The Natvig measures of component importance in repairable systems applied to an offshore oil and gas production system

For repairable systems we consider a time interval [0, t] and start by introducing some basic random variables (i = 1, . . . , n): Tij = The time of the jth failure of the ith component,

j = 1, 2, . . . , Sij = The time of the jth repair of the ith component,

j = 1, 2, . . . , where we define Si0 = 0. Let (i = 1, . . . , n and j = 1, 2 . . . ):

Uij = Tij − Sij−1 = The length of the jth lifetime of the ith component. Dij = Sij − Tij = The length of the jth repair time of the ith component.