Suppose at first that the explanatory variables are interval-valued (load, temperature, stress, voltage, pressure). If the model (7.3) holds on E0, then for all x1, x2 ∈ E0 the hazard ratio is

HR(x1, x2) = αx2(t)/αx1(t) = ρ(x1, x2), (7.4)

where ρ(x1, x2) = r(x2)/r(x1). It is evident that ρ(x, x) = 1. Suppose at first that x is one-dimensional. The speed of hazard rate varia-

tion with respect to x is defined by the infinitesimal characteristic:

δ(x) = lim ∆x→0

ρ(x, x+∆x)− ρ(x, x) ∆x

= [log r(x)]′. (7.5)

So for all x ∈ E0 the function r(x) is given by the formula:

r(x) = r(x0) exp

 

δ(v) dv

  , (7.6)

where x0 ∈ E0 is a fixed explanatory variable. Suppose that δ(x) is proportional to a specified function u(x) :

δ(x) = αu(x).