Preliminary analysis aid. Check the result against your own analysis and, where needed, a test on the intended part. Full disclaimer.
1. What it calculates
For each function of a system, delivered by k of n identical units each with single event modes and recovery chains, a continuous
time Markov chain is built and solved over the mission: availability against time and its mean, reliability as the probability of
no permanent loss and as the probability of no outage at all, expected outages by cause, expected unit resets and power cycles, and
time spent in solar storm conditions. Total dose enters as a lot level survival factor. The system is the product over functions.
The model is a JSON document you can save, edit, reload, and seed from a SEECA export.
In one line: per part SEE rates in, function and system availability and
reliability out, with the recovery design and the redundancy doing the work in between.
2. Inputs
- Mission. Name and duration in days. Three example models are provided; they are synthetic.
- Storms. Number of solar particle events per year that raise the rates at the part, their mean duration, and the
multiplier on each effect type during one. Zero events gives a constant environment.
- Function. Name; role (critical functions enter the system reliability, service functions only the availability);
whether any outage counts as a loss (uses the no outage reliability); n units, k required; hot or cold spares; for cold spares
whether failover happens on any fault or only on permanent failure; switchover coverage and the ground recovery time after a
failed switchover; the unit's part and lot for the record.
- Modes. One row per effect: type, rate per device per day in the quiet environment, and the type's parameters.
SEU and SET: the fraction of upsets that becomes a functional outage after mitigation, and the recovery time. SEFI: detection
coverage, detection latency for the uncaught fraction, the recovery action (reset or reconfiguration, power cycle, ground
intervention, none) and its time. SEL: whether protected, the power cycle time, and the fraction of protected events that are
destructive anyway. Destructive and stuck bit modes have a rate only.
- Total dose. Dose rate at the part in krad per year, the lot's median failure dose and log sigma, and whether the
units fail together (same lot) or independently.
3. Calculation
- Unit template. Up, restart outage, power cycle outage, failed. Modes are pooled into the three transitions out of
up by summing rates; the recovery rate of a class is the rate weighted mean duration, with coverage entering as latency added to
the uncaught fraction.
- Lumped chain. State = (units up, restarting, power cycling, failed) plus a ground recovery flag and a quiet or storm
flag. Hot: all units exposed, up when u ≥ k. Cold: k exposed, spares unexposed; failover rule sets whether a reboot of the active
unit is an outage. Switchover succeeds with the coverage; failure goes to ground recovery.
- Solution. One day transition matrix by matrix exponential (scaling and squaring), stepped over the mission; an
absorbing copy for the no outage reliability; expected counts by trapezoid integration of probability times rate.
- TID. S(t) = 1 − Φ((ln D(t) − ln D50)/σ) with D(t) linear in time; multiplied into the
function's reliability and availability; k of n binomial if the units are independent lots.
- System. Product of critical function reliabilities; product of all function availabilities.
4. Assumptions
- Single event arrivals are Poisson at the quiet rate and at the multiplied rate during storms; storms arrive and end at constant rates.
- Recovery times are exponential with the given means. Units of a function are identical and independent apart from the shared
environment and the lot level dose.
- Cold spares see no single events while unpowered.
- Functions are independent and in series.
- Dose does not change the single event rates.
5. Implementation notes
- The solver was checked against closed form results for two state availability, hot and cold redundancy, imperfect coverage and
storm modulated event counts (see the methodology). Agreement is to the precision of the daily grid.
- State counts: (n + 3 choose 3) times 2 for storms times 2 for ground recovery; eight units with both is 660 states and solves in
about a second. Units are capped at eight per function.
- The SEECA import runs the SEECA engine on the exported rows, groups them by function, maps consequence classes to recovery
classes (masked and data quality rows carry no outage; auto recover becomes a restart or power cycle outage; ground recover a
ground outage; loss rows a permanent failure), and sets storm multipliers from the ratio of SEECA's worst case to nominal rates.
Set redundancy and total dose after importing; SEECA does not carry them.
- Everything runs in the browser; nothing is uploaded.
6. Limitations
- No common cause single events across units except by modeling the shared part as its own function.
- Two environment levels only; phased missions are separate runs.
- The daily grid does not resolve individual outages; expected counts and mean availability are accurate, the shape of A(t) within
the first day is not.
- The coverage, latency and recovery numbers are design inputs. They decide the answer more often than the rates do, and the tool
cannot check them.
7. References
Boyd, M. A., An Introduction to Markov Modeling: Concepts and Uses, RAMS tutorial, NASA Ames, 1998, NTRS 20020050518. ·
Trivedi, K. S., Probability and Statistics with Reliability, Queuing and Computer Science Applications, 2nd edition, Wiley, 2002.
· Petersen, E. L., Single Event Effects in Aerospace, Wiley-IEEE Press, 2011. · Merrell, E. C. and others, Benefits of
Realist Ontologies to Systems Engineering, OntoCom 2021. · Becker, H. N., Miyahira, T. F. and Johnston, A. H., Latent Damage
in CMOS Devices From Single-Event Latchup, IEEE Transactions on Nuclear Science 49(6), 3009, 2002. · LaBel, K. A. and others,
Single Event Effect Criticality Analysis, NASA HQ Code QW, 1996.
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