The key thing to remember is that this is a business relationship and, like in any relationship, communication is key. Of course, before you trigger a SCAR, someone should be communicating with the supplier about short deliveries and the potential impact on to your operations. A SCAR is a formal request for correction and improvement, but most people would prefer to be notified as early and as gently as possible about their performance shortcomings.
Risks and criticality have to be assessed. There is no one size fits all type of behavior. If an organization has perfected inventory management and pretty much all parts are received "just-in-time", then partial/short deliveries can play havoc with the production planning, but very few organizations around the world are in that type of sophisticated environment. Have you asked around in your purchasing department? Maybe they are the ones telling the supplier to ship partial lots.
I used to be a soccer referee. In most cases, before I cautioned or ejected a player, I was communicating with them about their behavior. Escalation of feedback is the best protocol when dealing with business partners, in my experience.