Non-compliance is when you do not do something that rules, a law, a contract, or a doctor’s orders say you must do. It can be a failure (you did not manage it) or a refusal (you will not do it). Hospitals talk about non-compliance when a patient does not take the medicine. Companies get fined for non-compliance with safety rules. Though actually, the word often comes from the side that made the rule, so it can sound colder than “couldn’t” or “wouldn’t” — it names the break, not the person’s story. It is a formal word. In everyday English people say “didn’t follow the rules” or “didn’t do what they were told.”