When you inspect the bridge, even when you do it very carefully, you may miss a fatigue crack of small dimensions. That"s why probabilism was introduced in the assessment of an existing steel bridge.

Hi,

Based on the fatigue assessment approach, uncertainties can rise from various sources.

For eg: if you chose to use S-N approach for fatigue assessment then uncertainties can arise from:

1. S-N curve

2. Miner's Rule (Linear Damage Rule) 

to account for these uncertainties we use probabilistic approach.

Hi

I advice you to see these papers " Reliability-Based Calibration of Fatigue Safety Factors for Existing Steel Bridges" and "Fatigue Reliability Updating Evaluation

of Existing Steel Bridges".

You will find exactely what you need.

Best regards

http://ascelibrary.org/doi/abs/10.1061/(ASCE)BE.1943-5592.0000716

http://pustaka.pu.go.id/files/pdf/BALITBANG-03-B000984-714504122012111910-fatigue_reliability.pdf

Good question.. Please share me the best answer might you trust...

Regards…