This course addresses a significant set of problems an engineer is likely to face when attempting to represent a given subsystem by a mathematical model in order to analyze the overall system. The main objective is to develop a model that is both representative and efficient.
Course Focus: The main focus is on characterizing the continuous non-negative random variables used in various stochastic models, as in simulation, reliability and queueing theory. To illustrate this scope, imagine that a component you need for a critical application is advertised to have a mean time to failure of 4000 hours. Using reliability theory, you can model the expected effect of this component on your system's mission, but you wonder:
Applications: Although much of the material is focused on component lifetime, it can be extended to virtually any case in which individual components have different, random, continuous-valued performance measures. Applications include:
In addition, "time" could be any measure of duration or exposure, such as length of wire, number of on/off cycles, or area of a silicon wafer.
Topics: Specific topics include:
Specific Coverage: The particular models that will be considered in depth include those based on the exponential, the Weibull, the gamma, and the extreme value probability distributions. Acceleration will include censoring and Arrhenius models. Parameter estimation will focus on maximum- likelihood methods whenever possible.
Who should take this course: This course would be helpful for students with a background in one or more of the process analysis methods above that wish to improve their ability to use such tools in practical situations. However, such knowledge is not assumed. On the other hand, the student should have a knowledge of engineering probability and statistics.
Text: Statistical Models and Methods for Lifetime Data, 2nd ed., by J. F. Lawless. Wiley, 2003.
Instructor: John Mullen, Tel:(505)646-2958, email: email@example.com
rev: jpm 01dec05