  New theoretical and numerical analysis of the one-dimensional contact process
with quenched disorder are presented.
  We derive new scaling relations, different from their counterparts in the
pure model, which are valid not only at the critical point but also away from
it due to the presence of generic scale invariance. All the proposed scaling
laws are verified in numerical simulations. In addition we map the disordered
contact process into a Non-Markovian contact process by using the so called Run
Time Statistic, and write down the associated field theory. This turns out to
be in the same universality class as one derived by Janssen for the quenched
system with a Gaussian distribution of impurities.
  Our findings here support the lack of universality suggested by the field
theoretical analysis: generic power-law behaviors are obtained, evidence is
shown of the absence of a characteristic time away from the critical point, and
the absence of universality is put forward. The intermediate sublinear regime
predicted by Bramsom et al. is also found.
