Statistical Design of Experiments for Continuous Data

I wish to talk on the subject of how one would design an experiment and analyze the data when the results come in the form of a continuous curve, rather than just a single value. This is an area that would appear to have extensive application in science and engineering. For example velocity data, trajectory data, meterological data, thrust data, etc. As I just mentioned, I am interested in the design of experiments, which means I am not concerned with the evaluation of a single curve, but many curves obtained as a result of testing under several sets of conditions, and very likely each set of conditions will have some replications. To illustrate what I have in mind, I will use rocket motor thrust curves, although I could have used some other type of curve equally effectively. Now many results from rocket motor tests can easily be analyzed. For example average exhaust velocity effective average pressure total impulse specific impulse, etc. These are simple to analyze because the data for a given test usually comes in the form of one single number. However, if we want to estimate a typical or aveage thrust curve when a motor is tested under given conditions, this is quite a different problem. To keep this report unclassified, the thrust data which will be discussed will be completely fictitious. The data is not, to my knowledge, appropriate for any existing rocket motor, but the general shape of the curve is similar to what may be expected for a number of motors currently in use.