Stochastic Modelling and Survival Analysis
Unit code: HMS613
|Credit points||12.5 Credit Points|
|Contact hours||60 hours|
HMS215 Engineering Mathematics 3C or equivalent.
An elective unit of study in the
The unit HMS613 will also be available as an elective in Bachelor of Engineering degrees within the Faculty of Engineering and Industrial Sciences.
Aims and objectives
The unit will:
- Convey the fundamental probability concepts necessary for an understanding of stochastic processes
- Introduce stochastic processes and some important related concepts
- Illustrate the usefulness of stochastic modelling by considering various different types of stochastic processes and how they can be applied in a range of scientific, engineering and other contexts
- Examine how probability distributions can be used to model system reliability and lifetimes
Upon completion of this unit students will be able to:
- Understand the concepts of conditional and joint probability distribution, conditional expectation, covariance and correlation, use and interpret them.
- Understand the definitions of stochastic process and some related concepts and apply them in particular cases.
- Recognise situations where particular types of stochastic processes arise, and apply a sound working knowledge of the theory of each process to solve practical problems.
- Use simple survival analysis and life testing methods to model failure rates and investigate failure time distributions.
Generic skills outcomes
Students will be provided with feedback on their progress in attaining the following generic skills:
- Ability to apply knowledge of basic science and engineering fundamentals.
- Ability to communicate effectively, not only with engineers but also with the community at large.
- Ability to undertake problem identification, formulation and solution.
- Conditional and joint distributions: Conditional probability distributions, conditional expectation, joint probability distributions, covariance and correlation.
- Stochastic Processes: Definition and examples, stationarity, ergodicity.
- Some Types of Stochastic Processes and Applications: Markov processes (discrete and continuous parameter), martingales, Poisson processes, queuing systems, random walk, applications from engineering, science and other fields.
- Survival Analysis and Life Testing: Series, parallel and complex systems, time to failure, hazard rate, commonly arising distributions, life testing, examples.
Text booksRichards, D., HMS613 Stochastic Modelling and Survival Analysis, Swinburne University of Technology, 2011.
ReferencesBorovkov, K., Elements of Stochastic Modelling, World Scientific, 2003.
Hayter, A.J., Probability and Statistics for Engineers and Scientists, 2nd edition, Duxbury, 2002.
Helms, L.L., Introduction to Probability Theory With Contemporary Applications, Freeman, 1997.
Levine, D.M., Ramsey, P.P. and Smidt, R.K., Applied Statistics for Engineers and Scientists, Prentice-Hall, 2001.
Papoulis, A. and Pillai, S.U., Probability, Random Variables and Stochastic Processes, 4th edition, McGraw-Hill, 2001.