A Novel Solution-Technique Applied to a Novel WAAS Architecture

The Federal Aviation Administration has embarked on an historic task of modernizing and significantly improving the national air transportation system. One system that uses the Global Positioning System (GPS) to determine aircraft navigational information is called the Wide Area Augmentation System (WAAS). This paper describes a reliability assessment of one candidate system architecture for the WAAS. A unique aspect of this study regards the modeling and solution of a candidate system that allows a novel cold sparing scheme. The cold spare is a WAAS communications satellite that is fabricated and launched after a predetermined number of orbiting satellite failures have occurred and after some stochastic fabrication time transpires. Because these satellites are complex systems with redundant components, they exhibit an increasing failure rate with a Weibull time to failure distribution. Moreover, the cold spare satellite build-time is Weibull and upon launch is considered to be a good-as-new system with an increasing failure rate and a Weibull time to failure distribution as well. The reliability model for this system is non-Markovian because three distinct system clocks are required: the time to failure of the orbiting satellites, the build time for the cold spare, and the time to failure for the launched spare satellite. A powerful dynamic fault tree modeling notation and Monte Carlo simulation technique with importance sampling are shown to arrive at a reliability prediction for a 10 year mission.