Sample size is a function of a few key properties: the minimum difference you want to detect, your desired power, the standard deviation of the data, and your desired confidence level.
The detectable difference seems odd to many people at first glance, but it’s simply the smallest difference that you “have” to detect to be meaningful for your particular purpose. For example, if your engineers begin to care when a part’s width is more than 0.5″ from some specification, then your minimum difference would be 0.5. All else equal, the smaller the difference you want to detect, the larger your sample size will need to be.
Power is the probability that you’ll correctly reject the null hypothesis when you should. Power is generally set somewhere between 0.7 and 0.85, although your particular situation may dictate otherwise.
.
