Because the mode of heat transfer involved is steady state one dimensional conduction through the TPS thermal tiles, the following equation Eqn. D3 applies.
 

Eqn. D3

One Dimensional Steady State Conduction Equation

qx = -k A (dT/dX

qx = Heat Flux Through Material Direction X

k = Thermal Conductivity of Material

A = Area of Conduction in Direction X

(dT/dX) = Incremental Time Over Incremental Length

Eqn. D3 is a linear function which means the assumption that a linear straight line relationship exists between the thickness of the TPS material and the resultant skin temperature is completely reasonable.  Therefore: the straight line can approximate any coefficient value for TPS effectiveness between 0 and 1.