"责任追究制度" can be translated into English as "accountability system" or "system for holding individuals accountable".
"Accountability system" is a more concise and commonly used term in English to refer to a set of rules or mechanisms designed to ensure that individuals or organizations are held responsible for their actions or decisions.
"System for holding individuals accountable" provides a more detailed description, explicitly stating the purpose of the system, which is to hold individuals accountable.
In most contexts, especially in official or formal documents, "accountability system" would be a suitable and widely understood translation.