The University of Southampton
Courses

# FEEG6006 Systems Reliability

## Module Overview

This module introduces students to both the theoretical and practical aspects of systems reliability and design for improved reliability. Lectures on the theory of systems reliability will be followed by practical tutorial sessions where students will apply their knowledge on a variety of problems.

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• The role of probability in systems reliability
• The creation and application of statistical distributions in reliability engineering
• Basic statistical methods and how they can be used to determine goodness of fit, confidence and test hypotheses
• Modelling techniques such as reliability block diagrams & fault tree analysis and their use in determining the reliability of a system
• Monte Carlo simulations and the generation of distributed random numbers
• The impact of reliability on the design of a system
• The mechanisms of failure for mechanical and electronic systems and how they can be countered
• The impact of reliability on real world systems
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Evaluate the reliability of a system and its subcomponents
• Make intelligent choices regarding the modelling of the reliability of a system
• Make intelligent choices regarding design changes to improve reliability whilst taking into account design trade-offs
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Set-up and solve reliability problems using a variety of software tools such as Excel, Matlab and Vanguard Studio.

### Syllabus

Lectures: - Introduction to Systems Reliability (1 lecture) Overview of the module structure (assignments, assessment etc.) What is reliability and why is it important? - Probability theory (1 lecture) Probability rules & notation Series of events Sequence trees Bayes’ Theorem - Continuous variations (1 lecture) Probabilistic reliability Variations & probability concepts Continuous statistical distributions Variations in engineering (with examples) - Fitting Probability Density Functions (2 lectures) Method of moments Least squares Maximum likelihood estimation Fisher information matrix Parameter confidence limits Q test Pearson’s X2 test - Discrete Variations (1 lecture) Binomial distributions Poisson distributions Poisson approximation to a binomial distribution - Random Numbers & Monte Carlo Analysis (1 lecture) Uniform random number generation Distributed random number generation Monte Carlo analysis Quasi-random numbers Quasi-Monte Carlo analysis - Reliability Modelling (4 lectures) Series, parallel & m-out-of-n systems Reliability block diagram analysis Block diagram decomposition m-out-of-n consecutive and balanced systems Active & inactive redundancy Multistate models Optimal component assignment Determining component importance Fault tree analysis Markov analysis - Design for Reliability (1 lecture) Implementing “design for reliability” Failure modes and effects analysis (FMEA) Hazard operability study (HAZOPS) - Robust Design & Reliability (1 lecture) Robust regularisation, aggregation & randomised techniques for robust design Taguchi methods Automated reliability optimisation - Advanced Modelling (3 lectures) MLE for censored data Competing risk models Load sharing systems Multivariate PDF construction and applications - Maintenance & Inspection (2 lectures) Expected failure times Expected number of failures Optimum interval for constant interval replacement Optimum replacement age for minimum cost Optimum interval for minimum downtime Optimum replacement age for minimum downtime - Warranties (1 lecture) Warranty costs for non-repairable systems - Life Testing (1 lecture) Accelerated life testing and statistical analysis - Mechanical Reliability (1 lecture) Common failure modes (stress, strength & fracture etc.) Preventative measures - Electronic Reliability (1 lecture) Common failure modes (stress effects, manufacturing issues etc.) Preventative measures - Guest Seminar (2 lectures) Tutorials: - Introduction to continuous PDFs & CDFs in Excel and Matlab (1 Tutorial) Defining PDFs & CDFs using Excel & Matlab Using Excel and Matlab to solve simple reliability/probability problems - Fitting Probability Density Functions (1 Tutorial) Manually fitting PDFs to sample data using maximum likelihood Fitting PDFs using Excel’s solver & Matlab - Application of statistical methods (1 Tutorial) Assessing goodness of fit, confidence and hypothesis testing using Matlab - Introduction to Monte Carlo simulations (1 Tutorial) Generating distributed random numbers in Matlab Performing a Monte Carlo analysis on a “mystery” function and creating the PDF - Introduction of Vanguard Studio (1 Tutorial) Overview & introduction to Vanguard Studio - Deterministic & Stochastic Modelling in Vanguard Studio (1 Tutorial) Building a deterministic model Converting a deterministic model into a stochastic model Performing a Monte Carlo simulation - Reliability Block Diagrams in Vanguard Studio (1 Tutorial) Creating a redundant system with three components of varying reliability - CDFs and Reliability Integrals in Vanguard Studio (1 Tutorial) Introduction to “integral” and “makelist” functions Calculating CDFs and reliability analytically in Vanguard Studio - Complex Reliability Block Diagram in Vanguard Studio (1 Tutorial) Creation of a block diagram for a microcar Performing a Monte Carlo simulation and analysis of the reliability - Fault Tree Analysis using Vanguard Studio (1 Tutorial) Creation of a fault tree analysis for a laptop battery Simulation of the fault tree - Design for Reliability (1 Tutorial) Optimisation to maximise reliability Optimisation to perform a trade-off between reliability and other design metrics - Individual Project Surgery (1 Tutorial) Opportunity for students to ask questions regarding their IP

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include - Lectures - Computer sessions Learning activities include - Using Excel to solve simple reliability problems - Using Matlab to solve simple reliability problems and fit probability density functions - Using Vanguard Studio to develop and solve complex reliability problems using RBDs and perform fault tree analysis - Using Excel/Matlab optimisation algorithms to perform trade-off studies and optimisations for reliability/robustness

TypeHours
Lecture22
Practical classes and workshops12
Preparation for scheduled sessions16
Follow-up work15
Seminar2
Total study time150

O’Connor, P. Practical Reliability Engineering.

Elsayed, E.,. Reliability Engineering.

Soong, T.T. Fundamentals of Probability and Statistics for Engineers.

Vanguard Studio User Manual.

Crowder, Kimber & Sweeting. Statistical Analysis of Reliability Data.

### Assessment

#### Summative

MethodPercentage contribution
Coursework 15%
Coursework 15%
Individual project 70%

#### Repeat

MethodPercentage contribution
Individual project 100%

#### Referral

MethodPercentage contribution
Individual project 100%

#### Repeat Information

Repeat type: Internal & External