  In this article, we revisit the problem of coherent multi-detector search of
gravitational wave from compact binary coalescence with Neutron stars and Black
Holes using advanced interferometers like LIGO-Virgo. Based on the loss of
optimal multi-detector signal-to-noise ratio (SNR), we construct a hybrid
statistic as a best of maximum-likelihood-ratio(MLR) statistic tuned for
face-on and face-off binaries. The statistical properties of the hybrid
statistic is studied. The performance of this hybrid statistic is compared with
that of the coherent MLR statistic for generic inclination angles. Owing to the
single synthetic data stream, the hybrid statistic gives low false alarms
compared to the multi-detector MLR statistic and small fractional loss in the
optimum SNR for a large range of binary inclinations. We have demonstrated that
for a LIGO-Virgo network and binary inclination, \epsilon < 70 deg. and
\epsilon > 110 deg., the hybrid statistic captures more than 98% of network
optimum matched filter SNR with low false alarm rate. The Monte-Carlo exercise
with two distributions of incoming inclination angles namely, U[cos(\epsilon)]
and more realistic distribution proposed by B. F. Schutz are performed with
hybrid statistic and gave ~5% and ~7% higher detection probability respectively
compared to the two stream multi-detector MLR statistic for a fixed false alarm
probability of 10^-5.
