Systems Reliability

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.

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

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

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.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

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.

Repeat Information

Repeat type: Internal & External