Here are some options, along with examples:
* To assess/evaluate: "We need to assess the quality of the materials."
* To improve: "We are working to improve the quality of our products."
* To maintain: "The company strives to maintain high quality standards."
* To ensure: "Our team ensures the quality of all our services."
* To guarantee: "We guarantee the quality of our workmanship."
The best verb will depend on your intended meaning. Do you want to emphasize checking, improving, or ensuring the quality?