Interns 2009

Anna Fowler 
Completed MSci Hons Mathematics with Statistics/North America-Australasia at Lancaster University

Supervisors: Idris Eckley and Rebecca Killick

Detecting changes in regression for time series: a review and application
This project aimed to detect changes in regression (trend) in these datasets using industrial data sets, including several variables, provided by Unilever. Several existing methods for detecting changes in regression were investigated, including (normal) maximum likelihood (with and without penalty), residual sum of squares and cumulative sum of squares before conducting a simulation study looking at their effectiveness. From this simulation study, the most appropriate algorithm was chosen using statistical methods and finally the algorithm applied to the various industrial datasets. Anna produced a technical report of the findings and had the opportunity to present to statisticians at Unilever in Amsterdam.

Anna is now pursuing a PhD at Imperial College, London.  

Jak Marshall
Completed MSci Hons Mathematics/North America-Australasia at Lancaster University
Supervisor: Kevin Glazebrook

Optimal Control Policies in adjustable queue systems
Countless industrial processes include some variety of queueing system, for example, telecommunications and transport. Problems regularly arise in how queue operators manage the demand for their services. The challenge is to find an optimal way of allocating resource towards providing service across a collection of independent service stations serving customers in corresponding queues given the delicate balance of overspending on service infrastructure versus underspending and incurring costs due to system neglect. The approach to solving this problem relies heavily on computation and a good understanding of queueing objects in order to simulate an ideal queueing system. The key outcome of this project was to deliver a near-optimal method of managing queueing systems by considering a case study involving queues with only limited modes of service available at any time.

Jak joined STOR-i in 2010 to pursue a PhD in STOR. 

Erin Mitchell
Completed BSc Hons Mathematics at Lancaster University

Supervisor: Kevin Glazebrook

Queueing Systems and Optimisation of Computer Component Repairs
Repair companies often offer a promise of a turn-around period in which a faulty product will be repaired and returned to the customer, ensuring optimal customer satisfaction. In the majority of cases, the repair company will not complete all of the repairs themselves, if any at all, but will instead outsource the work to several different sub-companies. Upon receiving a broken product, a computer for example, the repair company must then decide to which of its contracted sub-companies to send the machine. Company A, for example, may be a larger, more specialist or more equipped business, and as such may be able to perform a given repair a lot quicker than Company B or C. If a company has a quick turnaround on their repairs, it may be desirable to send more broken machines to them than to the other companies. However, a balance must be struck between using the ‘best’ company and making efficient use of all the resources. With different companies being different distances away from a location (the repair company warehouse, for example), the time taken for travel and dispatch must also be considered. Taking into account all of these different factors, a model can be built in order to decide how many repairs to send to each company. Once a basic model has been designed, different probabilities can be assigned to factors, such as the probability of machine breakdown and machine repair, in order for choices and allocations to be made in the most intelligent manner. 

Erin started a PhD at Lancaster University in collaboration with Garrad Hassan in 2009.

Daniel Suen
Completed BSc Hons Mathematics at Lancaster University 
Supervisor: Joe Whittaker

Graphical modelling of divergence weighted independence graphs in the Criminal Justice System
Graphical models show how the relationships between several variables can be shown in graphical form. This project required learning the theory behind divergence weighted independence graphs and the modelling of such graphs using the statistical package, R. A key part of the research focused on illustrating how these graphs can be used to identify relationships between factors which affect trust in the Criminal Justice System. On completion of the internship, Daniel produced a comprehensive scientific report including applications using British Crime Survey data.

Daniel joined STOR-i in 2010 to pursue a PhD in STOR.