I work in the microelectronics industry, and I commonly work with tools that remove material from the surface of a wafer. Furthermore, we typically measure the amount of material removed from a single wafer at multiple sites on the wafer (usually 10 - 20 sites). From this data, we calculate various statistics. For example, we calculate a within wafer (WIW) mean and standard deviation. This metric is very straightforward, and we just calculate the mean and standard deviation of all the sites measured on a single wafer. However, people in my industry also talk about wafer-to-wafer (WTW) standard deviations, which I don't fully understand. Is it common in statistics to look at standard deviations of two groups/samples? If so, what would be the methods used to calculate this? Does it make sense to calculate the standard deviations of all of the wafer means, or is there some better method?
I hope this question is not too vague. If it is, please let me know and I will try to provide more information.