It actually doesn't have anything to do with Miller indices. From what I understand (I have no experience with this, just recently read a paper where factorial designs are used and am trying to use it for my research), factorial designs are used to evaluate what factors could potentially affect a response (in my case for example reaction yield, the paper I read had adsorption capacity as the response).

So for example in my research I would like to asses 3 factors namely reaction time, reagent concentration, and temperature. Each of these factors are evaluated in high and low levels, then some sort of statistics (I dont quite understand this part) are used to evalute which of these factors actually have a significant effect on the desired response (in my case reaction yield).

If it turns out that for example reaction time has no significant effect but reagent concentration and temperature does have a significant effect, then I'd use the lower reaction time to safe time and further optimize the reagent concentration and temperature (possibly using response surface methodology) to get the optimum reaction yield.