Cross-Section Estimation in the Presence of Uncertain Dosimetry

For parts that are to be used on-orbit, the final result of a set of heavy-ion tests is a prediction of the upset rate for a particular orbit. This prediction is made by combining the cross-section vs. LET for the part with a model of the on-orbit radiation environment. Typically a single cross-section curve is used when computing the upset rate prediction. However, the test data do not define the cross-section exactly-there will be uncertainty in the estimated cross-section vs. LET response due to finite count data, errors in the dosimetry, and other testing and device uncertainties. These uncertainties in the cross-section vs. LET response will result in uncertainties in the predicted on-orbit upset rate. We present methodology that can capture these uncertainties, and demonstrate how to apply it for the case of dosimetry errors. As well as estimating the uncertainty in the cross-section vs. LET response, we also estimate the actual fluences, and the size of the dosimetry errors. The cross-section vs. LET response is typically modeled by a Weibull curve when the cross-section estimate is used for on-orbit upset rate prediction. However, the use of a Weibull to model the cross-section vs. LET response is purely conventional; it has no physical justification. Other models (e. g. lognormal) can be used, and the resulting model uncertainty has an impact on the uncertainty of the on-orbit upset rate predictions. We fit a lognormal curve to the test data, and show the impact of model choice on the on-orbit upset rate distribution. Typically the Weibull curve is fitted in stages, using different approaches for the onset LET and the other parameters. We show how the approach presented here can include explicitly the constraints that are implicit in the standard approach, and also provide a method for overcoming the ill-conditioned nature of Weibull fitting. Using the uncertainty in the predicted on-orbit upset rates as a quality measure can give valuable information regarding when sufficient testing has been performed.