Multi target classification
At first the way you explained it, it sounded to me it is a multilabel classification (like e.g. CelebA) and approaches I have used for there was coming to my mind. Also I thought it is hierarchical classification because you have subcategories in your dependent variable. But at the end you mention that you want to 


  Predicting the accidents using the violation levels.


Aren't then your dependent variables (violation level , and accident) already correlated/related to each other? It seems to me that you do not have two independent dependent variable. I would try to reduce the problem to a simple multiclass classification, in your case 6 as follows (assuming you have these explicit labels for each data point): 


Severe-Yes
Severe-No
Medium-Yes
Medium-No
Light-Yes
Light-No


Then you have 6 classes/labels to build a model e.g. Gradient Boosting Tree or Neural Network.