Can a quasi-stationary approximation predict how long a small printer fleet lasts?

What it found

Follow-up to selfrep-extinction-kits. The slowest decay rate of the exact Markov chain gives a quasi-stationary estimate 1/λ₀ of the mean extinction time. Stylised, with assumed inputs, it overshoots a lone seed machine by 1.2 to 1.9 times (2388 h against 1465 h exact at 200 h life), but multiplied by the exact chance the fleet survives its start it lands within 5% in four of seven cases (for example 0.999 at 500 h life) and fails where the fleet rarely survives (ratio 1.4 at 200 h life, 42 at 75 h). Seed fleets help only up to the quasi-stationary time: 1 / 2 / 4 / 8 seeds give 1465 / 1983 / 2388 / 2666 h at 200 h life. The survival correction was chosen after seeing the overshoot, so it is a post-hoc fit. Stylised: every input is assumed; simulated only.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Self-replicating manufacturing

• Why do two exact extinction chains of the same printer shop disagree?Reconciles the two exact extinction chains of the lone printer shop (stylised, assumed inputs): the fleet-size chain is 1.5 to 7 times longer; adding the kit wait fixes small fleets but over-corrects large ones.
• Which part substitutions cut a printer's vitamins most, within a performance budget?Which assumed part substitutions (printed bushings and nuts, wooden rods) cut the Prusa Mendel's vitamins most under a penalty budget: all seven take closure from 43/22/16% to 60/36/48% (lines/mass/cost); best set depends on the assumed penalties. Stylised.
• What does a wooden rod cost a printer in stiffness?Beam model of the Prusa Mendel's smooth rods: a wooden rod sags 20 times a steel one at 8 mm and needs about 17 mm to match it, and selfrep-redesign's assumed dowel mass was twice the geometric one (stylised).
• What natural-frequency target does a printer’s rod have to meet, and what does a wooden rod cost?Carriage natural frequency on the Prusa Mendel's smooth rods: a vibration target, not a sag limit, sets the rod diameter; hardwood needs about twice steel's diameter (stylised).
• Does an aluminium rod fit the printer where a wooden one cannot?Aluminium rods in the printer redesign: matching a steel rod's sag takes 10.4 mm aluminium (fits the assumed 12 mm holders) against 16.9 mm hardwood (does not), at 39.5% vs 37.8% mass closure (stylised).
• How stiff a rod does a frequency target need, in aluminium and in wood?Sizing printer rods to a first-mode frequency target instead of a sag spec: at 0.3 kg aluminium reaches 40 Hz with 10.0 mm (fits the assumed 12 mm holders) where hardwood needs 16.0 mm (stylised).

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Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.