Each potentially SEL-susceptible part is assigned an onset LET (LET0) drawn from the
empirical distribution of SEL-susceptible unhardened CMOS parts in the augmented CERN + JPL
historical database (66 part types). The limiting cross section is sampled from the lognormal
model of the historical trend, σ_s = LN⁻¹(CL₁, m_ln, s_ln) with
m_ln = −1.82·ln(LET₀) − 4.42 and s_ln = 2.45.
The SEL rate is the Petersen figure-of-merit bound R_B = C_E·σ_s/LET₀²
reduced by the ratio r = B⁻¹(CL₂, α β), where the beta-distribution
coefficients follow the power laws α = 0.68·LET₀^0.53 and
β = 58.1·LET₀^−0.716 fitted to the 31 Weibull (w, s) pairs of the CERN
database. CL₁ and CL₂ are drawn at random, so each Monte Carlo trial is one realization
of a system built from parts statistically similar to the historical database.
In the CREME96 environment modes (default), each sampled part's SEL rate is computed by direct spectral integration: a full Weibull cross section is constructed from the sampled onset LET and limiting cross section, with shape parameters (w, s) drawn uniformly from the 31 Weibull pairs of the CERN database, and convolved with the CREME96 integral LET spectrum (RPP rate tables behind 100 mil aluminum, dimension ratio selectable under Advanced; 0.2 best-estimate default). This removes two layers of approximation from the published method the figure-of-merit bound and the beta-distributed bound-to-rate ratio fitted to the same 31 pairs, while drawing from the identical historical prior. The two methods are statistically consistent: at LET₀ = 10 MeV·cm²/mg the mean spectral-to-FOM rate ratio in GCR solar minimum is 0.18, matching the mean of the paper's beta distribution at that onset. The environment tables are identical to those in the site's SEE Rate Assessment Tool. The Petersen FOM options reproduce the source-paper engine exactly and are reported as a cross-check whenever an environment mode is primary.
Solar-flare environments (worst week, worst day, peak 5-minute) are transient and are never
applied for the full mission duration. They are modeled as episodes: the user specifies the
expected number of events per year, and each event contributes its flux for its episode
duration only (7 days, 1 day, and 5 minutes respectively). Because Poisson exposures add,
the tool folds episodes into a mission-averaged rate,
R = R_cont + R_flare·(D_ep·N_yr)/365.25, which keeps the expected
SEL count, the zero-SEL probability, and the constellation binomial exact over the mission
and makes the mission-duration sweep meaningful (longer missions accumulate
proportionally more episodes). The composite option applies GCR solar minimum continuously
plus worst-week episodes, a common design case.
Short missions: when the mission is shorter than one episode (a launch vehicle or
transfer stage), mission-averaging would answer the wrong question; the tool instead
assumes the event is in progress and applies the flare flux continuously for the entire
mission, the standard conditional planning case for launch. Mission durations from
0.1 hour to 30 years are accepted; the closed-form cross-check is flagged as outside fit
validity below 7 days. The peak-5-minute environment is best used
as a short-exposure stress check rather than a mission criterion. Published results
(closed-form Eq. (4), Figs. 3–6) are defined with the FOM bound for the GEO/interplanetary
GCR environment (CE = 400); expect environment-mode requirements to differ,
particularly for the solar-flare environments.
Testing to LETT eliminates parts with LET0 < LETT. Eliminated parts are replaced by fresh draws from the same prior, themselves screened once (some replacements are SEL-susceptible with LET0 ≥ LETT). Independently, each part carries a 3.5 percent chance (the 90 percent confidence bound implied by 0 of 66 database parts deviating) of remaining susceptible at LET just above the test LET regardless of screening; such parts are conservatively assigned LET0 equal to LETT. This floor means requirements can exceed the highest onset LET in the database (about 72 MeV·cm²/mg); results above that value are extrapolation governed by the floor.
Two criteria are selectable. The default matches the source paper: PS is the
fraction of Monte Carlo realizations whose expected SEL count over the mission is below one
(rate × TM < 1), the definition behind Figs. 3 to 6 of the system-level
paper and its closed-form LET_T = C₂ln²(T_M) + C₁ln(T_M) + C₀.
