PSI - Issue 28

Dmitry O. Reznikov et al. / Procedia Structural Integrity 28 (2020) 1360–1368 D.Reznikov, N.Makhutov,O.Yudina / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 1. Scenario assessment of HIF

Risk is a measure of probability and consequences of some adverse effects. In the view that risk is a very multifaceted concept, various risks are traditionally distinguished into individual, social and economic ones: - The individual risk R i is defined as the probability that an average unprotected (or some pre-selected) person permanently present at a certain location will be killed due to an accident at the HIF over one year period.

n

1 j R P S P f S     ( ) ( | ) i j j

(1)

where P ( S j ) is the probability of realization of the scenario S j at HIF in one year period, P ( f | S j ) is conditional probability that the predefined (or average) person will be killed due to realization of the scenario S j . - Social risk R S is defined as the relationship between frequency and the number of people suffering accidents at the HIF. It is assessed using the so-called FN -curves which describe the probability of exceedance for the random variable N that designates the number of victims due to accidents at the facility per year:

( ) F x f x dx 

(2)

) 1 ( )      N

( F N x

N

x

where F N ( x ) is cumulative probability distribution function of the number of fatalities per year N , f N ( x ) is the probability density function of the number of fatalities. A set of social risk indexes were developed to conduct quantitative assessment of societal risk. The mathematical mean of the number of victims E { N } is the most widely used social risk index commonly known as the integral society risk index:

{ } E N x f x dx       ( ) N

(3)

I

N

0

- Economic risk R e which is also described as a specially constructed distribution function of a random variable U that is economic losses from accidents at the facility in question per year period called FD-curve:



 

( F U x

) 1 ( ) F x

( ) f x dx

  

U

U

x