An inexpensive estimate of failure probability for high-dimensional systems with uncertainty

The failure probability of a system at an uncertain state can be estimated within a precise confidence interval using the Monte-Carlo sampling technique. Using this approach, the number of system parameters may be arbitrarily large, and the system may be non-linear and subject to random noise. For a given confidence level and interval, the number of required simulations can be exactly computed using the Beta Distribution. When failure probabilities are on the order of 1–10%, this technique becomes very inexpensive. In particular, 100 simulations are always sufficient for a failure estimate with a confidence interval of +/−10% at a 95% confidence level.In an engineering development process, this estimate limits the number of trials required to assess the robustness or reliability of high-dimensional and non-linear systems. When simulations are expensive, for example in vehicle crash development, using such a rule to minimize the number of trials can greatly reduce the expense and time invested in development.

► Failure estimates may be computed with very few sample points for any system.
► Bounds on failure rate are provided by Bayesian analysis of Monte Carlo sampling.
► Number of samples needed is not affected by high dimensionality or non-linearity.
► Only 100 sample points are needed for an estimate error of 10% with 95% confidence.