The resilience index

The resilience index is a measure of the extended reliability. It is defined here in terms of the Mean Time Between Incidences (MTBI):

Resilience Index = Predicted MTBI / Target MTBI

The resilience index may be used to assess the system resilience

Numeric definition of system resilience

A system is resilient if the resilience index is great than 1.

Using the resilience index

A regulator may define the target MTBI of a particular process to be 1000 years. The demand for the index > 1 implies that only plants in which the predicted MTBI is more 1000 years will be legitimate.

Numeric definition of MTBI

MTBI is the MTBF of incidences. MTBI may be defined numerically by the reciprocal of the expected risk due to all hazards, as follows:

MTBI = 1 / ExpectedRisk

ExpectedRisk may be computed by

ExpectedRisk = ∑ _{hazard ε all hazards} HR( hazard) * Risk( hazard) ,

where

a hazard is any event or state triggering the incidence,
HR(hazard), the hazard rate is the rate of instances of a particular kind of hazard and
Risk(hazard) is an estimate of the risk that the hazard imposes, normalized to be between 0 and 1.