In this article we revisit the problem of estimating the joint reliability against failure by stress rupture of a group of fiber-wrapped pressure vessels used on Space-Shuttle missions. The available test data were obtained from an experiment conducted at the U.S. Department of Energy Lawrence Livermore Laboratory (LLL) in which scaled-down vessels were subjected to life testing at four accelerated levels of pressure. We estimate the reliability assuming that both the Shuttle and LLL vessels were chosen at random in a two-stage process from an infinite population with spools of fiber as the primary sampling unit. Two main objectives of this work are (1) to obtain practical estimates of reliability taking into account random spool effects and (2) to obtain a realistic assessment of estimation accuracy under the random model. Here, reliability is calculated in terms of a “system” of 22 fiber-wrapped pressure vessels, taking into account typical pressures and exposure times experienced by Shuttle vessels. Co...