Statistics for Maintenance Modelling: Regression Modelling

# Satisfying an Accelerated Life and a Proportional Hazards Models¤

One can actually make S(t;x) satisfy both an accelerated life model and a proportional hazards model, so that:
S(t;x) = Sa0(tax) = Sp0(t) with the baseline functions standardised so that a0 = p0 = 1.

Then:

Sa0(t) = Sp0(t) =
for some > 0 (see The Reliability Function for the Weibull Distribution screen in the Continuous Lifetime Distributions 1 session) and px = ax. A proof of this property can be found in Cox and Oakes (1984), section 5.3.