Stochastic Modelling and Survival Analysis

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.

Teaching methods

Assessment

Tests (80-100%)
Assignments (0%-20%)

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.

Content

• 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.