Estimating Traveling Wave Tubes (TWTs) Failure Rate Using Bayesian Posterior Analysis From Spacecraft On-Orbit Flight Data

As a vital component for a communication payload transponder, the reliability of a traveling wave tube (TWT) plays a significant role in the satellite payload configuration design. Decisions regarding the level of transponder redundancy required are highly dependent on the predicted failure rate of the TWT. Based on observation of on-orbit performance, the existing MIL-HDBK-217 failure rate prediction model is deemed to be too conservative for the TWT. Derivation of a more accurate TWT failure rate value based on on-orbit flight data is preferred. To account for uncertainty of the on-orbit data, the failure rate value is typically estimated to its upper confidence bound. Since the data could change over time, a direct estimate from the on-orbit data may fluctuate severely. To avoid such severe fluctuation, and recognizing that the space industry has performed such estimation over a quite lengthy period of time, this paper proposes a Bayesian posterior analysis approach for the TWT failure rate estimation. Its confidence interval and bounds are derived. Prior distribution is established based on historic TWT failure rate estimates and special cases with assumed prior distributions are discussed. Results of examples indicate clear benefits by using the Bayesian posterior analysis when additional failures are observed. To evaluate the impact of each prior distribution parameter to the posterior estimate, a sensitivity analysis is performed and results are discussed.