DESIGNED EXPERIMENTS 2016
ST305 / ST410
Worksheet 7 (Week 9)
Exercise 1: Confounding and fractional replication (Lectures 16/17)
Discuss briefly the situations in which fractionally replicated factorial experiments may be
useful, and explain the term defi

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lectures 19: Response surfaces (cont.)
First-order designs
The most common first-order designs are 2k factorial designs,
PlackettBurman designs and simplex designs. We have already
studied 2k designs in some detail.

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Worksheet 6 (Week 7)
Exercise 1: Multiple Regression (Lecture 14)
The following data show the responses (%age of total calories obtained from complex
carbohydrates) for 20 male, insulin-dependent diabetics who had b

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Worksheet 5 (Week 6)
Exercise 1: Random Effects (Lecture 11)
A textile company weaves a fabric on a large number of looms. It would like the looms to be
consistent so that it obtains a fabric of uniform strength. Th

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lecture 20: Industrial Experimentation
Taguchi and Robust Parameter Design
Until quite recently statistical design methods were used in agriculture and industry to
assist experimenters to maximise yields of a produc

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lecture 12: Matrix approach to analysis of variance
Introduction
The basic model that we have used so far for most designs takes the form
.
Y
ij
i
j
ij
In matrix notation we can write this as
with
Y X
~ N (0, 2 I

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lecture 13 Regression
Simple Linear Regression
In general we consider a single dependent variable or response Y that depends on k
independent or regressor variables x1, x2, , xk. The relationship between these
varia

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lecture 14: Regression and matrix algebra
Preliminaries
One important aspect of experimental design, particularly in the industrial area, is to
determine the relationship between the value of a response (or dependen

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lecture 15: The 2n & 3n factorial series
Introduction
Factorial experiments in which each factor operates at two levels occupy a special
place in the theory of design. Binary experiments are not infrequently used in

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lectures 18: Response surfaces
Introduction
In experimental situations we frequently use quantitative factors, and rather than
simply estimating the means it is often far more important to develop an understanding o

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lecture 11: Random effects
Introduction
Thus far we have looked at models with only one random term, the residual
or
,
ij ijk
depending on the factor structure of the model. The only exception to this was the
split

DESIGNED EXPERIMENTS 2016
ST305 / ST410
Lecture 16: Confounding
Introduction
Its time to consider block structures with the factorial designs that we have recently
looked at. In agricultural experiments the empirical evidence is that trials start to lose