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Short term deviation is what would occur during a period of observation such as a day, week, or month. Long term deviation is what would occur over a long period of time such as a year. Long term deviation is assumed to be greater than short term deviation.
 
A robust design would have the short term deviation exceeding requirements so that the process would continue to meet requirements even when long term deviation occured.
 
David

The equations for standard deviation can be found in any text book on statistics, SPC, or Six Sigma. Also, there are ways of estimating standard deviation that were used before calculators and desk top computers existed.
 
As I said before, short term variability is your present data. Long term variability is your projection of what will occur in the future. You might assume that the variation will decrease as the operators get more experience. You might assume that the variation will increase as the machine gets older.
 
I am using the terms in the context of how Motorola six for the sigma level and why the stated PPM isn’t correct for the sigma level. If you are using a different context, it might help for you to explain the context.
 
David