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Topic: Estimate failure rate: Variable degree of freedom in chi-square
Replies: 3   Last Post: Mar 18, 2013 12:27 AM

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Posts: 517
Registered: 2/23/10
Estimate failure rate: Variable degree of freedom in chi-square
Posted: Mar 17, 2013 1:27 AM
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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,
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 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?

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