David said:
James,
I need to clarify one thing with my question. The formula is actually used
to determine the Process Sigma of a function, not the DPMO. In my haste to
post my question, I mistyped what I meant to ask. Regardless, the formula is
accurate. I have not yet had a chance to try the VBA link. I'll let you
know how that goes.
Thank you.
I've started looking at the problem and it is interesting indeed. Here
are some of my initial thoughts.
The function that is sought appears to be related to the Inverse Erf
function from:
http://mathworld.wolfram.com/InverseErf.html
That site also gives the Maclaurin series for that function.
Mathematicians like myself don't like to reinvent the wheel unless
they're still made of stone (the wheel, not the mathematician) or are in
some other state lacking completeness. For smaller values of x, say
greater than 0.5 and less than 0.5 {mathematically (0.5, 0.5)}, the
Maclaurin series should converge very rapidly. It looks like even x
values close to -1 or 1 should converge somewhat quickly. Using that
method seems to be verging on brute force so I'm going to try to find
something more elegant. It is known that the Error Function (Erf)
doesn't have a closed form solution so some numerical integration might
be involved. Even the existence of a closed form solution for the Error
Function would not have guaranteed that a simple non-iterative way to
calculate the inverse exists.
Numerical integration falls under the mathematical field of Numerical
Analysis, a subject in which I showed considerable talent and interest
at both the undergraduate and graduate levels in both the applied
mathematics and engineering versions. Also, the fact that a cumulative
distribution is involved presents some possibilities that would not be
present otherwise. The fact that the mathworld site gives the
derivative might simplify the process if fixed point interation becomes
involved. So far it looks like it is going to be a fun problem. I
suppose, though, that I won't look too capable if I don't come up with
something good
.
James A. Fortune
(e-mail address removed)
