Reliability Analysis of Coexistence of Fatigue and Corrosion at Multiple Locations  
In a more general situation, a tank car may have both fatigue damage and corrosion damage. Each type of damage may occur at multiple locations. The task of this section is to develop a methodology for quantifying failure probability of tank cars subjected to both fatigue and corrosion damage at multiple locations. It is noted that the multiple fatigue and corrosion locations considered in this work exist at different places, such that there is no interaction among and between the fatigue and corrosion locations. When a tank car has both fatigue damage and corrosion damage at multiple locations, tank car failure occurs when leakage happens at one or more of the fatigue or corrosion locations. Therefore, the tank car failure event is a union of both the fatigue failure events and the corrosion failure events. The figure below shows the failure probability of a tank car subjected to fatigue and corrosion at multiple locations. The tank car contains fatigue damage at four different locations as well as corrosion damage at another four different locations. The figure contains eleven curves: four dashed curves with symbols are for corrosion components; four solid curves with symbols are for fatigue components; one thicker dashed curve without symbols is for the multiple corrosions only; one thicker solid curve with symbols is for the multiple fatigues only. The upper curve labeled (f4c4) is for the tank car with both multiple corrosions and multiple fatigues. It is observed that in this case there are three regions in service life: (a) the tank car failure probability is most affected by the fatigue in the left portion of the curve; (b) the tank car failure probability is most affected by the corrosion in the right portion of the curve; and (c) both fatigue and corrosion are important factors in determining the tank car failure probability in the middle portion of the curve. 
