If I understand the OPs request correctly he has designed a widget and his boss wants some sort of statement as to the reliability for warranty purposes.
You might be able to get MTBF data from Microchip
The figure they might be able to give you is the MTTF - Mean Time
To Failure - MTBF is specified for sysems which are repaired when they fail and, on the whole, single chips aren't repaired.
As noted for the DS1307 individual chip MTTFs tend to be rather long since they are inherently pretty reliable.
Even if you know the MTTF of all your components you can't easily combine them into an MTBF for your product. At one level you can a little - after all it's just the arithmetic mean of the times to failure so if you knew the sample size you could easily combine two figures. One catch is that you don't know the sample size but you could just assume it is equal and combine two items with MTTFs of 5 years and 10 years and say that a system which uses both has a MTTF of 7.5 years.
Unfortunately as KJDS points out, you have a whole host of other factors to do with your design and construction which you dont know and can't easily find out or haven't measured. The MIL217 document lists some of the typical adjustment factors for failure rates which you might have to think about applying.
Even then the weakness of MTBF is that it doesn't tell you how the failures are distributed in time. In fact it sort of assumes they are linear but real failure often aren't like that. Something like a resistor probably does have a fairly constant failure rate with time. Other items might decline gradually until they need replacement (eg a rechargeable battery) generally with some variation in lifetime. Still others might be totally OK and then fail catastrophically with increasing chance of failure as time goes by (think lightbulb).
This means that failures occur according to the classic "bath tub" curve - there is a high number of early failures due to manufacturing problems, followed by a decline to relatively low levels, then gradually climbing with time as components start to fail with age.
MTBF tells you most if it is comparatively short compared with the replacement cycle time of the item - if I have 1000 of your widgets and a replacement cycle of 10 years then an MTBF of 5 years means I can reasonably expect to see (and budget for) 2000 repairs. If the MTBF is 20 years I'm not quite going to be sure whether that means I'll see 500 failures or none. If the MTBF is very long e.g. some hard disk drives have quoted MTBF's of more than 1 million hours, it's much more useful to know what the percentage failure per year of service is - but the drive manufacturers won't tell you that, even if they know it.
Back to your question - your boss basically wants to know "if I make 10,000 of these things and give a two year warranty how many do I have to figure on replacing" - it's a bit like the maintenance cost question but with a pretty short life cycle (the warranty period).
It's going to be difficult without actually making a few (hundred) and taking some real measurements of how your
system behaves. You might be able to get somewhere looking at the individual component MTTF's although doing so will overestimate your system's MTBF. It will, at least, be better than guessing (possibly not by much though).
One thing you can't do is say "there will definitely be no failures in 2 years", or three for that matter because there will
always be an early failure rate.
Have fun!
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