Design of Experiments – Introduction

Experiments are performed in various fields to understand the behaviour of a system. In this post we will analyse the common terms used during an experiment design.

Experiment :
An experiment can be defined as a test or a group of test wherein changes are made to the input variables and the effect of that changes observed in the output or the response variable. The aim of the experiment is to find what effects the input variables have on the output variable.

Strategy of Experimentation :
There are various ways of performing the test in an experiment.
One-at-a-time : In this strategy a baseline set of level is selected for each factor. subsequently, one of the factors if varied across its range and the other factors held constant at their baseline level. The test are repeated for other factors. This strategy has an advantage of simplicity, however, it fails to consider any interaction effects between factors. Interaction is defined as the failure of one factor to produce the same effect on the response variable at different levels of another factor.
Factorial: A useful method to deal with multiple input variables or treatments or factors is to use a factorial method of experimentation. In this method the factors are varied together instead of one at a time. However, if there are more than four factors the number of combinations of tests may be too high. It is therefore sometimes unnecessary to run all possible combinations of factor levels. A fractional factorial experiment is used. It is the variation of the factorial experiment where only a subset of the runs are made.

It is useful to understand three basic principles of experimental design before starting with an experimental design. These principles are replication, randomization and blocking.

Replication :
Replication is the term given to repetition of the basic experiment. Replication is used to allow the experimenter to determine the experimental error value. For example, if a sample mean is used to identify the effect of a factor, replication provides a more accurate measure of the sample mean. However, distinction has to be made between replication and repeated measurement. Replication entails performing the test to find out the variability both between the runs and possibly within the runs. A repeated measurement merely takes the value of the output variable multiple times or performs the experiment without changing the factors. Thus is does not capture the variability in the experiment due to the input factor.

The statistical analysis of the experiment is based on the assumption that both the experimental material and the selection of runs is random. The experiments themselves are performed randomly. The observations made should be independently distributed random variables. By choosing the randomization technique we can average out the effects of external factors.

Blocking is used to minimize the variability introduced in the experiment due to nuisance factors. Blocking is generally used when comparison of factors are made. Nuisance factors are the factors that influence the response variable but the experimenter is not interested in them. I.e. they are not part of the study, nevertheless, they do influence the study. Each level of the nuisance factor becomes a block and the experiment is carried out within blocks.

Experimental design – guidelines:

1. Understand and define the problem – Sometimes a single large experiment may not be able to provide the answers or may be difficult to perform. In such cases a series of smaller experiments may be performed.
2. Choice of input variables or factors, their levels and their range : The experimenter considers the design factors and the nuisance factors during this stage. The design factors are those that are changed during the experiment and their effects studied. They may be factors selected for the experiment, variables that are held at constant values during the experiment (hand held factors) and allowed to vary factors. The nuisance factor may be controllable, uncontrollable or noise factors. The experimenter can set the levels of controllable factors. The blocking principle can be used to deal with controllable factors. IF a nuisance factor cannot be controlled but can be measured then a strategy called analysis of covariance can be used to accommodate its effects. For noise factors the strategy is to minimize the variability due to noise factors. This is sometimes referred to as robust design problem.
3. Selection of response variables.
4. Choice of experimental design.
5. The actual experiment.
6. Analysing the data.
7. Conclusion of the experiment.

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