The attempt at a solution:
V1,V2 AND V3 ARE IN SERIES AND SS1 ARE IN PARALLEL TO V4 AND V5
(PV1 OR PV2 OR PV3) AND PV4 AND PV5
FT (t) = 1 − exp[−_λit] where i=1,2,3,4,5
If _λ1 = λ_2 = _λ3 = 0.05; λ_4 = 0.267; λ_5 = 0.189 (all in years−1),
For PSS FT (t) =1 exp [λ1+λ2+λ3*3] where t=3 = .36237
For PV4, FT (t) =1 exp [λ4*3]=.55112
For PV5,FT (t) =1 exp [λ5*3]= .43278
Therefore the probability of loss of flow from the manifold at time 3 years is
PSS1 AND PV4 AND PV5= .36237*.55112*.43278= .08643
