Probability Foundations for Engineers

Joel Nachlas is an Associate Professor Emeritus of the faculty of Industrial and Systems Engineering at Virginia Tech. He served on that faculty from 1974 until 2016. During his tenure in that department, he served as the coordinator for the department’s Operations Research faculty and curricula and was also the coordinator of the department’s international program. The foci of Dr. Nachlas research were the application of probability theory to reliability analysis and maintenance planning and of statistical methods to quality control. He earned the B.E.S. from at Johns Hopkins University in 1970 and the M.S. and Ph. D. from the University of Pittsburgh in 1974 and 1976 respectively. All three of his degrees are in Industrial Engineering with a concentration in Operations Research. Dr. Nachlas has received numerous awards for his research including the 1991 P. K. McElroy Award and the 2004 Golomski Award. He continues to serve as the editor of the Proceedings of the Annual Reliability and Maintainability Symposium. He was a member of INFORMS and IISE and he is a Fellow of the Society of Reliability Engineers and a Fellow of the American Society for Quality. During his tenure at VT, Dr. Nachlas served for twenty years as a visiting professor at Ecole Polytechnique de Nice in France. While on the VT faculty, he served for 35 seasons as head coach of the Virginia Tech men’s lacrosse team and was selected in 2001 as the US Lacrosse MDIA national coach of the year.

1. Introduction. 2. A Brief Review of Set Theory. 3. Probability Basics. 4. Random Variables and Distributions. 5. Joint, Marginal and Conditional Distributions. 6. Expectation and Functions of Random Variables. 7. Moment Generating Functions. 8. Approximations and Limiting Behavior.