Trans RINA, Vol 153, Part A4, Intl J Maritime Eng, Oct-Dec 2011 2.5 2 1.5 1 0.5 0 0


Hot-spot 1 Hot-spot 2 Hot-spot 3 Hot-spot 4 Hot-spot 5 Hot-spot 6


5 10 15 Time, years


Figure 8 – Beta reliability index, total damage 2.5


2 1.5 Beta index 1 0.5 0 05 10 15 Time, years


Figure 9 – Beta reliability index, only wave induced damage


The importance of the contribution of each variable to the uncertainty of the limit state function g x can be


assessed by the sensitivity factors which are determined by:


  i   i i 1


 


1


 


 


 


gx x


Figure 10 shows the sensitivities of the failure function with respect to changes in the variables for the hot-spot 4 in the case of full-welded joint. A positive sensitivity indicates that an increase in a variable results in an increase in the failure function and positively contributes to reliability.


It can be seen from Figure 10 that the importance of the uncertainty on fatigue damage and on the scale parameter of the Weibull distribution of stress range are almost identical and the overall uncertainty on fatigue stress estimation is quite important on the results especially the uncertainty on load calculation, which together with the


A-238   2  i


g x x


(15)


Considering the probability of failure of a series system of three hot-spots, each of which is modelled with a safety margin:


Mii X   , 13g,i (17)


The FORM probability of failure for ith hot-spot can be given as:


PPM P g Xii iP U         i  


P PM ; 


fi m i


s  1


m


    


 M   and Mj jjU T ii i U   is    .


linearized T


ij i j 01  βρ two (19)


where  m is the m-dimensional normal distribution between


function. It has been used that the correlation coefficient  ij


i fi 00  0T (18)


The series system fails if just one of the hot-spots fails, which may be defined as:


20 25 30


Hot-spot 1 Hot-spot 2 Hot-spot 3 Hot-spot 4 Hot-spot 5 Hot-spot 6


The probability of failure of any of the structural hot-spot is defined by:


Pt    fi, 1


where Pt is the probability of failure and i is the reliability index.


fi,    t  i  (16) 20 25 30 -0.40 -0.60 -0.80 0 5 10 15 Time, years Figure 10 – Sensitivities of the variables, Hot-spot 4 20 25 30


uncertainties rising from corrosion deterioration are by far the most important variables. It has to be pointed out the effect of corrosion determination has only to be accounted after the coating is finished.


0.60 0.40 0.20 0.00 -0.20


X1 X2 X3 X4 X5


safety margins T


©2011: The Royal Institution of Naval Architects


Beta Index


Sensitivity


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