Both robots sit in the same ionizing radiation field near a reactor core. Every second each one absorbs dose — measured in gray (Gy), the SI unit of absorbed radiation energy per kilogram of matter. That dose accumulates permanently: it is the robot's Total Ionizing Dose (TID), and it never resets while the mission runs.
dose(t) += fieldIntensity · rate · dt
robot FAILS when dose(t) ≥ TID_threshold
Ordinary "commercial off-the-shelf" (COTS) silicon accumulates trapped charge in its gate-oxide layer as radiation strikes it; past a few tens of gray, transistors stop switching cleanly and the chip locks up or dies — exactly what stalled remote equipment during real reactor decommissioning work. Radiation-hardened ("rad-hard") chips push that ceiling an order of magnitude higher using three real techniques: a thicker, more radiation-tolerant gate-oxide layer, triple modular redundancy (three copies of critical logic vote on every result, so a single-event upset in one copy is outvoted), and sapphire or silicon-on-insulator substrates that isolate transistors from stray charge collection.
- Radiation field intensity — how hot the zone is; higher intensity raises the dose-rate for both robots equally.
- Failure threshold — the TID at which each robot's electronics can no longer function; the rad-hard unit's threshold is far higher.
- Survival ratio — how many times longer the rad-hard robot lasts in the same field before failing.
Real-world relevance: this is the exact constraint that shapes robots sent into Fukushima Daiichi and Chernobyl's reactor buildings — standard electronics simply stop working after a bounded dose, so rad-hardened designs (or frequent robot replacement) are mandatory for any prolonged work near spent fuel or a damaged core.