Kishore kumar posted:
does it means manufacturing / assembly error .
if the rolling element missing ,bearing could not able to hold the load from the machine and it leas to immediate fail .
I would think that is somewhat dependent on the load. I would also, again subject to load as compared to rating, not suspect an "immediate fail".
As to the OP's original question "Is it possible to detect that a bearing is missing a rolling element by vibrational analysis?", I have no direct experience that would enable me to say "yes" or "no" but I do think that with proper instrumentation and tools, it would be detectable.