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.

#### Aims

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:
• evaluate and use the reliability function, hazard function, mean time to failure and reliable lifetime of lifetime distributions in common use;
• evaluate the reliability of systems of independent components;
• describe and use simple bounds on reliability;
• explain the notation used in fault trees and describe their uses;
• describe the differences between maintained and unmaintained systems and evaluate the availability in simple cases;
• calculate the number of spares required for maintained systems of independent components;
• describe the uses of censoring and acceleration in life testing; estimate exponential and Weibull parameters in such life tests.

#### Syllabus

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.