Single-event upset rate estimator

How it works

A memory or logic device in orbit, or at altitude on Earth, is upset by ions, protons and neutrons that flip stored bits. This tool estimates how often, from the device's measured cross section and the particle environment: by integrating a Weibull cross section against an LET spectrum, by Petersen's one-line figure of merit, or from proton and neutron cross sections and fluxes. It then shows what error correction with scrubbing leaves uncorrected.

1. Describe the cross section. Heavy-ion test data are fitted with a Weibull curve: zero below the threshold LET, then rising to a saturation cross section. The width sets how fast it rises and the shape how it bends. Cross sections can be entered per bit, in square micrometres per bit, or per device.sigma(L) = 0 for L <= L0; sigma(L) = sigma_sat x (1 − exp(−((L − L0) / W)^s)) for L > L0
2. Integrate against the LET spectrum. The environment is an integral LET spectrum: the flux of ions a day per square centimetre with LET above each value. The upset rate is the cross section folded with the differential spectrum. Written by parts it becomes an integral over the Weibull density, which the tool evaluates with Simpson's rule. Between spectrum rows the flux is interpolated log-log; above the last row it is zero.rate = integral of sigma(L) x (−dPhi/dL) dL = sigma_sat x integral of Phi(L0 + W x) x s x^(s − 1) x exp(−x^s) dx, per bit per day
3. Or use the figure of merit. Petersen's figure of merit replaces the whole calculation with one number. It treats the cross section as a step at the LET where the Weibull reaches a quarter of saturation, and the spectrum as a power law. The orbit enters through one coefficient. The tool reads L0.25 from the Weibull curve or takes your value.L0.25 = L0 + W x (−ln 0.75)^(1/s); rate per bit-day = C x sigma_sat / L0.25^2
4. Add protons and neutrons. Protons and neutrons upset devices through nuclear reactions, so they are handled by a cross section and a flux above the device's threshold energy rather than by LET. For terrestrial work the neutron flux is the sea level reference scaled by an altitude factor.proton rate per bit-day = sigma_p x flux above threshold; neutron rate per bit-day = sigma_n x flux (n/cm2/h) x altitude factor x 24
5. Scale to a device, a system and FIT. The rate per bit becomes a rate per device, per year, and in FIT (failures per billion device hours, with 1 Mbit taken as 1,048,576 bits). The mean time between upsets is the inverse of the system rate, and the mission total is that rate times the mission length.per device-day = rate per bit-day x bits; FIT = per device-day / 24 x 10^9; MTBU (days) = 1 / (per device-day x devices)
6. Error correction and scrubbing. With a single-error-correcting, double-error-detecting code, one upset in a word is repaired the next time the word is read or scrubbed. A word is lost when a second upset reaches it before that. Single upsets reach a word as a Poisson process; the share of upsets that flip two or more bits of the same word is uncorrectable at once.x = (data bits + check bits) x rate per bit-hour x (1 − multi-bit share) x scrub interval; P(2 or more) = 1 − exp(−x) x (1 + x); uncorrectable per device-hour = words x P / interval + multi-bit share x upsets per device-hour

Sources

The methods and default figures rest on these public sources. The wording here is our own; read the source for its full text.

• Suggested Single Event Upset Figure of Merit (opens in a new tab), IEEE Transactions on Nuclear Science, volume 30, issue 6 (E. L. Petersen, J. B. Langworthy, S. E. Diehl), December 1983. The original figure of merit: a step cross section, a power-law spectrum and one orbit constant.
• SEE Rate Calculations Using the Effective Flux Approach and a Generalized Figure of Merit Approximation, IEEE Transactions on Nuclear Science, volume 42, issue 6, pages 1995 to 2003 (E. L. Petersen), December 1995. The figure of merit restated with L0.25, the LET at 25% of the limiting cross section.
• The SEU Figure of Merit and Proton Upset Rate Calculations (opens in a new tab), IEEE Transactions on Nuclear Science, volume 45, issue 6, pages 2550 to 2562 (E. L. Petersen), December 1998. Orbit rate coefficients for heavy ions and a proton coefficient, different for hardened and unhardened parts. Cited for the method; its coefficient tables are not reproduced.
• 3.4. CREME96 and Related Error Rate Prediction Methods (opens in a new tab), NASA Marshall Space Flight Center (J. H. Adams Jr.), NASA Technical Reports Server 20120016823, 2012. Survey of rate methods: the RPP model, the figure of merit and its restatement with L at 25% of the limiting cross section.
• ECSS-E-HB-10-12A, Calculation of radiation and its effects and margin policy handbook (opens in a new tab), ECSS Secretariat, ESA-ESTEC, 17 December 2010. Clause 8.5: the RPP and integrated RPP methods, the Weibull cross section and proton and neutron rates from flux times cross section.
• Soft Error Rate in Space: A Unified Analytical Approach (opens in a new tab), arXiv 2501.06260, January 2025. The rate as a cross section folded with the LET spectrum, a comparison with Petersen's figure of merit (it overstates the rate at low thresholds and understates it at high ones) and why Weibull parameters from a fit are not unique.
• Reliability of Scrubbing Recovery Techniques for Memory Systems, IEEE Transactions on Reliability, volume 39, issue 1, pages 114 to 122 (A. M. Saleh, J. J. Serrano, J. H. Patel), 1990. The model of a single-error-correcting code with scrubbing: a word fails on a second upset between scrubs.
• Multiple Cell Upset Partitioning for Simulation of Soft Error Rates in Space Systems with Error Correcting Codes (opens in a new tab), arXiv 1704.07271 (G. I. Zebrev and others), 2017. Scrubbing efficiency of a simple SEC-DED code when some upsets flip several bits of one word.
• Heavy Ion Orbital Environment Single-Event Effects Estimations (application note SLVK046B) (opens in a new tab), Texas Instruments, May 2020, revised June 2025. A worked rate from an integral flux at the onset LET; the GEO worst-week point at LET 65 follows its example.
• JESD89A, Measurement and Reporting of Alpha Particle and Terrestrial Cosmic Ray-Induced Soft Errors in Semiconductor Devices, JEDEC Solid State Technology Association, October 2006. Cited by name. It takes New York City at sea level as the reference for soft error FIT rates; the reference neutron flux is commonly quoted as about 13 n/cm2/h above 10 MeV, so confirm it against the standard.