The University of Southampton
Courses

# MATH6027 Design of Experiments

## Module Overview

When planning experiments, it is essential that the data collected are as relevant and informative as possible. The statistical principles for the design of experiments include the choice of optimal or good treatments sets and appropriate replication of them, randomization to ensure unbiasedness and the use of blocking and other methods for reduction of variance

### Aims and Objectives

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• appreciate the advantages and disadvantages of a design for a particular experiment
• construct optimal or good designs for a range of practical experiments
• understand the potential practical problems in its implementation
• describe how the analysis of the data from the experiment should be carried out

### Syllabus

Emphasis throughout will be on the statistical principles underlying the methods and how they can be applied to and adapted for practical experiments. The following methods will be discussed and practised. 1) Basic ideas: objectives leading to choice of treatments; randomization to ensure validity of analysis; blocking to separate sources of variation in order to ensure efficiency of analysis, ANOVA methodology. 2) Choice of treatments: replication for unstructured treatments; optimal design for quantitative treatments; the factorial treatment structure and its advantages; incomplete factorial structures, including regular fractional factorials; screening experiments; response surface treatment designs for multiple quantitative factors; optimal design algorithms for choosing multifactor treatment sets. 3) Randomization: practical constraints on randomization. 4) Blocking: incomplete block designs for unstructured treatments, including balanced incomplete block designs; confounding for factorial designs; optimal blocked factorial and response surface designs; split-plot and other multi-stratum designs. 5) Special topics: Optimal designs for nonlinear models.

### Learning and Teaching

#### Teaching and learning methods

Lectures, computer practical sessions and self-directed computer work

TypeHours
Teaching36
Independent Study114
Total study time150

Atkinson, A.C., Donev, A.N. and Tobias, R.D. (2007). Optimum Experimental Designs, with SAS.

Mead, R, Gilmour, SG, and Mead, A (2012). Statistical Principles for the Design of Experiments.

Box, G.E.P., and Draper, N.R (2007). Response Surfaces, Mixtures and Ridge Analyses.

Dean, A.M. and Voss, D.T. (1999). Design and Analysis of Experiments.

Montgomery, D.C. (2009). Design and Analysis of Experiments.

Box, G.E.P., Hunter, J.S. and Hunter, W.G. (2005). Statistics for Experimenters.

Website on Blackboard.

Myers, R.H., Montgomery, D.C. and Anderson-Cook, C.M. (2009). Response Surface.

Wu, C.F.J. and Hamada, M. (2009). Experiments - Planning, Analysis and Parameter.

John, J.A. and Williams, E.R. (1995). Cyclic and computer generated designs.

### Assessment

#### Summative

MethodPercentage contribution
Coursework 40%
Weekly quizzes and puzzles 10%
Written assessment 50%

#### Referral

MethodPercentage contribution
Written assessment 100%

#### Repeat Information

Repeat type: External

Pre-requisites: MATH6153 OR STAT6083 OR MATH3014 OR (MATH2011 and MATH2010)

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.