huangyhg

rss equal to 3 sigma
i have an assembly of parts with defined size tolerances.
parts stack on top of one another. i must assume that tolerances for each part would fit within normal distribution.
when i calculate, rss, (taking the square root of the sum of the tolerances -->
1.00 +/- .002
.500 +/- .003
.75 +/- .004
.500 +/- .005
.600 +/- .003
(.002^2 + .003^2 + .004^2 + .005^2 + .003^2)^.5 = .0079
given above, is it reasonably safe to say that 99.7% of time part thickness will fall within 3.342 and 3.358
more simpler...does rss equate roughly to 3 sigma?
for some reason, i thought the rss was equal to 1 sigma equal to standard deviation but i think i've been wrong.

my understanding is that straight rss = +-3 sigma
kenat,
as is my understanding of rss.
v
arthur bender (back in 1963 or there about) suggested (in a sae paper) that a the rss value should be moderated with a safety factor (rss x 1.5). he did so (i think) because he was concerned about unpredictable sources of variation. back then there was not such attention to the individual contributors being statistical capable... they were commonly assumed uniform (or goalpost) distributions. never-the-less unpredictable variation exists and safety factors moderate the risk between the arithmetic and statistical stack... choose wisely considering the expected process control of the individual contributors!
paul
as far as i understand it, the rss method doesn't use any particular sigma value. the meaning of the rss limits depends on how the tolerance limits were converted into normal distributions (i.e. what sigma value was imposed).
if the calculation is done as drdherl has, the sigma values of all the detail part distributions and the rss total are assumed to be equal. so the overall thickness will be within the 3.342 to 3.358 range 99.7% of the time if the detail part thicknesses are within their tolerance ranges 99.7% of the time. the 99.7% comes from the properties of the normal distribution, where the range between -3 sigma and +3 sigma equals 99.7% of the area under the normal curve. this also equates to a cp value of 1.00.
if a sigma value of 2 was imposed, then the overall thickness would be within the 3.342 to 3.358 range only 95% of the time.
hope this helps. more later if needed.
evan janeshewski
axymetrix quality engineering inc.
drdhrl,
rss is a slang term...root sum squares...it actually is pirated from the electrical engineering community...and really does not have much revelance...boo!
i'm an experienced dimensional analyst & asme gdtp-s.
i'll try to explain the mathematics:
when we add those material thicknesses you listed the distributions must be added by the rules of statistical convolution. that's a pretty complicated term...and the mathematics are pretty complicated for most distributions...except impulse (constant) distributions...and normal distributions.
elementary statistics lesson 1...there are 4 moments that define a statistical distribution. those moments are 1st (mean), 2nd (variance), 3rd (skewness), and 4th (kurtosis).
variance is sigma squared.
next...i'll define the random process x as the sum of the material thicknesses you listed.
1. when the distributions are normal, the mean of x is the sum of the individual material thickness means.
2. when the distributions are normal, the variance of x is the sum of the variances of the individual material thicknesses.
therefore if we know +/- 3 sigma of the individual material thicknesses, we can figure out +/- 3 sigma of x...in setting up the equation you will just see a factor of 9 on both sides of the equation.
i have a mathematical explanation...tried to attach it to this post...i could send it if it does not appear.
michael


a simple way to answer this...
the sigma value of the rss tolerance analysis depends on the sigma value of the manufacturing process used to produce the part.
if the part is manufactured using a +/- 3-sigma process, then it will be a 3-sigma tolerance analysis result using rss. or, put another way, you will have 27 bad parts per 10,000 parts built since it would fall within a 99.73% distribution.
-rob
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