We consider the transient analysis of the M/G/1/0 queue, for which Pn(t) denotes the probability that there are no customers in the system at time t, given that there are n(n = 0, 1) customers in the system at time 0. The analysis, which is based upon coupling theory, leads to simple bounds on Pn(t) for the M/G/1/0 and M/PH/1/0 queues and improved bounds for the special case M/Er/1/0. Numerical results are presented for various values of the mean arrival rate λ to demonstrate the increasing accuracy of approximations based upon the above bounds in light traffic, i.e., as λ → 0. An important area of application for the M/G/1/0 queue is as a reliability model for a single repairable component. Since most practical reliability problems have λ values that are small relative to the mean service rate, the approximations are potentially useful in that context. A duality relation between the M/G/1/0 and GI/M/1/0 queues is also described.