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experimental conditions and are not valid outside the range of the experiment [refs.
165,166]. They provide a fast approach to model building without the need for
extensive and accurate knowledge of all process variables [ref. 165]. Theoretical
models are developed from first principles, based on the process scientific and
physical facts. They are usually more reliable and flexible in predicting the dynamic
behaviour of a process over a wide operating range. However, depending on the
complexity of the process phenomena, the resulting model equations may be difficult,
if not impossible, to solve [ref. 164].
Semi-empirical models are developed with regard to established fact or
knowledge of the process. They combine the advantages of theoretical and empirical
models to achieve modelling accuracy. They offer a standardised process modelling
strategy, even when the basic principles of the process are not understood [ref. 51]
2.6.4.1 Experimental design
Experimental design is the process of planning experiments so that appropriate
data will be collected for a representative statistical analysis to be performed, to reach
valid and objective conclusions [ref. 167]. The experimental design objectives range
from process analysis to developing models for process control and establishing
correlation between process inputs and outputs.
The most important part of planning an experiment, after defining the
objectives of the investigation, is the identification of the inputs and outputs of the
process, i. e. the factors that might affect the process behaviour, within a practical
range relevant to the process, and the factors that can be used for assessing this
change of behaviour [refs. 51,167]. Thought must be given to how the response will
be measured and the probable accuracy of these measurements.
Variables in an experimental design are usually categorized into two groups,
namely independent variables and dependent variables. Generally, the parameters that
are directly controllable, such as machine settings, are chosen as independent
variables. The responses of the process to changes in the independent variables are
considered as dependent variables. In gas metal arc welding, variables such as tip-to-
workpiece distance, welding speed, welding voltage, wire feed rate and gap are often
treated as independent variables, whereas welding current and bead geometry are
normally considered as dependent variables [refs. 51,168].
There are two approaches to experiment design. The planned and the intuitive
sequential experiment. The planned approach is usually based on full or fractional
factorial designs, while in a sequential experiment a trial and error approach is used,
and various input variable combinations are selected using process knowledge [ref.
51].
Factorial design is an experimental design technique with which, for any
complete trial or replication of the experiment, all possible combinations of factor
levels are investigated [ref. 167]. It provides a systematic way of performing the least
number of experiments to obtain a maximum amount of information in a multivariable
environment. Factorial design is orthogonal by nature, or in other words no
correlations exist between process independent variables. Consequently, experimental
errors are normally distributed [refs. 51,169]. It is only effective, however, for a
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