Selected topics in computable and applied mathematics

Supervisor(s): Dr Alexander Melnikov and Dr Matthew Harrison-Trainor

Supervisor’s webpage: https://www.massey.ac.nz/~amelniko/

Project Description

We propose a project which is focused on using abstract mathematical tools to solve problems in applied and contemporary subjects. The first and main part will be focused on the applications of mathematics to social science. When evaluating voting methods, it is desirable to understand how likely certain situations (such as cycles in the defeat relation) are to occur. Our proposed project is to analyse such situations under various hypotheses on the random distribution of ballots. Such studies involve algebraic and analytic methods which should not be beyond an excellent undergraduate student. If the student has early success with the main part, he will be asked to check whether some of the mathematical methods can be made more computationally efficient; this is the second (optional) part of the project.

Comparing the efficiency of control charts when using three different estimators for fraction of nonconforming 

Supervisor(s): Dr Julio Pereira

Supervisor’s webpage: N/A

Project Description

In the literature there are at least three known estimators for the proportion p of nonconforming items in a sample when the sample size is variable. A comparative study has not been found in the literature with regards the choice of the best estimator to be used in the calculation of the control limits for control charts of fraction of nonconforming.  In other words the effect of using one or another estimator in detecting an out of control process is unknown. The aim of this project is to carry out a simulation study to compare the impact of using three ratio estimators for nonconforming fraction in the calculation of the control chart limits when the sample size is not fixed. In this way we will be able to find out if there is any advantage or disadvantage in using any of the three estimators in various scenarios. Please feel free to contact Dr Julio Pereira by email: J.Pereira@massey.ac.nz if you have any questions about this project.