A test organization is trying to implement an improvement goal to develop a quantitative understanding...

As part of the Product Quality Evaluation process area (4.2), the specific goal "Project Goals for Product Quality and their Priorities are Established" includes the practice of identifying product quality needs. This involves understanding and defining what quality means for the product, determining quality characteristics (such as reliability, usability, etc.), and establishing priorities for these characteristics based on project goals.

Other practices such as establishing test process measures and measuring product quality quantitatively come later in the lifecycle or are part of other specific goals.

TMMi References:

In Product Quality Evaluation at TMMi Level 4, identifying product quality needs is critical for setting up measurable and prioritized goals for product quality​​.