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... distribution functions, F and G, the shift function is defined by A(t) = G-F(t)t. The shift function is the distance from the 450 line and the quantity plotted in Q-Q plots. In the analysis of lifetime data, A represents the difference between two treatments. The shift function can also be used to find crossing points of two distribution functions. The large-sample distribution theory for estimates of A is studied for right-censored data. It turns out that the asymptotic covariance function depends on the unknown distribution functions F and G; hence simultaneous confidence bands cannot be directly constructed. A construction of simultaneous confidence bands for A is developed via the bootstrap. Construction and application of such bands are explored for the Q-Q plot.