  We offer a numerical study of the effect of headstarting on the performance
of a Shiryaev-Roberts (SR) chart set up to control the mean of a normal
process. The study is a natural extension of that previously carried out by
Lucas and Crosier for the CUSUM scheme in their seminal 1982 paper published in
Technometrics. The Fast Initial Response (FIR) feature exhibited by a
headstarted CUSUM turns out to be also characteristic of an SR chart
(re-)started off a nonzero initial score. However, our main result is the
observation that a FIR SR with a carefully designed {\em optimal} headstart is
not just faster to react to an initial out-of-control situation, it is nearly
{\em the} fastest {\em uniformly}, i.e., assuming the process under
surveillance is equally likely to go out of control effective any sample
number. The performance improvement is the greater, the fainter the change. We
explain the optimization strategy, and tabulate the optimal initial score,
control limit, and the corresponding "worst possible" out-of-control Average
Run Length (ARL), considering mean-shifts of diverse magnitudes and a wide
range of levels of the in-control ARL.
