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?