Depends of: 1) power of the test, 2) standard deviation, 3) level number, and 4) maximun differences between means.
This is an interesting question that usually arises naturally.The number of experiments necessary to validate a hypothesis depends on the number of the investigated factors. It is also worth noting that sample size is one of the important aspects of experiments design, and it is always necessary to ensure that the sample size is not too high or too low (too low sample size -> the experiment would lack the precision/not provide reliable answers to the questions under investigation; whilst too large sample size is too large -> wastage of time and resources for insignificant gain).
Number of experiments required will depend upon the number of control (input) parameters, levels of input parameters.
If you are thinking of Taguchi Design of Experiments method. Then e.g. for 3 machining parameters and each of 3 levels, you will require to do 3^3 = 9 experiments. Then after analysis you can determine delta values to rank of input parameters.
Then you have to follow ANOVA analysis to get most significant parameter affecting the response factor with its percentage contribution on response.
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