In this paper, we employ a Bayesian approach to assess the reliability of a critical component in the Mars Sample Return program, focusing on the Earth Entry System's risk of containment not assured upon reentry. Our study uses Gaussian Process modeling under a Bayesian regime to analyze the Earth Entry System's resilience against operational stress. This Bayesian framework allows for a detailed probabilistic evaluation of the risk of containment not assured, indicating the feasibility of meeting the mission's stringent safety goal of 0.999999 probability of success. The findings underscore the effectiveness of Bayesian methods for complex uncertainty quantification analyses of computer simulations, providing valuable insights for computational reliability analysis in a risk-averse setting.

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