The Construction Specification Institute is a long standing player in construction quality. Their name suggests "specifications" as their focus; but in reality they define their mission as

The mission of CSI is to advance building information management and education of project teams to improve facility performance.

Quality is sometimes defined as "meeting properly prepared requirements". CSI is all about communicating and preparing requirements. They promote standard preparations of all types of construction documents so the documents collectively represent proper requirements.

They describe themselves as:

• A diversified membership base of allied professionals involved in the creation and management of the built environment.
• Continuous development and transformation of standards and formats.
• Education and certification of professionals to improve project delivery processes.
• Creation of practice tools to assist users throughout the facility life-cycle.

And they got a great magazine for all design and construction professionals and a very active LinkedIn presence.