HR should make sure that safety measures are followed, Discipline and employee relations / welfare. He has to make sure that company goes smoothly by following all statutory compliances and employees safety.
Your query is of very general nature.
By design in any company, all departments are HR department's customers. It is imperative to say that a good HR is fully people oriented. Operations could be thought of as the back bone of any Organization. Inspite of Customer Supplier relationship HR has to make sure that peoples’ interests are always taken care of.
Now let us focus on your query. Suppose an HR man finds that in Operations department lot of Overtime is occurring, it can certainly be questioned politely.
Take another example. Let us say that more accidents occur in an Operations dept. HR can again politely question the reasons for the same. They can ask the subsequent implementation of corrective and preventive actions.
In both the examples cited above, HR in turn is answerable to Statutory Authorities.
What is interference or involvement depends also on the Company culture.
HR is a staff function i.e. a "Support function".
Making things happen is a line function.
HR has no authority over the "line" and therefore it should only play an "advisory role".
It is the personality of the concerned HR that perhaps makes him interfere in the line function.
This could be happening with best of intention but should be curbed just as it could be happening with "power mongering" motivations to impose self importance also.
One must know the intentions before sitting in judgement or initiating any "corrective" actions. Unless one has all facts and has taken an objective view of the matter and issues, it would vitiate organizational atmosphere.
Unless you share more facts and state the purpose of your query, I am afraid you are unlikely to receive correct advise.
because as individual i think we have to create a situation where an employee can share his problem without any hesitation he have to believe that if he share his problem then we resolved that. when we create such type of atmosphere, he will work for only and only company growth.
so finally we can say that an HR can interfere in production but with care. because when any Hr is entering in production dept. that may be so many production people will not feel good and that will also not help full to HR job also.
So enter with care and your vision for entering must be clear and understood in positive way by the concern dept.