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# Module Code - Title:

MA4007 - EXPERIMENTAL DESIGN

2022/3

2

2

0

0

6

6

N

MA4004

# Rationale and Purpose of the Module:

To familiarise students with the theory and applications of experimental design. Introduce the concepts of orthogonal functions and orthogonal arrays within experimental design. To analyse the Japanese method of experimental design and to compare it with traditional (linear models) design.

# Syllabus:

Multiple Regression, Residual analysis leverage and influence points. Analysis of variance: Expanding one, two factors in orthogonal polynomials. Estimation of factorial effect, resolution of variation. robust techniques. Statistical Experimental Design: Screening, factors, level, responses, full and fractional factorials, composite design, orthogonal arrays, signal to noise ratio, blocking confounding and D-optimal design. Product Design, parameter design, tolerance design. Evolutionary Operations, response surface methodology, steepest ascent, canonical forms and the use of graphical techniques to classify surfaces.

# Learning Outcomes:

## Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

On completion of this module students should be able to: Construct confidence intervals and conduct hypothesis tests for mean(s) and variances. Construct an appropriate ANOVA table based on whether a single factor, multiple factors, blocking factors and/or Latin square design is under investigation and perform post hoc tests. Calculate a contrast table, main effects, sums of squares and ANOVA table for 2^k factorial designs, identify significant factors and optimise the response. Allocate runs to blocks, implement a fractional factorial design and determine the resulting alias structure. Describe, test and model the relationship between two or more quantitative variables. Construct Taguchis orthogonal arrays and allocate factors to appropriate columns using linear graphs. Calculate a response table for the mean and SN ratio and determine the optimal settings. Fit a response surface and determine the optimum settings.

N/A

N/A

# How the Module will be Taught and what will be the Learning Experiences of the Students:

Lctures and tutorials

# Prime Texts:

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

# Other Relevant Texts:

Montgomery, D.C. (2004) Design and analysis of experiments , Wiley

# Programme(s) in which this Module is Offered:

BSMSCIUFA - Mathematical Sciences
BEDEMAUFA - Design and Manufacture
BECBENUFA - Chemical and Biochemical Engineering

Autumn