  The luminosity function of white dwarfs is a powerful tool for studies of the
evolution and formation of the Milky Way. The (theoretical) white dwarf cooling
sequence provides a useful indicator of the evolutionary time scales involved
in the chronometry and star formation history of the galactic disk, therefore,
intrinsically faint (& old) white dwarfs in the immediate solar neighborhood
can be used to determine an upper limit for the age of the galactic disk.
  In this paper we examine the faint-end ($M_V > +14$) behavior of the disk
white dwarf luminosity function using the $1/V_{\rm max}$ method, but fully
including the effects of realistic observational errors in the derived
luminosity function. We employ a Monte Carlo approach to produce many different
realizations of the luminosity function from a given data set with
pre-specified and reasonable errors in apparent magnitude, proper-motions,
parallaxes and bolometric corrections. These realizations allow us to compute
both a mean and an expected range in the luminosity function that is compatible
with the observational errors.
  We find that current state-of-the art observational errors, mostly in the
bolometric corrections and trigonometric parallaxes, play a major role in
obliterating (real or artificial) small scale fluctuations in the luminosity
function. We also find that a better estimator of the true luminosity function
seems to be the median over simulations, rather than the mean. When using the
latter, an age for the disk of 10 Gyr or older can not be ruled out from the
sample of Leggett, Ruiz, and Bergeron (1998).
