Module Identifier MA47710  
Module Title RELIABILITY  
Academic Year 2000/2001  
Co-ordinator Dr J A Lane  
Semester Intended For Use In Future Years  
Next year offered N/A  
Next semester offered N/A  
Pre-Requisite MA26010  
Course delivery Lecture   19 x 1hour lectures  
  Seminars / Tutorials   3 x 1hour example classes  
Assessment Exam   2 Hours (written examination)   75%  
  Project report   About 2,000 words plus supporting graphs, tables etc   25%  
  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 staistics. 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, momotonic 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 censoring; reliability function, reliable lifetime. Arrhenius and power law models.

Reading Lists
** Recommended Text
D L Grosh. A Primer of Reliability Theory. Wiley