Strategy for Developing Prior and Likelihood Functions to Estimate the Reliability of Space Systems Using a Bayesian Approach

Risk-informed decision-making is crucial for the successful execution of any complex mission, especially space missions. A critical step towards risk assessment is to estimate various systems’ reliability. Based on estimation methodology, reliability is of two types: Design and Demonstrated reliability. As the former incorporates epistemic uncertainty and has limitations in assessing the system's success rate, estimating Demonstrated reliability becomes necessary. Demonstrated reliability is primarily estimated based on the classical approach. However, it does not provide a reasonable estimate of the reliability of new systems with limited data. Space systems generally are one-shot systems and fall into this category due to their complexity, time and cost associated with tests. In such cases, Bayesian approaches are widely used to obtain and update the system's reliability. It needs a prior and likelihood function to be defined, and the method's efficacy depends on these two functions. The prior is generally obtained from generic databases and expert opinion, whereas the likelihood function is obtained using the limited test data available. However, there are few challenges while applying the Bayesian approach in space systems. A novel strategy is proposed to address these issues by generating the (i) Prior function by encoding expert judgement proportionate to their knowledge/experience with due subjectivity and test equivalency; (ii) Likelihood function using heritage system's test data by accounting similarities and test data from the new system. The proposed methodology has eight unique advantages.