Failure Probabilities and Safety Indexes

Abstract

In Section 6.7 we discussed the problem of estimating risks for very rare ac-cidents, which are seldom observed but can have serious consequences. In that situation the applicability of direct estimation of the probabilities using the empirical frequencies of such accidents is limited due to lack of data or large uncertainty in values of the computed measures of risks. An alternative method to compute risk, here the probability of at least one accident in one year, is to identify streams of events A i , which, if followed by a suitable sce-nario B i , leads to the accident. Then the risk for the accident is approximately measured by λ Ai P(B i) where the intensities of the streams of A i , λ Ai , all have units [year −1 ]. An important assumption is that the streams of initi-ation events are independent and much more frequent than the occurrences of studied accidents. Hence these can be estimated from historical records. (Estimations of intensities λ i were discussed in the previous chapter.) What remains is computation of probabilities P(B i). We consider cases when the scenario B describes the ways systems can fail, or generally, some risk-reduction measures fail to work as planned. Hence P(B) describes the chances of a " failure " , which we write explicitly in the notation P f = P(B). We are particularly interested in situations when, as often seen in safety of engineering structures, B can be written in a form that as a function of uncertain values (random variables) exceeds some critical level u crt