Supplemental Material for Chapter 4
S4.1. Random Samples
To properly apply many statistical techniques, the sample drawn from the population of
interest must be a random sample. To properly define a random sample, let x be a
random variable that represent
Chapter 3
Design & Analysis of
Experiments 8E 2012
1
What If There Are More Than Two
Factor Levels?
The t-test does not directly apply
There are lots of practical situations where there are
either more than two levels of interest, or there are
several fac
Design of Engineering Experiments
The Blocking Principle
Text Reference, Chapter 4
Blocking and nuisance factors
The randomized complete block design or
the RCBD
Extension of the ANOVA to the RCBD
Other blocking scenariosLatin square
designs
Chapter 4
De
Chapter 5 Supplemental Text Material
S5.1. Expected Mean Squares in the Two-factor Factorial
Consider the two-factor fixed effects model
yij i j ( ) ij ijk
R1,22,a
|ij 1 b
S
|k 1,2, n
T
given as Equation (5.1) in the textbook. We list the expected mean sq
Design of Engineering Experiments
Chapter 2 Some Basic Statistical Concepts
Describing sample data
Random samples
Sample mean, variance, standard deviation
Populations versus samples
Population mean, variance, standard deviation
Estimating parameters
Simp
Chapter 1 Supplemental Text Material
S1.1 More About Planning Experiments
Coleman and Montgomery (1993) present a discussion of methodology and some guide
sheets useful in the pre-experimental planning phases of designing and conducting an
industrial expe
Chapter 4 Supplemental Text Material
S4.1. Relative Efficiency of the RCBD
In Example 4.1 we illustrated the noise-reducing property of the randomized complete
block design (RCBD). If we look at the portion of the total sum of squares not accounted
for by
Design and Analysis of
Engineering Experiments
Douglas C. Montgomery
Regents Professor of Industrial Engineering and Statistics
ASU Foundation Professor of Engineering
Arizona State University
Chapter 1
Design & Analysis of
Experiments 8E 2012
1
Design of
Chapter 2 Supplemental Text Material
S2.1. Models for the Data and the t-Test
The model presented in the text, equation (2.23) is more properly called a means model.
Since the mean is a location parameter, this type of model is also sometimes called a
loc
Chapter 3 Supplemental Text Material
S3.1. The Definition of Factor Effects
As noted in Sections 3.2 and 333, there are two ways to write the model for a singlefactor experiment, the means model and the effects model. We will generally use the
effects mod
Supplemental Material for Chapter 10
S10.1. Difference Control Charts
The difference control chart is briefly mentioned in Chapter 10, and a reference is given
to a paper by Grubbs (1946). There are actually two types of difference control charts in
the l
Supplemental Material for Chapter 9
S9.1. The Markov Chain Approach to Finding the ARLs for Cusum and EWMA
Control Charts
When the observations drawn from the process are independent, average run lengths or
ARLs are easy to determine for Shewhart control
Supplemental Material for Chapter 12
S12.1. Multivariate Cusum Control Charts
In Chapter 12 the multivariate EWMA (or MEWMA) control chart is presented as a
relatively straightforward extension of the univariate EWMA. It was noted that several
authors hav
Supplemental Material for Chapter 8
S8.1. Fixed Versus Random Factors in the Analysis of Variance
In chapter 4, we present the standard analysis of variance (ANOVA) for a single-factor
experiment, assuming that the factor is a fixed factor. By a fixed fac
Supplemental Material for Chapter 7
S7.1. Probability Limits on Control Charts
In Chapters 6 and 7 of the textbook, probability limits for control charts are briefly
discussed. The usual three-sigma limits are almost always used with variables control
cha
Supplemental Material for Chapter 5
S6.1. A Simple Alternative to Runs Rules on the x Chart
It is well-known that while Shewhart control charts detect large shifts quickly, they are
relative insensitive to small or moderately-sized process shifts. Various
Supplemental Material for Chapter 3
S3.1. Independent Random Variables
Preliminary Remarks
Readers encounter random variables throughout the textbook. An informal definition of
and notation for random variables is used. A random variable may be thought of
Chapter 5
Design & Analysis of
Experiments 8E 2012
1
Design of Engineering Experiments
Introduction to Factorials
Text reference, Chapter 5
General principles of factorial experiments
The two-factor factorial with fixed effects
The ANOVA for factorials
E