Design of experiments: estimation of selected interactions in factorial experiments

This project focuses on the construction of blocked or fractional factorial designs, to enable the estimation of all main effects and of selected interactions.

Start date

1 April 2023


Minimum of 3 years

Application deadline

Funding source

University of Surrey

Funding information

Full UK tuition fees and a tax-free stipend. This project is on offer in competition with a number of other projects for funding. This opportunity may be available with partial funding for overseas fees for exceptional applicants. However, funding for overseas students is limited and applicants are encouraged to find suitable funding themselves.


Experiments with factorial treatment structure are used widely in industrial experiments and have applications in many other areas, including medical research and the horticultural and agricultural industries. Their importance lies in their capacity to provide estimates of main effects and interactions with relatively small numbers of runs.

This project focuses on the construction of blocked or fractional factorial designs, to enable the estimation of all main effects and of selected interactions. Work in the literature predominantly focuses on designs with all factors at two levels. Further, designs are typically constructed under the assumption of the effect hierarchy principle, namely that “for given m, all m-factor interactions are equally important”. Thus, much of the existing work in this area uses minimum aberration criteria to maximise the number of estimable two factor interactions in designs with factors all at two levels.

In practice, knowledge of an experimental situation can mean that a subset of interactions is of interest, with the remaining interactions assumed to be negligible. It can be shown that designs constructed according to minimum aberration criteria are not necessarily the most appropriate designs in this situation. The project seeks design construction approaches with a focus on this scenario.

Proposed research directions

(i) Use of proper vertex colouring approaches in graph theory to aid construction of bespoke factorial and fractional factorial designs, with one form of blocking, enabling estimation of main effects and selected interactions. The aim is to extend work completed in (1) to construction of designs with factors at more than two levels and to encompass three factor interactions. 

(ii) Investigation of the various “folding” techniques available to de-alias effects of interest for factorial designs where sequential sets of small numbers of runs are planned. Regular and non-regular fractional factorial designs will be considered, both with and without blocking. See (2) and (3) for background reading.

The successful candidate will receive comprehensive research training related to all aspects of the research and opportunities to participate in conferences, workshops and seminars to develop professional skills and research network.


(1) Godolphin, J.D.,  2021. Construction of blocked factorial designs to estimate main effects and selected two-factor interactions, Journal of the Royal Statistical Society, Series B, 83, 5-29.

(2) Li, F., Jacroux, M., 2007. Optimal foldover plans for blocked fractional factorial designs. Journal of Statistical Planning and Inference, 137, 2439-2452.

(3) Li, W., Lin, D.K.J., 2003. Optimal foldover plans for two-level fractional factorial designs. Technometrics, 45, 142-149.

Eligibility criteria

Applicants should have a minimum of a first class honours degree in mathematics, the physical sciences or engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, though exceptional BSc students will be considered.

English language requirements 

IELTS minimum 6.5 or above (or equivalent) with 6.0 in each individual category.

How to apply

Applications should be submitted via the Mathematic PhD Research programme page on the "Apply" tab. Please clearly state the studentship title and supervisor on your application.

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Application deadline

Contact details

Cesare Tronci



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