What is the longevity and replacement schedule for turbine engine blades?
There are two primary modes of turbine blade failure, that can be predicted, and hence are used to determine the lives of turbine blades at which they need to be replaced. 

One is called "creep". The Wikipedia article describes the basic mechanism. The life of the blade is purely a function of "time at temperature". If the blades experiences flight time above critical material temperature limits, it accumulates a portion of creep fatigue. The total (cumulative) amount of creek fatigue is tracked, and when the blade hits that limit, it is removed and replaced with new blades. The type of algorithm used to measure creep life is called Robinson's rule, and looks like this (where c1, c2 &amp; c3 are coefficients related to the relative damage that occurs at the associated temperatures):

Total accumulated life = c1 x time above T1 deg + c2 x time above T2 deg + c3 x time above T3 deg.

Typically, each stage in the turbine will have its own life. (Each blade on the same stage is not individually monitored and lifed, but rather they are replaced as a set.)

Another failure mode is low cycle fatigue. This is caused by changes in centrifugal stress, caused by rpm changes from throttle cycles. When the pilot moves the throttle a significant amount, large changes in stress occur. These cause the blade material to behave like bending a wire in your fingers back and forth to make it break (you don't break it by just bending it once, or pulling hard on both ends). LCF lives are counted in a similar fashion to creep, but rather than counting time spent above a temperature limit, throttle cycles are counted. A throttle cycle might be defined as a change in rpm from one specific value to another.

If the engine is modern, the electronic control would count the creep and LCF lives consumed. If the engine is old, and only has a hydro mechanical control, the engine manufacturer will do an analysis on the type of flying the plane is expected to do, and determine the life limits in terms of flight hours. Periodically, they will try and confirm how the plane is actually being flown, and if the flight time before replacement needs to be shortened or can be lengthened. Generally, either the creep life or the LCF life is much shorter than the other, so only one failure mode is tracked for each engine stage.

This document gives a good description of turbine blade failure modes, and how they are monitored. I doubt you get information on actual lives, that is likely proprietary to the engine manufacturer. The only info you might find is probably for very old engines that they don't care about anymore. However, if you are lucky, you might finds some numbers burried in NTSB or other countries aircraft accident reports related to blade failure.

There are also periodic bore scope inspections, that may cause blades to be replaced for unscheduled (unpredictable) failure modes (FOD damage, coating loss, thermal distress) as also mentioned in the above document.