Efficient verification and validation of performance-based safety requirements using subset simulation

The safety and performance of aircraft systems must fulfill stringent requirements defined by certification authorities. Performance-based requirements are specified with a probability threshold. The probability of failure of the performance of the system must be below the threshold. Depending on the severity of the outcome, the probability thresholds are typically of the order 10⁻⁵ (less severe) to 10⁻⁹ (catastrophic result in loss of life). Estimation of such low probabilities using naive Direct Monte Carlo methods generates a significant computational load that increases development costs. This paper presents a Markov chain Monte Carlo toolchain concept that uses the Subset Simulation algorithm to efficiently estimate low probability of failure of performance-based requirements. The Subset Simulation algorithm targets the rare region of interest of the overall probability distribution to realize the probability of failure efficiently. Example scenarios consisting of estimating the accuracy requirement of an Air Data, Attitude and Heading Reference System and closed-loop hover requirements of an electric Vertical Take-Off and Landing aircraft demonstrate the application of the toolchain. More importantly, the samples generated during subset simulation are used to identify key parameters that significantly influence the failure of the requirement. Such information is very useful throughout the development process.