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TABLE 22.1
Five Classes of Experimental Problems Defined in Terms of What is Unknown in the Model, η = f (X, θ ),
Which is a Function of One or More Independent Variables X and One or More Parameters θ
Unknown Class of Problem Design Approach Chapter
f, X, θ Determine a subset of important variables from a given Screening variables 23, 29
larger set of potentially important variables
f, θ Determine empirical “effects” of known input variables X Empirical model building 27, 38
f, θ Determine a local interpolation or approximation Empirical model building 36, 37, 38,
function, f (X, θ) 40, 43
f, θ Determine a function based on mechanistic understanding Mechanistic model building 46, 47
of the system
θ Determine values for the parameters Model fitting 35, 44
Source: Box, G. E. P. (1965). Experimemtal Strategy, Madison WI, Department of Statistics, Wisconsin Tech. Report
#111, University of Wisconsin-Madison.
3.a. Which of seven potentially active factors are important?
b. What is the magnitude of the effect caused by changing two factors that have been shown
important in preliminary tests?
A clear statement of the experimental objectives will answer questions such as the following:

1. What factors (variables) do you think are important? Are there other factors that might be
important, or that need to be controlled? Is the experiment intended to show which variables are
important or to estimate the effect of variables that are known to be important?
2. Can the experimental factors be set precisely at levels and times of your choice? Are there
important factors that are beyond your control but which can be measured?
3. What kind of a model will be fitted to the data? Is an empirical model (a smoothing poly-
nomial) sufficient, or is a mechanistic model to be used? How many parameters must be
estimated to fit the model? Will there be interactions between some variables?
4. How large is the expected random experimental error compared with the expected size of the
effects? Does my experimental design provide a good estimate of the random experimental
error? Have I done all that is possible to eliminate bias in measurements, and to improve
precision?
5. How many experiments does my budget allow? Shall I make an initial commitment of the
full budget, or shall I do some preliminary experiments and use what I learn to refine the
work plan?

Table 22.1 lists five general classes of experimental problems that have been defined by Box (1965).
The model η = f(X, θ) describes a response η that is a function of one or more independent variables
X and one or more parameters θ. When an experiment is planned, the functional form of the model may
be known or unknown; the active independent variables may be known or unknown. Usually, the
parameters are unknown. The experimental strategy depends on what is unknown. A well-designed
experiment will make the unknown known with a minimum of work.

Principles of Experimental Design

Four basic principles of good experimental design are direct comparison, replication, randomization,
and blocking.

Comparative Designs
If we add substance X to a process and the output improves, it is tempting to attribute the improvement
to the addition of X. But this observation may be entirely wrong. X may have no importance in the process.
© 2002 By CRC Press LLC