How many runs are necessary to get useful results?
The answer to this question depends on the following:
The objective for the experiment, determines the type of design and best method to size the design.
An estimate for the standard deviation on the ANOVA after the model is fit to the response. The estimate can come from any of the following:
Historical data on the system being studied;
Historical data from a similar process;
A pilot study where nothing is intentionally varied; and
The experimenter’s best guess.
For factorial designs, finding effects is the goal. An effect is how much a response changes when factor levels are changed. Power is the probability of detecting significant effects.
For response surface designs the goal is generally optimization. Having a precise model is important to making good predictions for finding the optimum factor combinations. Fraction of Design Space (FDS) is the proportion of the design where the precision of the estimate is better than the acceptable margin of error.