Topic 1: Applied Probability. Basic probability theory, combinatorial analysis of random phenomena, conditional probability and independence, parametric families of distributions, expectation, distribution of functions of random variables, limit theorems.

Topic 2: Mathematical Statistics. Sampling distributions, properties of estimators, point and interval estimation, hypothesis testing, introduction to multivariate and nonparametric statistics.

Topic 3: Time-Series Modeling, Analysis, and Control. Methods for analytical modeling, analysis, prediction, and control of linear, stationary time series. Includes examples of advanced research in nonstationary time-series modeling and applications in manufacturing, financial engineering, geosciences, and other areas. Students complete a project on a topic of their choice. Same as: M E 384Q.3 Additional prerequisite: Graduate standing, Mechanical Engineering 364L or the equivalent, an undergraduate calculus-based course in probability and statistics or consent of instructor.

Topic 4: Reliability Theory and Modeling. Theory of probabilistic and statistical models of aging elements, reliability, replacement, and repair maintenance, and their integration in surveillance, quality control, and manufacturing problems.

Topic 5: Applied Stochastic Processes. Poisson process, renewal theory, discrete and continuous-time Markov chains, queueing and reliability applications.

Topic 6: Regression and Analysis of Variance. Fitting equations to data; joint confidence regions; partial correlation analysis; general linear hypotheses; dummy variables; diagnostics and remedial measures; design of experiments; fixed, random, and mixed models; factorial and nested designs. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 2) or consent of instructor.

Topic 7: Statistical Techniques in Image Processing. Statistical techniques for transformation, enhancement, restoration, segmentation, and classification of digital image data.

Topic 8: Queueing Theory. Introduction to the classical and modern theories of queueing systems. Simple Markovian queues; the M/G/1 and G/G/1 queues; Jackson and Kelly networks; multiclass networks; stability, scheduling, and routing in queueing networks; fluid and diffusion approximations. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 1) or consent of instructor.

Topic 9: Systems Simulation. Random number generation, simulation experiments, statistical verification, clock routines, simulation language applications, industrial problems.

Topic 10: Statistical Design of Experiments. Introduction to statistical design of experiments based on both classical analysis of variance and modern heuristic techniques. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 1) or the equivalent, 390R (Topic 2) or the equivalent, and 390R (Topic 6) or the equivalent.

Topic 11: Advanced Stochastic Processes. Markov renewal processes, generalized semi-Markov processes, marked point processes, Martingale theory, Brownian motion, Levy processes, and stochastic calculus.

Topic 12: Multivariate Statistical Analysis. Theory and applications of multivariate statistics, including multivariate parametric distributions, estimation, hypothesis testing, principal components analysis, canonical correlation, multivariate regression, and classification.

Topic 13: Operations Research: Stochastic Models. Stochastic processes and models in operations research; discrete- and continuous-time Markov chains; queueing and inventory models; simulation. May not be counted toward the Master of Science in Engineering degree with a major in operations research and industrial engineering. Additional prerequisite: Mechanical Engineering 335 or the equivalent.

Topic 14: Special Topics in Probability, Stochastic Processes, and Statistics. Study of specialized topics, such as advanced stochastic processes, Bayesian statistics, simulation, and stochastic optimization, intended to introduce and stimulate further research. Additional prerequisite: Consent of instructor.

Topic 15: Nuclear Safety and Security. Probabilistic risk assessment models and nuclear arms nonproliferation, including failure classifications; failure mode, effects, and criticality analysis (FMECA); fault and event trees; and reliability block diagrams. Discussion of specific areas from the Code of Federal Regulations. Only one of the following may be counted: Mechanical Engineering 337G, 388H, Operations Research and Industrial Engineering 390R (Topic 15).

Topic 16: Markov Decision Processes. The theory of Markov decision processes, also known as stochastic dynamic programming. Includes finite horizon, total discounted cost, and average cost problems; continuous-time and semi-Markokv models; and applications in finance, queueing, and control theory. Additional prerequisite: A course in stochastic processes or consent of instructor.

Topic 17: Decision Analysis. Principles and application of techniques for the logical illumination of complex decision problems within any context. Subjects may include utility theory, probability as a statement of belief, risk preference, value of information and control, probability assessment, influence diagrams, risk sharing and scaling, and life-and-death decision making.

Topic 18: Decision Engineering. Application of decision analysis in practice including framing, decision modeling, sensitivity analysis, discretization, psychological aspects of decision making, probability assessment, and challenges to the decision analysis framework. May include related subjects such as real options, bidding, and portfolio management.