The Bounding Problem: Single Event Effect Rate Prediction Using Markov Chain Monte Carlo

In this paper we present an algorithm to predict Single Event Effect (SEE) error rates for electronic components in the space environment with uncertainty. Spacecraft components sensitive to SEEs are described by an SEE cross section, which is a function of device geometry, lot variability, part performance, and other factors. Quantifying the cross section is a nontrivial problem and usually involves fitting the industry standard 4-parameter Weibull Cumulative Distribution Function (CDF) to radiation beam test data.The proposed method uses a Markov Chain Monte Carlo (MCMC) algorithm to fit the four Weibull parameters to test data while preserving their uncertainties and correlations. This is possible within the Bayesian framework, where prior knowledge and test data proportionally influence the posterior distributions on the Weibull parameters. A multi-dimensional posterior distribution on the Weibull parameters is estimated from the MCMC samples.A family of Weibull curves is generated by taking random samples from the correlated posterior distribution. At chosen intervals, cross section quantiles of interest are taken from the family of Weibull curves to quantify uncertainty in the spread of the curves. This predicts cross section values for the 5
^th
percentile, median, and 95
^th
percentile, but a regression to those quantile curves is required to back out the Weibull parameters. Parameterized 5
^th
, median, and 95
^th
curves are selected by solving for the in-family Weibull curve that minimizes the distance to the desired quantile curve.The test case in this paper analyzes Field Programmable Gate Array (FPGA) beam data and considers an ISS orbit. An environmental model generates a fluence curve, given a set of orbital parameters, and convolves it with the individual Weibull curves. The resultant set of SEE rate predictions with their uncertainties may be used to influence design decisions.