# CE 541/ME 583 - Reliability of Engineering Systems

This course describes how to determine the probability individual components (e.g., beams, columns or connections) will fail and the probability that a system of these components (e.g., a structural frame) will fail. In a philosophical sense, it helps one realize that engineers can't guarantee a given outcome, rather we are providing reasonable odds that the outcome will be as desired. It also helps an engineer view things from a systems perspective, e.g., whether or not redundancy improves the reliability of the system -- it doesn't always -- and how reliable each component must be to improve the reliability of the system. These concepts form the basis of performance-based design.

All the current LRFD structural and geotechnical design codes are derived from reliability concepts. The course describes how these codes are derived.

### Details regarding class organization... and Engineering Outreach and Contact information

 Class Date Topic Assignment 1 Aug 20 Introduction 2 Aug 22 Review of Probability 3 Aug 24 Probability Distributions Homework #1 4 Aug 27 Extreme Value Distributions; Mathcad Example 5 Aug 29 Asympotitic Distributions; Gumbel's Classifications Homework #2 6 Aug 31 Order Statistics; Order Stat Ex, Spreadsheet Sep 3 Labor Day 7 Sep 5 Bayes' Theorem, Bayes' Theorem Example 8 Sep 7 Transformation of Variables; Mathcad Example 9 Sep 10 The Reliability Problem Homework #3 10 Sep 12 Second Moment Formulations 11 Sep 14 Linear Limit States, Example 12 Sep 17 Invariant Formulations 3.6 and Homework #4 13 Sep 19 Nonlinear Limit States 14 Sep 21 Transformation Methods 15 Sep 24 Example 1, Example 2 5.1 and Homework #5 16 Sep 26 Determination of the Safety Index 17 Sep 28 Monte Carlo Simulation 18 Oct 1 Examples: Mathcad, FOSM comparison 5.4 and Homework #6 19 Oct 3 EXAM #1 (Old Exam) 20 Oct 5 Importance Sampling; Example Project Assignment 21 Oct 8 Latin Hypercube Sampling, 4.1, 12 22 Oct 10 Latin Hypercube Example 23 Oct 12 Antithetic Sampling; Antithetic Sampling Example. Comparison 24 Oct 15 Correlated Random Variables, Example Project Proposal 25 Oct 17 System Reliability Homework #9 26 Oct 19 Series System Probability Bounds 27 Oct 22 Ditlevsen Bounds, Example 28 Oct 24 Parallel Systems 29 Oct 26 Enumeration Methods for System Reliability 9.1 30 Oct 29 Probabilistic Enumeration Methods for System Reliability Project Progress Report 31 Oct 31 Element Replacement Techniques 32 Nov 2 Codes and Structural Reliability, Example Homework #11 33 Nov 5 Exam #2 Old Exam 34 Nov 7 Code Calibration, Mechanistic Empirical Pavement Design Guide 35 Nov 9 Modeling of Uncertainty 36 Nov 12 Quantification of Uncertainty 8.2, 3 37 Nov 14 Distributions 38 Nov 16 Human Error Project Progress Report Nov 19-23 Thanksgiving Recess 39 Nov 26 Time Dependent Reliability 40 Nov 28 Discrete Processes Homework #13 41 Nov 30 EXAM #3 Old Exam, Excel Sol'n 42 Dec 3 Discrete Process Examples, Mathcad Worksheets: 1 year, 50 years, tL years 43 Dec 5 Fatigue, Example 44 Dec 7 Presentations 47 Dec 12 12: 45 P.M. Presentations

The reading assignments should be completed before each lecture.

Homework is due on the dates shown.