Date: Mar 17, 2013 1:27 AM
Author: Paul
Subject: Estimate failure rate: Variable degree of freedom in chi-square

I've found conflicting information about the degrees of freedom to use
in the chi-square distribution when estimating failure rate from the
number of failures seen over a specified period of time. To be sure,
the lower MTBF (upper failure rate) always uses 2n+2, where n is the
number of failures. However, the upper MTBF (lower failure rate) is
shown as using both 2n and 2n+2, depending on the source. I haven't
found an online explanation of exactly how the chi-square distribution
enters into the calculation (other than http://www.weibull.com/hotwire/issue116/relbasics116.htm,
which I'm still chewing on). So I haven't been able to determine
whether 2n or 2n+2 is correct from first principles at this point.
Based on the reasoning in the above weibull.com page, however, I am
inclined to believe that the degrees of freedom should be 2n because
we're talking about the two tails of the *same* distribution for upper
and lower limits. But this leaves the mystery of why 2n+2 shows up
frequently. Is the reason for this straightforward enough to explain
via this newsgroup?