Many manufacturers will give you an estimated design life
in hours based on various RPM's @ a certain pressure/flow
rates based on years of field testing, but I've found those
to be about as reliable as the operating environment of any
pump.  Maintenance and abuse are HUGE unknown key factors.  

Hydraulic pumps are prone to environmental conditions and
contamination damage which can take place in several hours
at any point in an expected 5,000 hour life span.  Using
non spec or aging hydraulic fluids can have a minimal effect
over time until wear particles contaminate the fluid to a
point that wear rates increase exponentially over a few
hours.  Cavitation damage due to air entrainment in the
working fluid can also be a major wear issue.

For my non critical applications, hydraulic pumps get the
black or white test of, "After an internal visual and
measurement inspection,  Do they meet the specified flow
and pressure requirements without making excessive noise,
vibration or leaking fluid?  If yes, you're good to go!

From a budget standpoint, its a good idea to ask yourself,
what will this cost if a questionable pump goes out in a
worst case scenario at the least opportune time and is it
worth spending the money to avoid that?

In critical applications like aircraft, spacecraft,
submarines, nuclear reactors, etc., if those concerned
are doing their job correctly, once any pump hits its
rated life span, even if it looks, works, and sounds
perfect, it goes into the trash can and gets replaced
with a new pump.  You'll find that in many critical
applications, in addition to hourly and/or cycle time
design life limits, double, even triple system redundancy
is often the best policy.  Aircraft engines, which are
really just hydraulic pumps, are a good example.

The short answer is, there's no sure way to accurately
estimate the design life of hydraulic pumps.


Chumley

A rough rule of thumb that I use is the life is a function of horsepower*hours.  Take the rated life and horsepower, and then keep this number constant.  As you draw more horsepower from/through the pump, the number of hours to failure decreases.  I use this as a linear relationship, and it works well as long as the system is kept within NORMAL operating limits (i.e. no cavitation/turbulent flow).

Thanks.  I like the horsepower idea.  We have been theorizing about using some form of Energy Analysis or even calculating Herzian stresses and trying to figure out a damage analysis from that. Any other ideas?