Wes Bucey said:
Without an investigation into the root cause of the failure, the analysis you propose will only add numbers to a problem you already know you have; it will do little to help you reduce or eliminate the problem.
That's the crux of the issue. Given the data you posted, you know that about 66% (of the failed bolts) fail within 1000 hours, and that fewer than 1% survive 1600 hours. After 1000 hours the failure rate trends downwards at about the same rate it increases prior to 1000 hours. I also notice that your "buckets" overlap; for example, 800 hours is counted in two groups.
There is some prime data missing. What sort of a population are we talking about? Your data address 108 failed bolts. If the total population is 108 (e.g.,
all bolts fail within 1600 hours) your strategy might be different than if the population is 10,000 or 10,000,000. The significance of failure is also important; as Wes suggests, if they're shear bolts that are expected to fail as a protective measure, it's a different problem than if the bolts are expected to perform indefinitely. It's also a different problem if, when the bolts fail, a 12-ton object falls and crushes people, as opposed to just creating an annoying inconvenience for the customer.
I also agree with Wes in advising you to (if you haven't already) ascertain
why the bolts are failing in terms of what's expected of them. Premature failure of fasteners is almost always due to one of three causes: poor design of the assembly being held together by the fasteners, "bad" fasteners, or misuse of the equipment by the end user. How you approach the problem depends on the cause.