Bayesian Reliability Analysis with Slice Sampling in Launch Vehicle Applications

Mission reliability for launch vehicles is the probability of successfully placing a payload into its delivery orbit within the required accuracy constraints accounting for design and process reliability. Launch vehicle design reliability provides an estimate of reliability by accounting for potential failure modes that originate within the system hardware and software while process reliability includes consideration of failure modes introduced by manufacturing, infrastructure, assembly, ground processing, and system integration activities. In order to account for the failure modes described above, the design reliability predictions are updated with historical flight successes and failures from similar launch vehicles to get the overall mission reliability. The small sample size of similar launch vehicle flights dictates a Bayesian inference approach for calculating mission reliability. In these calculations, a likelihood using the previous mission successes and failures from similar vehicles updates a prior constructed from the design reliability. Sampling from the resultant posterior distribution via Gibbs sampling, a Markov chain Monte Carlo (MCMC) method yields the mission reliability for the launch vehicle. While the tools to complete these calculations exist, multiple software programs are often required to carry out the analysis. Slice sampling, an alternative MCMC sampling method to Gibbs sampling, can be more efficient and easier to implement. A slice sampling routine using the 'stepping -out, shrinking in' method as well as many statistical distributions exist as built-in functions within MATLAB. This paper explores how slice sampling and its integration into one MATLAB application can improve the ease and efficiency of performing Bayesian inference updates for calculating launch vehicle reliability. Additionally, this method may be used as a model for replication in other industry applications where similar constraints and or considerations necessitate the method demonstrated herein.