Consider a complex subsystem such as a missile which undergoes testing in stages. That is, the subsystem is testednitimes withxirecorded successes at thei-th stage of testing. The reliability of thei-th stage is estimated asri=xi/ni. In this paper, exponential smoothing is used to assess the overall reliability of the subsystem at the end of each stage of testing. That is, fii, the overall reliability at thei-th stage of testing is related to the reliabilities at the earlier stages by the equation Ri= αiri+ (1 – αi)Ri–1where Ri–1is the overall reliability at the (i– 1)-th stage and αi∊ [0, l] is thei-th stage smoothing constant. Methodology (Bayesian and empirical) is developed to determine, objectively, estimates of the smoothing constants.