I don't think there is a better way of doing this. Bigchain DB has listed a few use cases of Blockchain in the automotive sector. Automotive parts provenance and tracking is one of them. Similar to what you have suggested, assigning a unique ID for each and every part at the time of creation and recorded along with immutable timestamps. This data can be made available to the owner of the vehicle to verify which parts have been replaced, to the manufacturer to efficiently execute recalls, or to the service center to know when a part has reached its usage limit. Yeah like a QR code, crypto-enabled tags that speak directly to the Blockchain can be embedded directly into the part to add another layer of authenticity protection.
From mitigating reputational damages from counterfeit spare parts to cutting down expenses to streamlining supply chain process to fully autonomous cars, the automotive industry can accomplish a lot by embracing Blockchain technology.
https://blog.bigchaindb.com/how-automakers-can-use-blockchain-adab79a6505f