Design of Experiments

For honours courses please contact the School Office.

Description

All processes are subject to some random variation , and replicates will not be identical. Despite this, we aim to understand and improve the process. The purpose of designing an experiment is to ensure that you will be able to answer the questions posed at the outset of the investigation and to make the most efficient use of resources. The definition of an experimental design is: the specification of the conditions at which experimental data will be observed.

Objective

To introduce students to statistical methods for the design and analysis of experiments. Students should be able to choose a suitable design for an experimental programme, and be able to recommend a sample size that will be sufficient to meet the experimental objectives. Students should be capable of analysing data from experiments using the open source program R, and proprietary software, and reporting the results in a succinct and straightforward manner.

Content

Single sample experiments and choice of sample size. Comparison of proportions. Comparing two treatments and choice of sample sizes. Comparison of several means, fixed and random effects. Sample sizes for comparing means. Latin squares, Graeco-Latin squares, and incomplete block designs. Two level factorial experiments Fractional two level factorial experiments Response surfaces, and concomitant variables Hill climbing experiments Robust design Hierarchical(nested) designs Two factors at several levels Crossed and nested factors, and split plot designs Mixture designs Discrete response Optimal experimental design Analysis of ; lattice squares; cyclic designs; cross-over designs Analysis of linear model with components of variance Examples will be taken from: agriculture and biological sciences, social sciences and engineering.

Andrew Metcalfe Lecturer for this course

Delivery

Two 1 hour lectures per week.

Assessment

A 3 hour examination (80%) and 5 class exercises (20%)

Graduate attributes

• Applying mathematical knowledge (1)
• Interpreting data and drawing conclusions (2)
• Formulating mathematical problems (3)
• Problem solving skills (4)
• Flexibility in working environment (5)
• Team participation and leadership (7)
• Self-directed study (8)
• Career development (9)

Linkage past

No past linkages have been noted.

Linkage present

No present linkages have been noted.

Linkage future

This course is not recorded as prequisite for other courses.

Restrictions

Cannot be counted with STATS 3000 Industrial Statistics III

Recommended text

Design and Analysis of Experiments (6E) – D.C. Montgomery [2005, Wiley] References: I Anderson Combinatorial Designs and Tournaments Oxford 1977 AC Atkinson and AN Donev Optimum Experimental Designs Oxford,1992 GM Clarke and RE Kempson, Design & analysis of experiments, Arnold1997. CJ Colbourn and JH Dinitz Handbook of Combinatorial Designs CRC 1996 Y Dodge, VV Fedorov, HP Wynn (eds) Optimal Design and Analysis of Experiments North Holland 1988 BS Everitt, The analysis of contingency tables (2E) Chapman & Hall, 1992. JC Hsu, Multiple comparisons Chapman & Hall, 1996. JA John and MH Quenouille Experiments: Design and Analysis Griffin, 1977 O Kempthorne The Design and Analysis of Experiments Wiley 1952 J Maindonald and J Braun Data Analysis and Graphics using R (2e) Cambridge 2007 R Mead The design of Experiments CUP 1988 DC Montgomery, Design and analysis of experiments (6E) Wiley, 2005. A Pazman Foundations of Optimum Experimental Design Kluwer 1986 AP Street and DJ Street Combinatorics of Experimental Design Oxford 1987 WD Wallis Introduction to Combinatorial Designs(2e) 2007 CFJ Wu and M Hamada, Experiments, Wiley, 2000. BS Yandell, Practical data analysis for designed experiments, Chapman & Hall, 1997.