Spares Analysis given confidence level

I don't know the answer to the question, but think there are two confidence values involved, even if you use the same one twice.

Given some number of LRU operating hours and some number of failures, you can calculate an MTBF confidence interval. That interval narrows as you have more hours and more failures:

Row\Col	A	B	C	D	E	F	G	H	I
1					Confidence		Hours2Go
2					90%		10,000
3
4	Case	Hours	Failures	MTBF	Low Limit	High Limit	Failures @ Conf	P(r)
5	1	50,000	1	50,000	10,540	974,786	2	93%	E5 and down: =2 * Hours / CHIINV((1 - Confidence) / 2, 2 * (Failures + 1))
6	2	500,000	10	50,000	29,477	92,159	1	95%	F5 and down: =2 * Hours / CHIINV((1 + Confidence)/2, 2 * Failures)
7	3	5,000,000	100	50,000	42,344	59,425	1	98%	G5 and down: =MAX(0, PoissonInv(Confidence, Hours2Go/E5))
8	4	50,000,000	1,000	50,000	47,456	52,711	1	98%	H5 and down: =POISSON.DIST(G5, Hours2Go/E5, TRUE)

All of those show the same MTBF (hours/failures), but the width of the intervals varies dramatically.

Let's say your case is case #2; 10 failures in 500K hours. You are 90% confident that the MTBF is >= 29,477 hours. The UDF PoissonInv calculates the number of failures at some probability for a Poisson failure process, and in the example, I'm using the same confidence value again. But it seems like double-dipping to calculate the the MTBF interval at some confidence, and then apply another confidence test for the maximum expected failures -- know what I mean?

I'm sure there is a way to only use one, but don't know what it is.

Here's the UDF:

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You're welcome.

That routine was due for some cleanup:

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Further modified to accommodate large values of Mean:

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