```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 usein the chi-square distribution when estimating failure rate from thenumber 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 thenumber of failures.  However, the upper MTBF (lower failure rate) isshown as using both 2n and 2n+2, depending on the source.  I haven'tfound an online explanation of exactly how the chi-square distributionenters 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 determinewhether 2n or 2n+2 is correct from first principles at this point.Based on the reasoning in the above weibull.com page, however, I aminclined to believe that the degrees of freedom should be 2n becausewe're talking about the two tails of the *same* distribution for upperand lower limits.  But this leaves the mystery of why 2n+2 shows upfrequently.  Is the reason for this straightforward enough to explainvia this newsgroup?
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