Heavy-ion cross-section fitting and SEE rates
Heavy-ion SEE cross sections, Weibull fitting, proton bounds, and rate calculation. Enter effective LET, events and fluence for each run (or cross sections directly), fit the four-parameter Weibull curve with a 95 percent Poisson interval on every point, and fold it with a CREME96 environment into heavy-ion and proton rates, a mission probability and a report.
For preliminary analysis and educational use only: verify every result against your own analysis before a design, test or mission decision. Full disclaimer
Device
Cross-section data
| # | Effective LET (MeV-cm2/mg) | Events | Fluence (ions/cm2) | σ (cm2/dev) | Lower 95% CI | Upper 95% CI |
|---|
Enter effective LET, events, and fluence. Cross-section and 95% Poisson confidence intervals are computed automatically.
Paste from Excel: Select a cell and paste (Ctrl+V) tab-delimited rows of [LET, Events, Fluence]. Multi-row paste supported.
Weibull fit
All data points weighted equally.
Slider: log10 scale. Text: enter value directly (e.g. 1.5e-5)
Hold keeps a parameter at its current value in the next maximum likelihood fit and takes it out of the count of free parameters. State a held value with the result.
Single-point estimation (Ladbury method)
Have only one cross-section point or a saturated cross section? Estimate a bounding threshold and Weibull response from the Extended Historical SEL Priors (EHSP 2026-09, global or class trend) or the Ladbury CERN-database relationship (IEEE TNS 2023, 2025). Methodology and uncertainty: SEL threshold methodology.
Step function assumes W≈0 (maximum rate). Database-informed uses the empirical β-distribution of rate ratios from the CERN w–s database to produce a realistic but still conservative Weibull shape (Ladbury et al. IEEE TNS 2025).
The fit
Step 2Proton and neutron cross sections from the heavy-ion curve
Estimates proton/neutron cross-sections from heavy-ion Weibull parameters using the Edmonds Upper Bound model (Edmonds & Irom, IEEE TNS Vol. 55, No. 1, Feb 2008). σmodel(E) = (β(E)/a) × ∫ (1/L2) × σHI(L) dL, where β(E)/a coefficients are tabulated at 50, 100, and 200 MeV (protons) and 14 MeV (neutrons).
Step 3On-orbit rates
Heavy-ion environment
Where is this environment? See its orbit and a real mission in 3D
Proton environment
Step 4Mission probability and reports
How it works
From beam counts to an on-orbit rate in three steps
Turn counts into cross sections
Each run gives events divided by fluence at its effective LET, with an exact 95 percent Poisson interval. A run with no events still counts: it bounds the cross section from above and helps pin down the threshold.
Fit the Weibull curve
A four-parameter Weibull, onset, saturation, width and shape, is fitted by least squares, Poisson likelihood or reduced chi-squared. Sliders move any parameter afterward, and a single point can stand in for a bounding curve.
Fold it with the orbit
The curve is integrated against the CREME96 environment's effective flux for a sensitive volume of aspect ratio Z/X, protons are added from the Edmonds estimate or a measured cross section, and the rate becomes a mission probability.
How the numbers are computed
Cross sections and intervals. Each run gives σ = N/F, events over fluence. The 95 percent interval is exact: χ20.025(2N)/(2F) to χ20.975(2N+2)/(2F), and a run with no events has an upper bound of −ln(0.025)/F, about 3.69/F. In direct cross-section mode no count or fluence is assumed: a point carries an interval only if you enter its lower and upper 95 percent bounds. Details: help, section 3.
The curve. σ(L) = σsat [1 − exp(−((L − LETth)/W)s)] above LETth, and zero below. The default fit is Poisson maximum likelihood on the counts: each run contributes N ln μ − μ with μ = F σ(L), a run with no events included, over LETth, log10 σsat, ln W and ln s inside the slider ranges, by a Nelder-Mead simplex from 18 starting points. Two earlier methods remain for comparison with earlier analyses: least squares on log10 σ of the points with events, where a run with no events only adds a penalty when the curve rises above its 95 percent upper bound, and reduced chi-squared, which sums (N − μ)2/μ. Direct cross sections are fitted by least squares on log10 σ, weighted when every point has bounds. A parameter can be held at its current value.
How much the data determine. A fit is classed by ν, its constraints less its free parameters; the constraints are the distinct LETs with events, plus one if a run with no events lies below the lowest of them. With fewer than two LETs with events no curve is fitted. With ν below 1 the fit is descriptive: the curve is one of many that fit, and the rate range of step 3 is the result to report. With ν of 1 or more, and at least as many LETs with events as free parameters, it is predictive, unless the intervals then show that two or more parameters are not bounded within the slider ranges, in which case it is descriptive. The earlier methods, and direct cross sections without bounds, give no intervals: a fit by one of them is classed by its count alone and is not called predictive. Details: help, section 3.
Goodness of fit and intervals. The Poisson deviance of the counts is compared with its distribution in 200 data sets drawn from the fitted curve and refitted (a parametric bootstrap), which gives the p value; it is not reported when ν is below 1. R2 on log10 σ over the points with events describes the curve and is not a test. Each parameter has a 95 percent profile likelihood interval; an interval marked open reaches the end of the slider range, which means the data do not bound the parameter on that side within that range. These levels, and that of the rate range, rest on the chi-squared approximation to the likelihood ratio and are generally approximate at low counts. A curve set by hand or by an earlier method is compared with the maximum likelihood fit by 2ΔlnL, with 9.49 as the edge of the 95 percent region for four parameters.
