Mr. Bender wrote a SAE paper in the 1960s about doing a statistical stack calculation to determine the expected overall dimension for sets of individual dimensional tolerances occurring in a linear path. His recommendation basically was to multiply the square root of the sum of the squared tolerance values by 1.5. Hence when a linear tolerance stack outcome is Benderized the RSS (root sum-of-squared) tolerances has been multiplied by 1.5.
Basically if you took your tolerances and generated a large set of random normally distributed values for each one within its limits,
then you randomly picked one from each of the tolerance value groups, and then added them together and repeated the process until the individual groups were gone,
you would end up with a distribution of stacked tolerance sums. It would be normally distributed and the spread between its +&- 3 sigma limits would equal the RSS value of the tolerances stacked. That process of randomizing and adding the random parts is called a Monte-Carlo analysis. If RSS = +/- 3 sigma limits — Benderizing it makes it +/- 4.5 sigma limits.
Paul
.
