ABSTRACT
Suppose that degradation under the explanatory variable x(·) is determined by a stochastic process (cf. (3.11))
Zx(·)(t) = Z
t∫
eβ T x(s) ds
. (13.1)
Set
m(t) = E(Z(t)), mx(·)(t) = E(Zx(·)(t)) = m
t∫
eβ T x(s) ds
. (13.2)
The moment of the nontraumatic failure under explanatory variable x(·) is
Tx(·) = sup{t : Zx(·)(t) < z0}.
