Consistent with viscoelastic behavior, a power law form in terms of the stress intensity factor is used to specify crack kinetics (growth rate) in the central crack problem under Mode I conditions.  The crack growth rate is integrated to obtain the crack size as a function of time.  The crack is allowed to grow in a controlled, load dependent manner until it reaches the size at which it becomes unstable.  The corresponding time is taken as the lifetime of the material.  The specialized creep rupture case of behavior is generalized to a probabilistic formalism.  The theoretically predicted lifetime distribution functions are verified with data upon a polymeric composite.