Is is possible to calculate the MTBF or Failure rate from a given datasheet when manufacturer have not given these details?
Lacking anything more specific from the manufacturer, the best you can do in my opinion is to use MIL-217F.  You need to know something about the part you're interested in - for example is it bipolar, CMOS, SiGe; how many devices (gates); package type (plastic, ceramic, hybrid/MCM) number of pins/pads; the environment (lab, aircraft, space) and temperature range; duty cycle (some components are stressed more a turn-on), etc.

With that information in hand, you should be able get a very rough estimate of a part's expected lifetime.  Emphasis here is on the phrase "very rough".  If you're designing this into a high rel product, then the manufacturer needs to step up or you need to find a different manufacturer to work with - one that is used to dealing with the needs of customers designing hi-rel products.