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School of Mathematics

# MATH30018 - 2006/2007

General Information
• Title: Reliability and Survival
• Unit code: MATH30018 (semester 2)
• Credits: 10
• Prerequisites: MT2131, 257 (ex-UMIST), MT2131, MT2232 (ex-VUM)
• Co-requisite units: None
• School responsible: Mathematics
• Member of staff responsible: Dr Mike Tso (Ferranti C.14, Tel: 63219)
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## Specification

### Aims

To provide an understanding of the statistical foundations of the study of failure time data. To introduce some applicable techniques in the contexts of medicine and engineering.

### Brief Description of the unit

This course introduces some of the main concepts arising in the study of systems subject to random failure, ranging from the planning of optimal replacement policies in reliability engineering to statistical analysis of survival data.

### Learning Outcomes

On successful completion of the course students will

• understand basic properties of reliability/survivor function and hazard function;
• know the common statistical distributions arising in the study of failure time data;
• be able to prove and apply results developed e.g. through elementary renewal theory to determination of optimal replacement policies;
• be able to apply state dependent (Markov) models to failure of systems with redundancy;
• be able to apply techniques of statistical estimation to censored data.

### Future topics requiring this course unit

MATH40762 Survival Analysis

### Syllabus

1. Reliability (survivor) function. Hazard function. Mean time before failure (MTBF).
2. Common failure time distributions. Exponential, Weibull, Gamma families.]
3. Series and parallel systems. k-out-of-n systems.
4. Replacement policies. Block replacement. Age replacement.
5. Redundancy. State dependent models.
6. Censored data. Estimation of survivor function. Maximum-likelihood estimate. Kaplan-Meier product limit estimate.

### Textbooks

L. Wolstenholme, Reliability Modelling - A Statistical Approach, Chapman & Hall, 1999,
L. M. Leemis, Reliability - Probabilistic Models and Statistical Methods, Prentice-Hall, 1995,
D. Collett, Modelling Survival Data in Medical Research, Chapman \& Hall, second edition, 2003.

### Teaching and learning methods

Two lectures per week plus one weekly examples class.

Assessment
End of semester examination (2 hours) 100%.

## Arrangements

Online course materials are available for this unit.