Bayesian Modeling of Spacecraft Safe Mode Events

When a spacecraft experiences an unexpected anomaly that could cause permanent damage to the vehicle, the spacecraft enters a pre-specified minimally operating state called safe mode in order to protect itself from further harm. Based on data collected by the Jet Propulsion Laboratory (JPL) which spans beyond-Earth missions from the past 30 years, previous analyses have modeled the occurrence of safe mode events and the duration of their recoveries. These analyses modeled failure and recovery rates according to two Weibull probability distributions which assume independent identically distributed (iid) data across all missions and mission timelines. Model-based risk assessment teams at JPL have applied these statistical analysis directly to flight projects resulting in tangible adjustments to the mission design process, specifically for trajectory planning on future missions. In the present analysis, we argue that the iid assumption does not hold across missions. Instead, recovery times and times between safing events should be grouped and analyzed by destination rather than treated as one population. Here, this grouping is achieved through a hierarchical Bayesian architecture which prioritizes the sharing of mission data (failure and recovery times) across missions with the same destination. The hierarchical nature of the model allows for prediction of new mission safing rates without making an iid assumption. The Bayesian model is implemented using the Gibbs Sampler, a Markov Chain Monte Carlo (MCMC) technique which allows for flexible specification of distributions. An exploration of non-constant failure rates over the timeline of individual missions is also included.