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 impact of reliability on the design of a system
- 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
- The mechanisms of failure for mechanical and electronic systems and how they can be countered
- 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 real world systems
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- 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
- Evaluate the reliability of a system and its subcomponents
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
Type | Hours |
---|---|
Completion of assessment task | 68 |
Seminar | 2 |
Preparation for scheduled sessions | 16 |
Wider reading or practice | 15 |
Practical classes and workshops | 12 |
Follow-up work | 15 |
Lecture | 22 |
Total study time | 150 |
Resources & Reading list
Textbooks
Elsayed, E.,. Reliability Engineering.
Crowder, Kimber & Sweeting. Statistical Analysis of Reliability Data.
Vanguard Studio User Manual.
O’Connor, P. Practical Reliability Engineering.
Soong, T.T. Fundamentals of Probability and Statistics for Engineers.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Individual project | 70% |
Coursework | 15% |
Coursework | 15% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Individual project | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
Method | Percentage contribution |
---|---|
Individual project | 100% |
Repeat Information
Repeat type: Internal & External