Quality is an attribute of a product or service. Productivity is an attribute of a process. They have frequently been called two sides of the same coin because one significantly impacts the other.
There are two ways that quality can drive productivity. The first, which is an undesirable method, is to lower or not meet quality standards.
For example, if testing and rework components of a system development process were eliminated or reduced, productivity as measured in lines of code per hours worked would increase.
This is often done under the guise of completing projects on time. The second, and more desirable method to improve productivity through quality, is to improve processes so that defects do not occur, thus minimizing the need for testing and rework. Quality improvement should be used to drive productivity.