selecting the most probable ("best") multinomial cell. Such procedures have a number of real-world applications — for instance, which is the most popular television show in a particular time slot, or which manufacturing strategy has the highest probability of yielding the largest profit on a particular trial? The indifference-zone procedures we examine all satisfy a probability requirement that guarantees to correctly select with high probability the best multinomial category under a variety of underlying probability configurations. We show by Monte Carlo and exact calculations that certain sequential sampling procedures perform better than others. We also offer various extensions and thoughts for future research

A general framework on the computing budget allocation problem

Master'sMASTER OF ENGINEERIN

Simulation Optimization for Manufacturing System Design

A manufacturing system characterized by its stochastic nature, is defined by both qualitative and quantitative variables. Often there exists a situation when a performance measure such as throughput, work-in-process or cycle time of the system needs to be optimized with respect to some decision variables. It is generally convenient to express a manufacturing system in the form of an analytical model, to get the solutions as quickly as possible. However, as the complexity of the system increases, it gets more and more difficult to accommodate that complexity into the analytical model due to the uncertainty involved. In such situations, we resort to simulation modeling as an effective alternative.Equipment selection forms a separate class of problems in the domain of manufacturing systems. It assumes a high significance for capital-intensive industry, especially the semiconductor industry whose equipment cost comprises a significant amount of the total budget spent. For semiconductor wafer fabs that incorporate complex product flows of multiple product families, a reduction in the cycle time through the choice of appropriate equipment could result in significant profits. This thesis focuses on the equipment selection problem, which selects tools for the workstations with a choice of different tool types at each workstation. The objective is to minimize the average cycle time of a wafer lot in a semiconductor fab, subject to throughput and budget constraints. To solve the problem, we implement five simulation-based algorithms and an analytical algorithm. The simulation-based algorithms include the hill climbing algorithm, two gradient-based algorithms biggest leap and safer leap, and two versions of the nested partitions algorithm. We compare the performance of the simulation-based algorithms against that of the analytical algorithm and discuss the advantages of prior knowledge of the problem structure for the selection of a suitable algorithm