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:

- What does "mean time to failure of 4000
hours"
*really*mean? Am I being encouraged by the vendor to make some unwarranted assumptions? Are there some hidden assumptions there that could make my reliability analysis invalid? - How would I go about verifying this claim?
- How would I go about verifying this claim in the next month (720 hours), which is just a fraction of the expected mean time?
- If I were to design a component, how would I go about determining the characteristics of that component's longevity?
- Why do I suddenly have this desire to take a bath? (inside joke)

**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:

- Communications and computer systems effectiveness
- Evaluation of residual property value in utility regulation
- Assessment of risk in many areas for insurance and planning
- Characterization of such diverse phenomena as relationship of survivability to response time, distribution of wind speed in storms, expected crop yield, impact of medicine or medical treatments, duration of telephone conversations, and effectiveness of preventive maintenance

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:

- Lifetime Distributions
- Lifetime Models
- Accelerated Life and other Specialized Models
- Renewal Models
- Basic Parameter Estimation
- Maximum-likelihood estimation
- Parameter Estimation in Advanced Models
- Non-parametric Estimation models.

**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.

**References:**

*Introduction to Probability Models*, 7th ed. by Sheldon M. Ross. Harcourt Academic Press. 2000.*Accelerated Testing: Statistical Models, Test Plans, and Data Analysis,*by Wayne Nelson. Wiley Interscience, 1990.*NIST/SEMATECH e-Handbook of Statistical Methods*, http://www.itl.nist.gov/div898/handbook/

**Instructor: **John
Mullen, Tel:(505)646-2958, email: jomullen@nmsu.edu

rev: jpm 01dec05