From: Stan Hilliard
Date: 11 Oct 1999
Time: 13:28:55
Greetings Scott,
From a sampling standpoint, this is an n=1 problem, because you detect errors one at a time. Here is the method that I would use:
1) Calculate the within-order standard deviation for each of the four total-weight categories. To do this, select a typical order in each of the four categories: a,b,c,d. Fill each order multiple times. Maybe 10 times. Each time measure the total weight. Eliminate/correct any filling errors. Use the standard deviation formula that has (n-1) in it.
2) Calculate the four tolerances: a,b,c,d, by multiplying students-t times the standard deviation, that is: t(alpha=.01,df=9)*Stdev
Discussion: This method will only work if the system is sufficiently sensitive to detect weight changes of the size that occur with filling-errors. It will not work if there is too much measurement variability, or too much variability in the tare weights of pill bottles (within item), or too much variability in the overall packaging.
To evaluate this, determine the minimum size error in weight that must be detected when the filling is in error. Compare this to the variability in tare, boxes, weighing, etc.
If this approach works out, you might want to recalculate the standard deviations with larger sample size, at least 30.
I hope this helps, Stan Hilliard