  Searches for rare physics processes using particle detectors in
high-luminosity colliding hadronic beam environments require the use of
multi-level trigger systems to reject colossal background rates in real time.
In analyses like the search for the Higgs boson, there is a need to maximize
the signal acceptance by combining multiple different trigger chains when
forming the offline data sample. In such statistically limited searches,
datasets are often amassed over periods of several years, during which the
trigger characteristics evolve and system performance can vary significantly.
Reliable production cross-section measurements and upper limits must take into
account a detailed understanding of the effective trigger inefficiency for
every selected candidate event. We present as an example the complex situation
of three trigger chains, based on missing energy and jet energy, that were
combined in the context of the search for the Higgs (H) boson produced in
association with a $W$ boson at the Collider Detector at Fermilab (CDF). We
briefly review the existing techniques for combining triggers, namely the
inclusion, division, and exclusion methods. We introduce and describe a novel
fourth in situ method whereby, for each candidate event, only the trigger chain
with the highest a priori probability of selecting the event is considered. We
compare the inclusion and novel in situ methods for signal event yields in the
CDF $WH$ search. This new combination method, by virtue of its scalability to
large numbers of differing trigger chains and insensitivity to correlations
between triggers, will benefit future long-running collider experiments,
including those currently operating on the Large Hadron Collider.
