Predicting chain link strength knowing failure strength of several chains

[Petras]

I ran some materials tests earlier today, and this is the most basic way to describe my problem:

I have n chains, each with x links on them. If I test each of the n chains to failure. Only the failure strength is recorded. How can I predict the mean failure strength of each chain link?

Thanks in advance to anyone who replies

[Dason]

I suppose if you put some distributional assumption on the failure strengths you could then consider each trial an observation of the minimum failure strength in that group of x links. Then you could probably set up some likelihood based the n observations and use some iterative approach to find a maximum likelihood estimate? But that's just a first thought that I had and if somebody forced me to give an estimate in the next hour that's probably how I would do it. But this has probably been looked into already so there's probably a journal article out there somewhere describing a better method.