Overlapping Normal distributions

#1
Hi all,
I am trying to find formulae for calculating the overlap between two normally distributed populations.
There are some online calculators specifically for this but they do not have the resolutinion i require.

So for M1,σ1 and M2,σ2, (where M is Mean and σ is StDev) what formula will give me the probability of samples from these populations overlapping.

Im trying to find the % interferance fit between an OD and ID

I have been using JMP so far as a stop gap but i know this is not entirely accurate, the method below is what im using

by finding the % of Group 2 below the point M1+3(σ1) and vise versa, then multiplying the two % (Using CpK analysis)

M+3(σ) still leaves 0.15% of the population unacounted for and i want a more accurate result.

Your comments on a better fast method aswell as the formuala are welcome and appraciated

Thanks
 

Dason

Ambassador to the humans
#2
Hi all,
I am trying to find formulae for calculating the overlap between two normally distributed populations.
You need to be more specific. The normal distributions take a support on the entire real line so their overlap is the entire real line. If you just care about where the middle 95% overlap then that's a different question.
M+3(σ) still leaves 0.15% of the population unacounted for and i want a more accurate result.
Once again you need to refine your question. You're going to have part of the population unaccounted for if you aren't satisified with the answer of the entire real line.
 
#3
Ok, so im not familiar with "entire real line" but im assuming its the graphical line supporting the distribution line.

What im looking for is a method more accurate than the one which i am using, or alternatively a method which i can use to replace the JMP calculations as i am unsure how JMP is calculating the % below spec in CpK and if it is relevant/correct for my problem.

I would be satisfied with 0.15% of the population unaccounted for if the calculations were completed manually by me, the formula for this is what i need.

Its the uncertainty of JMP that im trying to get rid of.

Sorry if i wasnt clear.