An Introduction to Predicting Failures on Highly Reliable Aerospace Equipment documents the author's research and work as the Boeing GPS Space and Ground Segment Manager developing and using predictive algorithms that are today, part of the prognostics and health management (PHM) technology, the author used to identify premature aging in normal appearing GPS satellite subsystem electrical and mechanical equipment's analog and digital telemetry on the 12 U.S. Air Force/Boeing GPS Block I satellites that led to the funding of the GPS program by the DoD and awards of two contracts to Boeing for 40 more improved GPS satellites, with improvements based on the results from the author's routine prognostic analysis on, on-orbit GPS satellites as well as satellites at the factory, and the results of the author's prognostics analysis of the NASA/Fairchild/U.C. Berkeley, Space Science Laboratory's Extreme Ultra-Violet Explorer (EUVE) class, low earth orbiting space science satellite, one of many sister ships to the NASA Hubble Space Telescope. Now called prognostics and health management or PHM technology, the predictive algorithms developed and used by the author on the 12 Boeing GPS satellites as the Boeing GPS Space and Ground Segment Manager were a follow-on to the Naval Research Laboratory''s two failed navigation technology satellite (NTS) that were the proof of concept satellites for the Air Force's GPS program. PHM and the prognostic analysis was first used by the author to predict on-board Boeing's GPS Block I satellite's cesium and rubidium atomic frequency standard failures for replacement prior to and during critical, system-wide, multi-service test and evaluation program that used the initial 12 GPS Block I (a.k.a. Phase I) constellation of MEO satellites launched by the author into a 12,000 mile altitude, 63 degree inclination circular Earth orbit. The author completed the routine prognostic analysis on all Block I GPS satellites for achieving the maximum satellite and system performance by switching out the navigation payload units that were predicted to fail with certainty using the author's predictive algorithms. As the Boeing GPS Space and Ground Segment Manager, the author was responsible for Boeing's Block I GPS satellite design and redesign, launch, early orbit operations and final 3-axis stabilized on-orbit operations during the Phase I of 3 phases of the GPS program. The routine, prognostic analysis completed by the author were documented in monthly and quarterly orbital test reports as CDRL's submitted to the GPS Program Office located at AFSMC in Los Angeles, CA. The 12 Boeing Block 1 GPS satellite constellation was used by the author to win funding for the GPS program from the Pentagon based on the extremely high system performance as a result of completing routine prognostic analysis on each on-orbit GPS satellite. Using predictive algorithms, the author completed routine prognostic analysis on each on-orbit satellites. Boeing was awarded two follow-on contracts for 40 additional improved Boeing GPS Block II and IIA satellites with the improvements identified as a result of the routine prognostic analysis by the author, who discovered many improvements in equipment and subsystem functional configuration and equipment performance using predictive algorithms. With the GPS program funded by the DoD, the two existing and well-established Navy, satellite-based navigation and timing programs called TIMATION and TRANSIT were retired. The Introduction to Predicting Failures on Highly Reliable Aerospace Equipment documents the author's many years of work in developing and using PHM technology on both the Boeing GPS satellites and the NASA/Fairchild/U.C. Berkeley EUVE low earth orbiting space science satellite. The NASA EUVE used one of 10 Fairchild's multi mission satellite Bus' purchased by NASA hoping to lower the cost of an expected group of future space science missions.