Single point. The onset LET is estimated from σsat with the selected trend and its lognormal scatter, and taken at the chosen confidence on the low side, since a lower onset means a higher rate. The shape is either a step (W = 0.01, s = 1) or the database-informed shape from the β-distributed rate ratio. The result is a bound and should be reported as one. Details: help, section 4.
Protons. The Edmonds integral ∫ σHI(L)/L2 dL of the heavy-ion curve is multiplied by β/a = 1.06e-5 (14 MeV neutrons), 4.60e-6 (50 MeV), 5.39e-6 (100 MeV) and 7.13e-6 (200 MeV). The quick classification reads LETth above 15 MeV·cm²/mg as likely proton immune, 5 to 15 as low susceptibility and 5 or below as susceptible. Details: help, section 5.
Rates. The heavy-ion rate is Edmonds' effective flux form, R = ∫ Φeff dσ: the curve is cut into LET bins, 20 per decade from LETth (from 10−6 MeV·cm²/mg when LETth is lower, and the cross section the curve has reached at that LET is then the first term of the sum), each bin's step in cross section is multiplied by the environment's effective integral flux at the bin's log midpoint, and the result is interpolated between the tabulated Z/X ratios that bracket yours. The upper bound uses, at each LET, the largest effective flux over all tabulated Z/X. The proton rate applies the 200 MeV Edmonds value, or your measured cross section, above the threshold energy against the integral proton flux of the environment. The combined rate at the selected Z/X adds the heavy-ion and proton rates, the combined upper bound adds the heavy-ion upper bound over Z/X and the same proton rate, and MTBE is the reciprocal of each. The two cases differ only in the sensitive-volume geometry; the proton term is the same in both, and it is itself an upper bound when it comes from the Edmonds estimate. The rate range over the fit is the largest and smallest combined rate at the selected Z/X found over the Weibull parameters whose 2ΔlnL from the fit is at most 2.71 (one-sided 95 percent each way): for each curve shape the allowed interval of σsat is found by a one-dimensional search, and the shape is searched numerically over the slider ranges, their edges included. It measures the fit only, a held parameter stays at its value, and where an extreme lies on an edge of the slider ranges the range is conditional on those ranges. Details: help, section 6.
Mission. The probability of at least one event over t years is 1 − exp(−R × 365.25 t), for a rate that stays constant over the mission.
Environments and data provenance
The heavy-ion environments are LET spectra in silicon for Z = 2 to 92 behind 100 mil of aluminum, stored as effective-flux tables for 11 sensitive-volume aspect ratios from Z/X = 1 to 0.01, with the integral spectrum kept for the plot. The proton environments are integral proton flux above energy from the same transported CREME96 runs; the 1470 km proton table is a legacy AP-8 table kept as delivered. Each card names its orbit, shielding and source, and the help page lists the run settings.
An imported CREME96 heavy-ion .LET file in the native format is converted in your browser to the same kind of effective-flux table; a two-column file of LET and differential flux gets the isotropic geometric factor only, with no aspect-ratio correction. An imported proton file is converted to integral flux per cm² per day; for a two-column file the unit is the one chosen at import. Nothing you enter or import leaves your browser.
Files the tool reads and writes
Import CSV reads one row per run, comma or tab separated: LET, events and fluence in events mode, or LET and cross section in direct mode; a first line that contains letters is taken as a header and skipped. Rows are added to the active dataset. You can also paste tab-delimited rows straight from a spreadsheet into the table.
Export CSV writes the active dataset: in events mode with the computed cross section and 95 percent interval of each row, in direct mode LET, cross section and the two optional bounds. Export PNG saves the plot next to it. Export Text Report writes the device information, the fit and its settings, the Edmonds estimates, the rates (once computed) and the data. Export PDF Report writes the same with the plots and tables; it needs the jsPDF library, which the page loads from the network.
Disclaimer
Disclaimer: This tool is provided for preliminary analysis and educational purposes only. Results have not been independently verified or validated for use in mission-critical decisions. Users are solely responsible for verifying all outputs against their own analysis and applicable standards before making any design, test, or mission decisions. Space RHA LLC makes no warranties, express or implied, regarding the accuracy, completeness, or fitness for any particular purpose of the results produced by this tool, and shall not be held liable for any damages arising from its use. See the Help & Reference page for methodology details and references.
References
L. D. Edmonds and F. Irom, "Extension of a Proton SEU Cross Section Model to Include 14 MeV Neutrons," IEEE Trans. Nucl. Sci., vol. 55, no. 1, pp. 649 to 655, Feb. 2008.
R. Ladbury et al., "Statistical Analysis of Historical SEL Test Data to Provide A Priori Risk Estimates for Use of Unhardened CMOS Parts," IEEE Trans. Nucl. Sci., vol. 72, no. 4, pp. 1094 to 1101, Apr. 2025; and the CERN SEL database trend of Ladbury et al., IEEE TNS 2023.
Extended Historical SEL Priors (EHSP 2026-09): the trends behind the single-point estimate, derived in the SEL threshold methodology.
A. J. Tylka et al., "CREME96: A Revision of the Cosmic Ray Effects on Micro-Electronics Code," IEEE Trans. Nucl. Sci., vol. 44, no. 6, pp. 2150 to 2160, Dec. 1997.
The full list, with the Poisson interval and proton model references, is in section 10 of the help page.