Statistical thermodynamics physics of failure reliability model

From statistical mechanics it is known that the distribution function gives the statistical distribution of any macroscopic body, when the body is a small part of some larger closed system and it is also called Gibbs distribution, (it was obtained by Gibbs in 1901) is represented as proportional to an exponential function. This function exponent has energy of the system associated with the system thermodynamic free-energy in the numerator and the Boltzmann constant multiplying the body absolute temperature in the denominator. This is one of the most important formulas in statistical physics Conventional Reliability Models lack unified phenomenological interpretation and are not well correlated to physical stresses (mechanical, thermal, electrical, etc.). The Physics of Failure (POF) can express failure mechanisms as function of the internal stresses which are function of the free energy. One such relationship is called the Thermally Activated Time-dependent (TAT) Model. The TAT Model was originally used to describe parametric changes in resonators, voltage degradation in batteries and to model the phases of creep, i.e., the creep TAT Model includes the explicit relationship between strain change and crystal lattice free activation energy. Catastrophic time to failure models such as S-N Models do not explicitly relate the thermodynamic free activation energy to material degradation parameters. However, parametric time to failure models can. Failure Rate results of US-MIL-HDBK-217 for hardware devices in Electronic Equipment do not have explicit relation to activation energy, nor to some important physical parameters. That is, the Mechanical Stresses and the Failure Rates as given in the conventional Reliability Models and US-MIL-HDBK-217 lack correlation to the crystal lattice activation energy.