Mean field approximation and network reliability

According to wikipedia entry, MFT simply the behavior of large and complex stochastic models by studying a simpler model. Such models often consists a large number of small interacting individuals.  The effect of all the other individual on any given individuals is approximated by "a single average effect", thus reducing the many-body problem to a one-body problem.

I should apply mean field approximation in network reliability studies. The challenge is that biological networks are heterogeneous, and simple 'average' might leave some interesting properties. In any case, this is an interesting direction that I should explore.

In Bialek, Nemenman, Tishby 2008, Predictability, complexity and learning, BNT08 discussed a Ising model as

BNT08 used Boltzmann distribution to describe spins {$\sigma_i$}.

The Boltzmann distribution is basically exponential decay function that is often used in reliability models. So, there seems to be a natural connection between statistics physics and reliability modeling.

There may be a problem or challenge for the mean field approach to study aging. Based on reliability model, system ages are determined by extreme values of components. So, mean field approximation may not capture this maximal-minimal nature of aging.










Reference:
http://en.wikipedia.org/wiki/Mean_field_theory