The probability for each decay mode is expressed in terms of the branching ratio \Gamma_i/\Gamma, where \Gamma_i is the partial decay rate for the specific process and
\Gamma = \sum_i \Gamma_i
is the total decay rate. The mean lifetime is \tau = 1/\Gamma.
It is possible to define a partial lifetime \tau_i = 1/\Gamma_i for each decay mode. This doesn't really have the same significance as a mean lifetime, because all of the decay modes compete. So whereas we can define a total half-life
\tau_{1/2} = \tau \ln 2
as the time it takes for half of the pions in a sample to decay, a quantity like
\tau_{e^+\nu_e} \ln 2
doesn't really correspond to the time it takes for half of a sample of \pi^+ to decay to positrons, since over that period of time, most of the sample will have instead decayed to muons.
