Module Identifier MA37710  
Module Title RELIABILITY  
Academic Year 2001/2002  
Co-ordinator Dr J Lane  
Semester Semester 2  
Pre-Requisite MA26010  
Course delivery Lecture   19 x 1 hour lectures  
  Seminars / Tutorials   3 x 1 hour example classes  
Assessment Project report   About 2,000 words plus supporting graphs, tables etc   25%  
  Exam   2 Hours (written examination)   75%  
  Resit assessment   2 Hours (written examination) Project passed: assessment as above, project mark carried forward; Project failed: 2 hour written examination - 100%   100%  

General description

This module will consider the mathematical methods underpinning the often life-and-death issues of safety and risk assessment in modern high technology industries. Some of the questions studied such as life testing, also have counterparts in medical statistics. The module includes a short project.


To introduce students to the properties of lifetime distributions, and their estimation, to study the reliability of systems of components and gain an appreciation of how high levels of reliability and safety may be achieved in practice.

Learning outcomes

On completion of this module, a student should be able to:


1. STATISTICAL FAILURE MODELS: Reliability and hazard functions, mean time to failure, reliable lifetime; distributions (Exponential, Weibull, Gamma, Gumbel, Log Normal) competing risks; simple bounds on reliability.
2. SYSTEMS RELIABILITY: Series, parallel, k out of n systems. Path and cut sets, monotonic systems, modules. Bounds on system reliability. Fault trees.
3. MAINTAINED SYSTEMS: Availability, systems availability; maintenance. Spares problems; NBU components.
4. FITTING MODELS TO RELIABILITY DATA: Life tests: type 1 and 2 censoring, progressive censoring; accelerated life tests. Kaplan-Meier estimator. Maximum likelihood estimation for exponential and Weibull with censoring; reliability function, reliable lifetime. Arrhenius and power law models.

Reading Lists

** Recommended Text
D L Grosh. (1989) A Primer of Reliability Theory. Wiley 047163820X