A random distribution of relaxation/retardation rate constants is derived and incorporated into the thermodynamic theory of strength of imperfect (real) polymer fibers, which is used to analyze empirical polyethylene (fiber) strength data. The results, weighted equally with previous results, give for the perfect polyethylene fiber - the only unique reference state -at 25 degreesC: sigma (c)(strength) approximate to 7.5 GPa, K-c(modulus) approximate to 325 GPa, epsilon (c)(strain) approximate to 0.023, and W-c(failure work) approximate to 0.087 GPa. These numbers represent the best currently available for the characterization constants of a perfect fibrilliform single crystal of finite molecular weight polyethylene. The widths of uncertainty are ca. 15%. Also, these numbers are exactly those calculated with the thermodynamic theory of failure based on stress-induced fusion with a constant heat of fusion. Such figures indicate the general strength of the fusion theory.