TheChallengerdisaster evoked a national resolve to reduce the risk of future space flight tragedies. A part of that resolve was to estimate the present risks as accurately as possible. This article illustrates and compares several such ways of incorporating past experience into the process of estimating such risks. Failure data from five military solid rocket programs, as well as pre- and post-Challengerspace shuttle data, are used in selected Bayes, empirical Bayes, and Bayes empirical Bayes methods. The derived posterior distributions are used to estimate the required probability of catastrophic failure of the solid rocket boosters on the space shuttle for theGalileomission, which occurred in October 1989. The point estimates are in fairly close agreement, while the credibility intervals differ substantially. We estimate the probability of catastrophic failure to be 1/60 with 90% credibility interval of 1/578 to 1/21.