  The physical significances and the pros and cons involved in the usage of
different time delay formalisms are discussed. The delay time matrix introduced
by Eisenbud, where only s-waves participate in a reaction, is in general
related to the definition of an angular time delay which is shown not to be
equivalent to the so-called phase time delay of Eisenbud and Wigner even for
single channel scattering. Whereas the expression due to Smith which is derived
from a time delayed radial wave packet is consistent with a lifetime matrix
which is Hermitian, this is not true for any Eisenbud-type lifetime matrix
which violates time reversal invariance. Extending the angular time delay of
Nussenzveig to multiple channels, we show that if one performs an average over
the directions and subtracts the forward angle contribution containing an
interference of the incident and scattered waves, the multichannel angle
dependent average time delay reduces to the one given by Smith. The present
work also rectifies a recently misinterpreted misnomer of the relation due to
Smith.