The strict alternative takes the confidence-level quantile of the system-rate distribution and
requires the Poisson probability of zero SELs, exp(−R_CL·T_M), to meet
the reliability target; every SEL is treated as mission-ending. At 99 percent reliability the
strict criterion tolerates a rate roughly 100 times lower (−ln 0.99 ≈ 0.01 expected
events versus 1), so its required LETT is substantially higher; the difference is
resolved in the regime where the 3.5 percent beyond-database floor dominates. Whichever
criterion is primary, the other is reported as a cross-check.
The constellation criterion extends the single-system model to a fleet of m identical
satellites, each carrying the specified number of potentially SEL-susceptible parts.
Because the satellites share one design, each Monte Carlo realization draws a single set of
part characteristics from the historical prior and applies it to the whole fleet, part-quality (epistemic) uncertainty is fully correlated across satellites, while SEL
occurrences in flight are independent Poisson processes per satellite. Per realization, the
per-satellite zero-SEL probability is p = exp(−R·T_M) and the
constellation survival is the binomial tail P(≥n of m) =
Σk=nm C(m,k)·pᵗ(1−p)ᵖ⁻ᵗ.
Since this is monotone in R, the confidence quantile over the prior is applied to the rate
distribution and the binomial tail is evaluated at that quantile. Setting n = m = 1 recovers
the strict zero-SEL criterion. Every SEL is conservatively treated as satellite-ending; a
fractional-lethality factor can be emulated by scaling the mission duration.
The closed-form coefficients implemented here follow the fits shown in Figs. 7 and 8 of the system-level paper. The equations as typeset in the text, Eqs. (7) to (9), contain apparent typographical errors: the sign of the C₀ slope term (printed +2.0807, fitted −2.0809), the C₀ intercept coefficient (printed 2.2087, fitted 2.087, which reproduces the Fig. 7 coefficient table), and the C₁ linear coefficient (printed 0.2285, fitted 0.0227; the RADECS summary of the same work prints 0.0228). The corrected form reproduces the paper's text anchors (for example about 70 MeV·cm²/mg for a complex 50-part, 15-year, 99 percent system).
Two onset-LET priors are provided (Advanced): the default Extended Historical SEL Priors (EHSP 2026-09) global onset CDF, built from 739 uniform LET@1e-8 onsets (Poisson-MLE Weibull fits to per-run data plus onset brackets, mechanism-screened, all eras; F(37) = 0.68, F(75) = 0.93, F(100) = 0.98, closure extrapolated to 120 MeV·cm²/mg), and the original TNS 2025 66-part CDF digitized from the paper's percentile plot, retained for traceability to the published curves. The CDF table is editable; editing it makes the prior custom. The technology-mix device-count mode assigns each part its category's susceptible fraction from the same model, modern stratum (Bulk CMOS 0.45, ADC/DAC 0.83, BiCMOS 0.39, DRAM 0.29, SRAM 0.83, SRAM-based FPGA 0.32, SOI 0.06, …). The derivation of the model, its data sources, and its validation are documented in full in the SEL Threshold Predictor methodology. Common random numbers are used across LETT evaluations so the bisection solve is stable. Against the source paper this implementation reproduces the untested system-rate distributions of Fig. 2, the greater-than-200x rate reduction for screening at 20 MeV·cm²/mg (about 900x here), the exponential decrease of failure probability with LETT within about a factor of two across three decades, and required-LET solutions typically within 10 to 15 percent, on the conservative side, of the paper's fitted curves. Results are guidance for test planning, not a substitute for device characterization; rates for parts with actual Weibull data should be refined with the part-level methods of the TNS 2024/2025 papers.
R. Ladbury and M. Joplin, "System-Level Risk Assessment for Single-Event Latchup (SEL) Based on
Historical Data," IEEE Trans. Nucl. Sci. 2026, DOI 10.1109/TNS.2026.3706172.
R. Ladbury, G. R. Allen, F. Irom, R. Gaza, S. Vartanian, J. D. Barth and R. F. Hodson,
"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. 1094-1101, 2025.
R. Ladbury, "Under-Constrained SEE Data: Implications for Estimating and Bounding SEE Rates,"
IEEE Trans. Nucl. Sci. vol. 71, no. 4, pp. 680-689, 2024.
E. L. Petersen, "The SEU Figure of Merit and Proton Upset Rate Calculations," IEEE Trans. Nucl.
Sci. vol. 45, no. 6, pp. 2550-2562, 1998.
