JB-PI use a modification to the risk matrix, based on Bernoulli's utility model. The tolerable risk becomes consequence-dominated at low likelihood levels, with a value dependent on the capacity of the risk-bearing entity to absorb the effective cost.
The graph below shows the risk classes given in API RP 580 / 581 correlated with the likelihood and consequence levels tabled in ASME CRTD Vol 20-1. Lines of constant risk, based on a conventional likelihood-consequence product, are compared with the class boundaries suggested by the Bernoulli model. The model is proposed and its full derivation is given in the paper referenced below (a copy of which is available on request).
Brear, J.M., Jarvis, P and Middleton, C.J.
“Managing the pay-off between risk, reliability and remaining life – weighting the consequences”
ETD Int Seminar ‘Risk Based Management of Power Plant Equipment’,
Inst Matls, London, 21-23 Oct 2002