Dan Cellucci gave this answer to Puzzle 4:

> the dependency graph of spacecraft failures, where \\(\le\\) would indicate "leads to" or "increases the likelihood of".

Indeed, this kind of example is very important in applications! A [PERT chart](https://en.wikipedia.org/wiki/Program_evaluation_and_review_technique) is a way of planning tasks, where the edges indicate dependencies:



There's more to a PERT chart than a mere preorder, as [Simon Willerton has explained](https://golem.ph.utexas.edu/category/2013/03/project_planning_parallel_proc.html). We may get into that later. However, any PERT chart gives rise to a preorder.