io^'i") 





(8) 



where, ^ and n are non-dimensional wave amplitude and period, respectively, 

 given by 



5=^ (9) 



where, a = wave amplitude 

 T = wave period 



T = mean wave period = 2Tr (m /m^ ) 



o i 



/ 2 



V = 'm m^/m, - 1 

 o z 1 



m, = k-th moment of the wave spectrum 



Let us consider the conditional probability that the wave amplitude will 



exceed a certain value, c, , given that wave periods fall into a certain 



range of values, n-i and t\j. It is given by 



?^- 



U^>?li,<i<7A=-^ 





(10) 



^,0 



Here, c; is the extreme wave amplitude in non-dimensional form and is 



unknown at this stage. The values of non-dimensional peribd, n-, and ri„ in 



Equation (10) are for the range of wave periods for which the system's 



behavior in a seaway becomes critical. They may be chosen in practice as 

 the lower and upper bound period for which the response characteristics 



of the system are large. Using the joint probability density function 



given in Equation (8), Equation (10) becomes (Ochi and Whalen 1979a), 



100 



