Software reliability predictions can increase trust in the reliability of safety critical software such as the NASA Space Shuttle Primary Avionics Software System (Shuttle flight software). This objective was achieved using a novel approach to integrate software-safety criteria, risk analysis, reliability prediction, and stopping rules for testing. This approach applies to other safety-critical software. The authors cover only the safety of the software in a safety-critical system. The hardware and human-operator components of such systems are not explicitly modeled nor are the hardware and operator-induced software failures. The concern is with reducing the risk of all failures attributed to software. Thus, safety refers to software-safety and not to system-safety. By improving the software reliability, where the reliability measurements and predictions are directly related to mission and crew safety, they contribute to system safety. Software reliability models provide one of several tools that software managers of the Shuttle flight software are using to assure that the software meets required safety goals. Other tools are inspections, software reviews, testing, change control boards, and perhaps most important-experience and judgement.