Where does criticality collide?

The state of a fissile assembly in which each fission, on average, triggers exactly one further fission, so a chain reaction is exactly self-sustaining. Duderstadt and Hamilton's 1976 Nuclear Reactor Analysis sets this out through the effective multiplication factor k, the ratio of neutrons in one generation to the previous one: below k = 1 the reaction dies away (subcritical), above it the reaction grows (supercritical), and at k = 1 the assembly is critical. The referent here is an engineered operational condition of a specific physical system, indexed by k and tied to a critical mass of fuel, and it is not a dynamical regime studied in complexity physics or a ranking of how dangerous a failure would be.[1]

Unit

A fissile assembly's neutron balance, indexed by the multiplication factor k

Recovery means

Not applicable

Measured by

By the effective multiplication factor k (neutrons produced in one generation divided by the previous generation); k = 1 is exactly critical

The condition of a system sitting at or near a phase-transition point, where there is no characteristic scale and event sizes follow power laws. Bak, Tang, and Wiesenfeld's 1987 paper on self-organized criticality argued that many driven systems evolve on their own toward such a critical point, without any parameter being tuned, and then produce scale-free avalanches, which they offered as an explanation of widespread 1/f noise. The referent is a statistical regime of a many-body system, marked by power-law distributions and critical exponents, and it is distinct from the tuned k = 1 state of a nuclear assembly and from a failure-severity ranking, even though it shares the word and, with the nuclear meaning, the general idea of a critical point.[2]

Unit

A many-body system's state at or near a phase-transition critical point

Recovery means

Not applicable

Measured by

By power-law (scale-free) distributions of event sizes and by critical exponents, often reached without tuning any control parameter

A measure of how important a potential failure is, combining how severe its effect would be with how likely it is to occur. The U.S. Department of Defense standard MIL-STD-1629A (1980) defined the procedure for a failure mode, effects, and criticality analysis (FMECA), in which each failure mode is assigned a criticality number, and later work such as Bowles and Peláez (1995) refined how those rankings are computed. The referent is an analyst's ranking of failure modes for attention, built from severity and probability, and it comes from the everyday meaning of critical as crucial or dangerous, not from the physics idea of a critical point, so it collides with the other two meanings by spelling alone.[3][4]

Unit

A single failure mode, ranked by how severe and how likely its effect is

Recovery means

Not applicable

Measured by

By a criticality number, or a related risk priority number, that combines severity with probability of occurrence in an FMECA