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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8

means such a level of risk whose achievement does not require unreasonably high costs or unreasonably large efforts. This is the principle of minimizing risks taking into account practical feasibility (ALARP principle) which implies the maximum possible risk reduction achieved using limited actually available resources. According to the ALARP principle, risks falling into the region of conditionally acceptable should be reduced to the tolerable level of practical feasibility R i * . The required level of R i * is determined taking into account the ratio between the estimated value of the cost of protective measures per salvation of one life C SLS (adjusted cost per statistical life saved) and the so-cold life cost value that is the value of the cost of human life adopted in a given country that characterize the price the state is ready to pay for saving the life of one employee) L c : In the process of implementing the program of protective measures as the risk decreases, the company has to resort to more and more expensive actions to ensure further risk reduction. It means that the C SLS value is steadily increasing and at a certain moment it becomes excessively (or disproportionate) high in comparison with the value of L c . When developing a criterion for compliance with the ALARP principle, the so-called disproportionality factor ( k dp > 1) between the adjusted cost of efforts to save life of one employee C SLS and the cost of human life saved L c is introduced as a governing parameter (Makhutov and Reznikov, 2012; Bowles and Anderson,2003; Bowles, 2004). ALARP principle reads that individual risks that fell in the region of conditionally acceptable risks { R i }< R i <[ R i ] should be reduced until the cost of statistical life saved C SLS becomes disproportionally high in comparison with accepted life cost value L c :

(6)

lim L i k R C C K R   ( ) / ( ) dp i SLS

where K lim is a predetermined limit function, C SLS = ( C pm -B e )/Δ N , C pm is the cost of the implementation of protective measures, B e is the economic effect of the implementation of protective measures, expressed in the reduction of economic losses expected in an accident as a result of protective measures:

m

m

(7)





( ) j   ( ) j U f    

( ) j

( ) j

B f 

U



e





1

1

j

j





where m - and m + are the number of failure scenarios before and after the implementation of protective measures, f - ( j ) and f + ( j ) are the probabilities of the scenario S ( j ) before and after the implementation of protective measures, U - ( j ) and U + ( j ) are the economic losses expected under the scenario S ( j ) before and after the protective measures. Δ N is the expected decrease in the number of accident victims after the implementation of protective measures.

m

m

(8)





( ) j   ( ) j N f    

( ) j

( ) j

N N N f    

N











0

0

j

j





here N - ( j ) and N + ( j ) are the number of victims during the implementation of the S ( j ) scenario before and after the implementation of protective measures. According to ALARP risk reduction efforts should be continued until the moment when k dp reaches the limit line lim ( ) i i K R a R b    (9)

where a and b are constants that can be determined from the conditions (10) and (11):

:

lim 10 K  ;

(10)

for

4

[ ]    

10



i i R R

for

:

lim 3 K  ;

(11)

6 { } 10  

i i R R

  

In other words we have the following condition for termination of the risk reduction efforts: