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School of Mathematics

# MATH38102 - 2009/2010

General Information
• Title: Reliability and Survival
• Unit code: MATH38102
• Credits: 10
• Prerequisites: MATH20701
• Co-requisite units: None
• School responsible: Mathematics
• Members of staff responsible: Dr. Mike Tso
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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 this course unit 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

MATH48142 Survival Analysis.

### Syllabus

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

### Textbooks

• Wolstenholme, L., Reliability Modelling - A Statistical Approach, Chapman & Hall 1999.
• Leemis, L. M., Reliability - Probabilistic Models and Statistical Methods, Prentice-Hall 1995.
• Collett, D., Modelling Survival Data in Medical Research, 2nd edition, Chapman & Hall 2003.

### Teaching and learning methods

Two lectures and one examples class each week. In addition students should expect to spend at least four hours each week on private study for this course unit.

### Assessment

End of semester examination: two hours weighting 100%

## Arrangements

On-line course materials for this course unit.