# Product Reliability

## Lecture notes

Introduction to reliability engineering [lecture video][lecture notes]

Review of probability and statistics - part 1 [lecture video][lecture notes]

Review of probability and statistics - part 2 [lecture video][lecture notes]

Review of probability and statistics - part 3 [lecture video][lecture notes]

Review of probability and statistics - part 4 [lecture video][lecture notes]

Limit-state function and FOSM [lecture video][lecture notes]

MVFOSM and FORM [lecture video][lecture notes]

FORM [lecture video][lecture notes]

FORM - continued [lecture video (part 1)][lecture video (part 2)][lecture notes]

SORM [lecture video][lecture notes]

MCS [lecture video][lecture notes]

IS and LHS [lecture video][lecture notes]

SS - Part 1 [lecture video][lecture notes]

SS - Part 2 [lecture video]lecture notes]

Response surface method [lecture video][lecture notes]

Response surface method - continued [lecture video][lecture notes]

Polynomial chaos expansion [lecture video][lecture notes]

Gaussian Process [lecture video][lecture notes]

Some advanced topics in surrogate models [lecture video][lecture notes]

Design of experiments [lecture video][lecture notes]

System reliability analysis [lecture video][lecture notes]

Time-dependent reliability analysis and way forward [lecture video][lecture notes]

## Syllabus

General overview of the structural reliability

Brief review of statistics and probability

Taylorâ€™s series-based approach for reliability analysis: FOSM, FORM, SORM.

Simulation based method for reliability analysis: Monte Carlo simulation, Importance sampling, subset simulation, directional simulation

Surrogate based approaches for reliability analysis: response surface method, polynomial chaos expansion, Kriging, Neural Network, High-dimensional model representation, etc.

System reliability analysis: series system, parallel system, k out of n system

Time-dependent reliability analysis

Reliability based design optimization and way ahead.

## References

Lecture notes and references will be provided on the course web site. The following books are recommended:

Haldar, A., & Mahadevan, S. (2000). Probability Reliability And Statistical Methods In Engineering Design. John Wiley & Sons.

Haldar, A., & Mahadevan, S. (2000). Reliability assessment using stochastic finite element analysis. John Wiley & Sons.

Stanton, A., Wiegand, D., & Stanton, G. (2000). Probability reliability and statistical methods in engineering design.

Bishop, C.M. Pattern recognition and Machine learning, Springer, 2007.

Murphy, K.P. Machine learning: A Probabilistic Perspective, MIT press, 2012.

## Homework

## Projects

Explanation video on Project [video link]

## Course info

**Credit: **3 Units (3-0-0)

**Lectures: **MW (11:00 AM - 12:30 PM)

**Instructor****:**** **Dr. Souvik Chakraborty

**Teaching Assistants:**** Tu****shar**

**Course Objective:** The objective of this course offered by the Department of Applied Mechanics is to introduce the concepts of Reliability engineering to the students. The course will dive into the fundamental concepts of reliability engineering and its application in solving scientific and engineering problems. Different reliability analysis methods will be discussed. The course will emphasize on the mathematical learning of these concepts along with applications. The course is particularly designed for PG and Ph.D. students.

**Intended audience:** PG and Ph.D. students