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

MTBI = 1 / ExpectedRisk

Theoretical estimation

Theoretically, 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) is the rate of instances of a particular hazard and
• Risk(hazard) is an estimate of the risk that the hazard imposes, normalized to be between 0 and 1.

An HR(hazard) may be defined in terms of the source reliability and the protection layer, as follows:

HR(hazard) = FailureRate( hazard) x [ 1 - PrRecovery( hazard) ]

where  FailureRate( hazard) = 1 / MTBF( hazard)

and PrRecovery(hazard) = PrAlarming( hazard)  x PrPerception( hazard)  x PrTroubleshooting( hazard)  x PrResumption( hazard)

where the probabilities are of successful operational activities.

Practical considerations

Typically, during initial operation, there is no data enabling estimation of the factors required for the prediction.

These data may be gathered only after considerable operational time.

Event then, the data gathered is only partial, related to expected hazards. The most significant resilience factors are about unexpected events, and there is no way to gather information about this kind of events.

Related topic

Updated on 20 Oct 2016.