Design of Experiments

Even after the objectives of an experiment are laid out, various possibilites for the route to be adopted can emerge. Thus, two main questions that arise during experimentation are: (1) Among the various options, find the one that is the best, subject to constraints of accuracy and cost; (2) For a given experiment, what is the best action plan, in terms of spacing between data points, duration of the experiment and other such decision variables. These questions are addressed in the theory of design of experiments. The subject is illustrated below through examples.

Example 1: The response of a system is expected to vary as

An experiment is designed to determine the constant by a least squares procedure. It is required that data be collected at equal time intervals with a total of points.What should be the duration of the test? Let be the total time needed for the experiment. If is very small, the decaying feature of the function is lost. If is very large, the time step also becomes large and results in large resolution errors.